Definition Definition and 1000 Threads

Hi I am a person who always have had a hard time picking up new definitions. Once I do, the rest kinda falls into place. In the case of abstract algebra, Stillwell's Elements of Algebra saved me. However, in the case of Spivak's Calculus on Manifolds, I get demotivated when I get to concepts...

Hi, N00b question :-) I have read articles about redshift and blueshift and have a good idea about them. What I would like to know is how you decide if something is "unshifted" - what is the definition of this? is there a standardized way of defining/mapping an element's unshifted spectral...

HI Guys, I am getting an error in Ansys Maxwell that says Maxwell2d solver, process solver2d: Internal Solver Error: 'In the Material: M270-35A_12 , the SLOPE of the End Two Points in this BH curve is 56519.1, which is more than 2 times of Mu0; This may lead to a non-physical solution...

It so happens that last night I was rereading Einstein's famous 1905 paper On the Electrodynamics of Moving Bodies. I think this is one of the most fascinating scientific papers in history, but some people say it's not at all clear. In any case I love reading Einstein's papers. Clocks...

Hello! I am not sure I understand the concept of blackbody. The definition is that it absorbs all the incoming light and doesn't reflect any. However, it emits thermal radiation. Isn't thermal radiation still EM radiation, so technically still light, just at another frequency? So if it emits...

Consider the definition (https://en.wikipedia.org/wiki/Hyperboloid) of the hyperboloid in ##\mathbb{R}^3## with the metric $$ds^{2}=dx^{2}+dy^{2}+dz^{2}.$$ The one-sheet (hyperbolic) hyperboloid is a connected surface with a negative Gaussian curvature at every point. The equation is...

In the book General Relativity for Mathematicians by Sachs and Wu, an observer is defined as a timelike future pointing worldline and a reference frame is defined as a timelike, future pointing vector field Z. In that sense a reference frame is a collection of observers, since its integral lines...

Hi, I read definition of GCD theorem, from book and from mathWorld website. " There are two different statements, each separately known as the greatest common divisor theorem. This does not make sanse 1. Given positive integers and , it is possible to choose integers and such that ...

So I was reading this book, "Euclidean and non Euclidean geometries" by Greenberg I solved the first problems of the first chapter, and I would like to verify my solutions 1. Homework Statement Homework Equations [/B] Um, none that I can think of? The Attempt at a Solution (1) Correct...

Hi. Sorting the exchanges of heat and mechanical work in a thermodynamic cycle by the signs and summarizing, I get ##Q_{in}>0##: heat transferred into the system ##Q_{out}<0##: heat transferred to the cold reservoir ##W_{out}<0##: work done by the system ##W_{in}>0##: work done on the system...

I am now in the process to define a cubic volumetric source in mcnp code, does anyone have a clear explanation for that.

Homework Statement (please ignore something that is not english) Homework Equations ac=v^2/r Fc is about 6.0E3 N and ac is about 5.0 m/s^2 (b) is the problem... The Attempt at a Solution what is 'with the vertical' here? the direction/opposite of ac or the direction of v?

There are 2 things taught to us:variables(litersls ) and constants . If we let a value 'a' as a constant ,meaning it would remain unchanged and also it is a set of real numbers . If we take 'x' as a variable, meaning it can change and it is also a set of real nos. For ex. Lim (x>a) x = a...

lim 1/x as x->0 is infinity, but the function taking it to infinity is continuous, but for continuous functions f(a)= lim f(x) as x->a, so by defininition 1/0 is infinity, what is wrong with this logic?

How does the value of ##\displaystyle \sqrt[a]{-1}## vary as ##a## varies as any real number? When is this value complex and when is it real? For example, we know that when a = 2 it is complex, but when a = 3 it is real. What about when ##a = \pi##, for example?

Okay, so in Griffith's introduction to electrodynamics, Griffith clearly defines surface current density as follows: "when charge flows over a surface, we describe it by the surface current density, K. Consider a 'ribbon' of infinitesimal width dL running parallel to the current flow. If the...

