Definition Definition and 1000 Threads

Gibbs phase rule says f = r-M+2 with f: thermodynamic degrees of freedom; r: number of components; M: number of phases I wonder whether the defintion of "phase" is restricted or almost arbitrary. For example, consider a system of H2O, O2 and H2 in a closed vessel. Let there be the contstraint...

Hi, I would like to know if is possible define a set rule explicitly. ex.: Define the set A explicitly where ξ = ℕ and A = {x | x < 3}. The maplesoft said the (N) is a representation of Natural Numbers. f:=proc() local a,b; a:=N; b:= 3; print(a<b); end proc; when I...

Hi, I read about definition of microgravity. It is usually described as reduced g, but not zero g. How can one say then that an object is in microgravity? I was looking hours for a clear definition, like an object is in microgravity if there are just 10^-6g left (clearly wrong, because I read...

Consider the Lie derivative of the vector field ##\bf{Y}## with respect to the vector field ##\bf{X}## on manifold ##M^{n}(x)## defined as ##\displaystyle{[\mathcal{L}_{\bf{X}}Y]_{x}:=\lim_{t\rightarrow 0} \frac{[{\bf{Y}}_{\phi_{t}x}-\phi_{t*}{\bf{Y}}_{x}]}{t}}## Now, I understand that...

As I understand it, the proper length, ##L## of an object is equal to the length of the space-like interval between the two space-time points labelling its endpoints, i.e. (in terms of the corresponding differentials) $$dL=\sqrt{ds^{2}}$$ (using the "mostly plus" signature). Furthermore, this is...

When I learned magnetostatics. My teacher and book said that it is the case of steady current. However, if I consider a circular loop, the electrons are in fact moving in uniform circular motion. That means they are accelerating. How come we can still define it to be a magnetostatic situation

Hi folks, I am reading Poisson's Teatrise on Mechanics. In the introduction he talks about the infinitesimals. Let's say A is a first order infinitely small quantity, a differential of the first order, if the ratio of A to B is infinitely small too it means B is an infinitesimal of the second...

Young's Modulus is usually defined as the intrinsic property of a material indicating it's stiffness, or it's ability to resist deformation. Though, it is measured in Pa, meaning it should have some statistical description. Spring constant, for example, can be define as the stiffness of an item...

Homework Statement Centre of gravity - the point at which: 1) gravity acts on a body or 2) weight of a body may be considered to act. The answer is 2) and I understand why - because gravity acts all over but it is easier to calculate a single point, an average point of where the mass is...

Homework Statement Hi, this is a question that has been bothering me for a while. (Im in calculus II at the moment) Why do i need to derivate some functions by definition and other times i dont? for example if somebody asks me to calculate the partial derivatives of a branch function in a a...

Since 97% of everyday weight scales (both in doctor offices and at home) measure our actual mass either in lbm and/or kg, and NOT force (lbf or N), then why does oxford choose to define weight to be relative? "a body's relative mass or the quantity of matter contained by it, giving rise to a...

So I just got beat up by this question on my midterm. I'm not sure if these problems are always called definition of success but that is how my professor refers to them as. The question: (paraphrased) When you walk into your dorm room you like to throw your keys onto the center of your desk...

Is there a good mathematical definition of time?

In some elementary introductions to integration I have seen the Riemann integral defined in terms of the limit of the following sum $$\int_{a}^{b}f(x)dx:=\lim_{n\rightarrow\infty}\sum_{i=1}^{n}f(x^{\ast}_{i})\Delta x$$ where the interval ##[a,b]## has been partitioned such that...

$\displaystyle s_n=\left(\frac1n-1\right)^n$ My attempt: For large $n$, the sequence oscillates between $e^{-1}$ and $-e^{-1}$ and therefore diverges. Now for the proof. Assume, for the sake of argument, that the sequence converges to $L$. $\exists N\in\mathbb{N}$ such that $|s_n-L|<0.1$...

I have been studying about computers and found that they evolved from the basic mechanical devices with limited functions to the amazing machines we have today. Its all very new and interesting to me. I believe that programming is the act of writing an algorithm in a higher or lower level...