If we define ##|a| = \sqrt{a^2}##, then why can't we do something like ##\sqrt{a^2} = (\sqrt{a})^2 = a##? Or equivalently ##\sqrt{a^2} = (a^2)^{1/2} = a^{2/2} = a##? Isn't this a contradiction? Also, how would this relate to showing that ##\sqrt{|a|} = |\sqrt{a}|## is true or false?

Hello! This is more of a set theory question I guess, but I have that the definition of the boundary of a subset A of a topological space X is ##\partial A = \bar A \cap \bar B##, with ##B = X - A## (I didn't manage to put the bar over X-A, this is why I used B). I think I have a wrong...

Homework Statement The book I am reading says that given a point mass(m) at the point x, the quantity mx is the "moment about the origin)" It then defines the moment of a collection of points as M = m(1)x(1) + m(2)x(2) + ... m(n)x(n) where m(1) = mass of first point and x(1)=distance of first...

Hello! I just started reading an introductory book about topology and I got a bit confused from the definition. One of the condition for a topological space is that if ##\tau## is a collection of subsets of X, we have {##U_\alpha | \alpha \in I##} implies ##\cup_{\alpha \in I} U_\alpha \in \tau...

On wiki measurement is defined as: Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events. So a number. For scalars, I agree because they are described by a single number. But what about vectors? They have...

One thing I find frustrating when trying to get a handle on this theorem is the number of different forms presented in the literature. I understand this to be due to it being very general theorem applicable to many different contexts. Not that the world needs a new, slightly different looking...

So I'm reading in the news and a group of scientists from the New Horizons missions appear to be reopening "The Pluto Debate" with yet another new definition of planet at the Lunar and Planetary Science Conference in March:rolleyes:. If accepted their definition of planet would increase the...

Let ##G## be a group. I have shown that ##H_a = \{x \in G | xa=ax \}## is a subgroup of G, where ##a## is one fixed element of ##G##. I am now asked to show that ##H_S = \{x \in G ~| ~xs=sx,~ \forall s \in S\}## is a subgroup of ##G##. How would proving the former differ from proving the latter...

I think I understand these terms, not fully though and I can't distinguish between the two and define them.

I'm reading a very general definition of parameter on this site Parameter definition - Math Insight. I didn't understand why we call the variable $t$ of the curve $\alpha(t)=(\cos t,\sin t)$ a parameter. For me $t$ in this case is a variable too according to the definition of the site I...

Homework Statement The texts are taken from http://ingforum.haninge.kth.se/armin/fluid/exer/deriv_navier_stokes.pdf and https://simple.wikipedia.org/wiki/Stress_(mechanics)Homework EquationsThe Attempt at a Solution The formula for stress is ##\sigma=\frac{F}{A}## (I). From the document...

Joseph A. Gallian, in his book, "Contemporary Abstract Algebra" (Fifth Edition) defines an irreducible element in a domain as follows ... (he also defines associates and primes but I'm focused on irreducibles) ... I am trying to get a good sense of this definition ... My questions are as...

Joseph A. Gallian, in his book, "Contemporary Abstract Algebra" (Fifth Edition) defines an irreducible element in a domain as follows ... (he also defines associates and primes but I'm focused on irreducibles) ... I am trying to get a good sense of this definition ... My questions are as...

Can we say that TIME is essentially the progression of energy from one state to another, in its long cosmic quest to achieve equilibrium? Without the movement of electromagnetic waves and transfer of energy, the entire universe would come to a standstill — an inanimate, “frozen” world. Time...

I have been thinking around the definition of a unit in a ring and trying to fully understand why the definition is the way it is ... ... Marlow Anderson and Todd Feil, in their book "A First Course in Abstract Algebra: Rings, Groups and Fields (Second Edition), introduce units in a ring with 1...

I have been thinking around the definition of a unit in a ring and trying to fully understand why the definition is the way it is ... ... Marlow Anderson and Todd Feil, in their book "A First Course in Abstract Algebra: Rings, Groups and Fields (Second Edition), introduce units in a ring with 1...

Hello, please note that the following is only about special relativity, not general. Of course, if there are any things to point out that fall in general relativity, feel free to do so, but I don't know GR, so I won't understand arguments based in GR. I also am not great with a geometry-based...

Hello! (Wave) I want to show that the language $L=\{ n \in \mathbb{N}_0 \mid T_n(1) \text{ defines a totally defined function }\}$ is not decidable. What does it mean that $T_n(1)$ defines a totally defined function? Does it mean that $T_n(x)$ is a totally defined function and $1$ belongs to...

Hello, Just a really quick question on definition of discrete subgroup. This is for an elliptic functions course, I have not done any courses on topology nor is it needed, and most of the stuff I can see online refer to topology alot, so I thought I'd ask here. I need it in the complex plane...

in the limit definition of a sequence, why does epsilon has to be greater than 0 and not greater or equal to 0? thanks in advance.

I thought the definition was: a vectorial field that interacts with a moving charge But wikipedia says it's a field generated by electric currents and magnetic materials... https://en.m.wikipedia.org/wiki/Magnetic_field Why is in the definition the way it is Generated? When we had defined the...

First of all I want to clarify that I posted this question on many forums and Q&A websites so the chances of getting an answer will be increased. So don't be surprised if you saw my post somewhere else. Now let's get started: When it comes to definitions, I will be very strict. Most textbooks...

Hi. Since there haven't been observed magnetic monopoles so far, what exactly do we mean when we talk about the north/south pole of a magnet? Is it something like "north is where the field lines exit a solid body" and "south is where they enter" or is there a more rigorous definition?

In Schwartz's book, 'Quantum Field Theory and the Standard Model' P.696, he starts to derive an expression for a parton distribution function in terms of matrix elements evaluated on the lightcone. Most of the derivation is clear to me, except a couple of things at the start and midway. The...

Homework Statement I am not sure whether the meaning of the equation ##(3)## which used for deriving momentum is as same as equation ##(4)##.I will make a detailed description below. The lagrangian function for a free particle is ##L=-mc^2\sqrt{1-\frac{v^2}{c^2}} \quad (1)## The action from...

Demonstrate the definition with a chemical equation for HCl. Express your answer as a chemical equation. Identify all of the phases in your answer. My Answer: HCl(g)+H2O(l)→H3O+(l)+Cl−(aq)What the answer said: There is an error in your submission. Make sure you have formatted it properly.

Consider the following momentum-space Feynman diagram https://upload.wikimedia.org/wikipedia/commons/b/b5/Lepton-interaction-vertex-eeg.svg This Feynman diagram is the leading-order contribution to the any of the following processes: 1. ##e^{-} \rightarrow e^{+} + \gamma## 2. ##e^{+}...

Hello. I finished working through Spivak's Calculus 3rd edition chapters 13 "Integrals", and 14 "The Fundamental Theorem of Calculus". By that I mean that I read the chapters, actively tried to prove every lemma, theorem and corollary before looking at Spivak's proofs, took notes into my...

Consider the definition of 1m. It is the distance traveled by light in 1 / 299,792,458 seconds (lets call this X). Fair enough a definition. Now let's assume, for an instant, that somewhere in our past, while scales were being developed, man erroneously decided that instead of the distance...

hello everyone. i need help understanding this statement: d(lnΩ)/dE = 1/kbT so Ω are the posible microstates for energy E, and the derivative of Ω w.r.t E is 1/kbT. why? what i understand so far is: looking at the division of energy of two "connected" systems the energy will divide itself in a...

Homework Statement True or False: If u, v, and w are linearly dependent, then au+bv+cw=0 implies at least one of the coefficients a, b, c is not zero Homework Equations Definition of Linear Dependence: Vectors are linearly dependent if they are not linearly independent; that is there is an...

The following question has stumped me. I am not getting the answer marked. Instead I am getting option a). I have produced my attempt below. Also I have no idea which formula to use when the question says Doppler width. Since frequencies form a distribution, there are multiple notions of width...

The standard unit of mass is defined to be "equal to the mass" of a cyliner of platinum and iridium in france. I have always wondered what this means? Why are all sources saying mass is defined in terms of mass? What were the steps taken to decide this unit? I know that base quantities have to...

I've tried repeatedly to get clear, succinct definitions of the following terms over and over again, but invariably the definitions provided clash, and I'd like to put an end to that. The terms I am trying to define clearly are: - Relation - Definition (Mathematical definition) - Function -...