Homework Statement Hi, If an object is undergoing uniform circular motion, then the net force is acting perpendicular to the instantaneous velocity, and this is called the centripetal force. However, if the object is moving in a circle but the magnitude of its instantaneous velocity is not...

There has been SO much talk of HP and HP vs torque, it can make your head spin. I've been trying to help with some clarification for those that seem to be very confused of the physics and concepts that i came up with a new "definition" to augment what is commonly read as the definition of HP...

I know that I'm kinda asking for a lot here, but can any of you give me, a person with lesser experience in physics, a basic explanation of spin? I've found out that a particle's spin can be compared to a transistor, but that didn't really tell me what it actually is. What does it define? For...

Homework Statement Proof that: ##\lim_{x \to 1} \frac{1}{1+x} = \frac{1}{2}## using the epsilon-delta definition of a limit. (Problem below) Homework Equations ##\lim_{x \to 1} \frac{1}{1+x} = \frac{1}{2} \iff \forall ε>0, \existsδ>0, \forall x ∈ \mathbb{R}\backslash\{-1\}: 0 < |x-1| < δ...

Homework Statement "For the given series, write formulas for the sequences an , Sn, Rn and find the limit as n->∞ (if it exists) Homework Equations ∑∞1 ((1/n) - 1/(n+1) The Attempt at a Solution I know how to take the limit, that's no problem. I'm a bit confused about what an , Sn, Rn are...

I was wondering if there is an actual definition given by a recognised organisation over what is meant by the word "rocket". In case there is not, I wanted to reflect upon what do we really mean when we say rockets.

Hello experts, I would like to learn the implementation of object_definition function in SQL server. I'd like the one with 2 parameters. Could you help me ? Thank you.

Homework Statement Hey I'm trying to prove the rigorous definition of limit for the following function: Lim (x,y) approaches (1,1) of f(x,y)=(y*(x-1)^(4/3))/((x/1)^2+abs(x)*y^2) Homework Equations abs(x^2)<abs(x^2 +y^2) The Attempt at a Solution I know the rigorous definition of limit. I...

http://www.utdallas.edu/~pervin/ENGR3300/Boaz.pdf see page 493 he said that first variation of I is δI = dI/dε * dε http://www.colorado.edu/ASEN/asen5227_offline/slides/292-334.pdf but this pdf said (see page 309) that first variation of I is δI = dI/dε * ε (y and I commute, α and ε...

So I have the following: F = {(1,3)(2,2)(3,2)(4,2)(5,5)} G = {(1,1)(2,3)(3,4)(4,5)(5,2)} Am I right in saying that F o G would be: F o G = {(1,3)(2,2)(3,2)(4,2)(5,5)(1,1)(2,3)(3,4)(4,5)(5,2)} If not, does F o G actually mean? Thank you.

Hello! Why is the stress energy tensor defined as a (2 0) tensor? I understand that it needs 2 one-forms as arguments, but using the metric, can't we bring it to (1 1) or (0 2)? So is there is any physical or mathematical reason why it is defined as (2 0), or it is equally right to define it as...

The exercises in my imaginary textbook are giving me an ε, say .001, & are making me find a delta, such that all values of x fall within that ε range of .001. The section that I'm working on is called "proving limits." Well, that is not proving a limit. All that's doing is finding values of...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Section 4.1 on Generating and Cogenerating Classes ... ... In particular I am trying to understand and get a good sense of the notion of a module being finitely cogenerated ... Bland defines a finitely...

The definition from the current Wikipedia article is a good start: My technical question is whether "each further term" is a function of only the values of the preceeding terms, or is it also a function of the index of the "further term"? For example, if we are given that the values of two...

Whats is r ? knowing that formula is T = F x r... please help me. thank you!

The definition of a limit of a sequence, if the limit is finite, is: lim n >infinity un (un is a sequence) = l <=> ∀ε> 0, ∃N: n > N => |un - l| < ε This just means that un for n > N has to be a number for which: l -ε < un < l + ε Now, I'm wondering, can't we just say: n > N => |un -l| <...

I don't want to be an adult, this idea freaks me out and makes me feel old Is 18 still an adolescent or is considered adult? When are you an adult and no more an adolescent? 20? What's the difference between teen and adolescent? And how did you dealed with the teen-adult transition? Was it...

On chapter over regular surfaces, In definition 1 point 2. He says that x: U → V∩S is a homeomorphisms, but U⊂ℝ^2 onto V∩S⊂ℝ^3. I am confused, how can it be so!

The definitions I have seen of "field" seem rather unsatisfactory. Wikipedia starts off by saying that a field is any function with spacetime as its domain, but this seems awfully broad, since there are 2|ℝ| number of functions with spacetime as a domain. Further down, Wikipedia basically says...

Homework Statement I know that if a proposition can not be evaluated then it is meaningless, but how about statement like this? 4+1. Homework EquationsThe Attempt at a Solution I think "4+1" itself is meaningless because it can't be evaluated. Thanks!

So, on wikipedia is said that a plasma is an ionized gas, just that, but when we think about plasma we think that is hot, so here's the question: What is the right definition of plasma? Does being a ionized gas also imply being hot and then saying only that is an ionized gas is enough? I mean...

So, I was reading the mathematical description of a conservative force o wikipedia : https://en.m.wikipedia.org/wiki/Conservative_force and at the line "Many forces (particularly those that depend on velocity) are not force fields. In these cases, the above three conditions are not...

What is an eigenframe?

I have only encountered questions that f(x)-L that can be factorize to get a constant, and delta is epsilon divide that number, as a high school student. I have no idea how to choose a epsilon for this question. Thanks.

hi, I have seen that christoffel symbol definition or logic is shown in different ways. For instance, in first attachment ( RED box) you can see a normal vector (n) next to the christoffel symbol, but in second image everything is same except that there is a normal vector. Is there a confusion...

I am reading the wikipedia article on the Cauchy stress-tensor. The article says that given some object, let ##P## be a point in the object and let ##S## be a plane passing through that point. Then "an element of area ##\Delta S## containing ##P##, with normal vector ##n##, the force...

Hi all, I'm working through a derivation of the general relationship between Cp and Cv and there's one point which is confusing me. I understand that and and that this implies the following: but isn't this equal to 0? Shouldn't the two partial derivatives on the right...

I learned a lie group is a group which satisfied all the conditions of a diferentiable manifold. that is the real rigour definition or just a simplified one? thanks

hello everyone, i would like please to know what is Effective Compression Ratio for an RC 2stroke Engine that i have ? the value in the info is 9.7, so i need to know the meaning and what values are the best ? what is the range ?

The word molecule has several definitions, but which one is considered the right one? The biggest question is if a single atom is still a molecule. Some call a helium atom a (monatomic) molecule. But others state that a molecule is a bond between two or more atoms. Some also say a molecule is...

I'm working through Wald's "General Relativity" right now. My questions are actually about the math, but I figure that a few of you that frequent this part of the forums may have read this book and so will be in a good position to answer my questions. I have two questions: 1) Wald first defines...

Hello! (Wave) I want to show the embedding $W^{1,p}(0,1) \subset C^0 [0,1]$. So we pick a $u \in W^{1,p}(0,1)$ and want to show that $u \in C^0 [0,1]$. Let $x_n \to x$. We want to show that $u(x_n) \to u(x)$. Since $u \in W^{1,p}(0,1)$ we have that $u \in L_p$ and $u' \in L_p$. And you...

Homework Statement I know that for constant volume ∂q=du and so du=Cv.dT However i don't understand how did we get to ∂q=du by neglecting the vdP term of enthalpy What I am trying to say is, is enthalpy this ∆U+P∂V+V∂P or this ∆U+P∂V? I don't understand since the definition of enthalpy is...

we all know the equation for KE 1/2mv^2 you do this simple math and you get an number that is in KE units , Joules. so, why is the KE unit equation, 1 Joule = Kg x (m^2/s^2) ?? 1Kg traveling at 1m/s would have a KE of 1Joule, but using the KE equation, it would be 1/2 a Joule. why is...