Definitions Definition and 274 Threads

My teacher, textbook and the internet have differing definitions. First of all: Equivalent. My teacher says that two parallel vectors with the same magnitude are equivalent, but my textbook says that two vectors in the same direction are equivalent. ×--> <--× are these equivalent?And...

Hi all. I'm reading up on types of atmospheric motion, and when discussing the meridional transport of various properties, the motion is generally split into three components: 1. Mean meridional circulation 2. Transient eddies 3. Stationary waves However, depending on what book...

I was hoping someone could help me understand the equivalence between the definitions for functions to be continuous between topological spaces, ie: For X and Y topological spaces, and f:X-->Y a function, my notes don't prove why these definitions are equivalent (possibly because I'm missing...

Elliptic function -- different definitions Hi, I have recently discovered, that the definition of the complete elliptic integral of the first kind in Wolfram Mathematica (EllipticK[m]) is different from the usual (K(m)), given in Abramowitz-Stegun. Their domains are not the same. In...

Let's say we are working with the Schwarzschild metric and we have an emitter of light falling into a Schwarzschild black hole. Suppose we define the quantity u=t- v where dv/dr= 1/(1-r_{s}/r) where r_s is the Schwarzschild radius. What is the u as observed by the emitter? I just need a...

Could someone look over this and see if I have any mistakes? I'm trying to show that ∫ y' dx = ∫ dy through definitions. http://imgur.com/6zCHYo5 Thanks!

I'm not entirely sure on the properties of limits, but this seems to work. Could someone look over this for me? http://imgur.com/6zCHYo5

Homework Statement What do you understand by the following terms; (i) principal stretch (ii) an anisotropic material (iii) a dilatant deformation, (iv) a Lagrangian description of a deformation, and (v) a pure deformation. Homework Equations Am just trying to find descriptions for...

The width of a pulse is typically given in the time domain, correct? The effective width is the term to describe this. What is the spectral width in the frequency domain? How do you calculate spectral widths and effective widths? Thanks for your time.

Hello (a) The universe U is a topological space whose elements are called events and as each event has a neighborhood homeomorphic to R^4. (b) A local coordinate system is a homeomorphism between an open subset of U and a bounded subset of R. (c) A world line segment is a continuous...

Hello, I noticed in my physics textbook that we define certain relationships to be true. I can see how this is considerably helpful in deriving other relationships from these definitions; for instance, take position: we define these quantities to be so, and from it we can define other...

Hello It is question of specifying mathematical definitions which are cummunes in several theories. In classical physics, in special relativity, in quantum theories (wave functions and state vectors) and in general relativity, we can assert : (a) The universe U is a topological space...

I was wondering if the O notation definition could be exchanged with the Ω notation and o could be exchanged with the ω notation. I ask this because of this: 2n² O(n²) means that 2n² <= c*n² which it is true for c=3 and n>=1 for example Instead, it would be like this: c*2n² <= n² which...

Hi all, Just a few question about FOL logic. What is the difference between terms and atoms, I read lot's of differents definitions, then when I think that I've understood, I find an exemple where both are used without any difference (for ordering by instance). An another question is : What...

Just a few definitions I would like to verify so I'm not studying the wrong stuff. Interior Point : A point Q \in S \subseteq ℝ^n is an interior point of S if \forall \delta > 0, \exists N_{\delta}(Q) \subseteq S. The interior of S consists of all interior points and is denoted S˚ Boundary...

I really need it now! Someone helps me

I was wondering if my understanding on Magnetic flux and Faraday's law was correct or not, is this okay? Magnetic flux is the number of lines in a magnetic field (Φ) Magnetic field strength (B) is the number of magnetic field lines over a given area B = Φ/A Other names for magnetic field...

I cannot find a consistent definition of the studentized residual and the RMSEP, because I've noticed that various websites, lecture notes and software packages mix up 1 or 2 definitions along the way to the point that a "compound" definition ends up very different between one reference source...

Geometric Tolerances - Do standards for defining "general geometric tolerances" exist For example, if I want to define non-geometric tolerances for the whole part, I just write what type of IT it is. For instance, IT8. And then the manufacturer just looks at the chart to know the tolerances he...

Homework Statement Let E be a vector space and p,q 2 norms on it. By definition p,q induce the same topology on E, iff they assign the same neighborhood basis to the 0 vector. *QUESTION: What does the bolded part mean ? Does this mean that, if whatever A included in the system (=basis?)...

My probability class has me wondering about pure math questions now. We started with the axioms and are slowly building up the theory. Everything was fine but then a definition of Conditional Probability P[A|B] = \frac{P[AB]}{P[B]} appeared and it's just not sitting right with me. I know that...

I am having some difficulty in understanding the reason for the various types of acids/bases, of which i refer to bronsted-lowry, arrehenius, and lewis acids/bases. A bronsted acid donates an H+ and a bronsted base accepts a H+. However, a lewis accept acceps an e- pair and a lewis base donates...

what is the nature of the relationship, if any, between the two? if parsimony is simplicity in explanation and reductionism is simplicity of mechanism, then is reductionism externally projected parsimony?

Hi guys! There is something I would like to get your help with... I am looking at the equation: W^{\mu}=-\frac{1}{2} \varepsilon^{\mu\nu\lambda\sigma}M_{\nu\lambda}p_{\sigma} Which is, if I understand correctly,a Casimir Operator. Now, I wish to look at a particle in its rest reference...

Hi, I wanted to see what people think about my current viewpoint on recognizing structures in abstract algebra. You count the number of sets, and the number of operations for each set. You can also think about action by scalar or basis vectors. So monoids groups and rings have one set...

Just began a serious study of the Fourier transform with a couple of books. One of them defines the Fourier transform on \mathbb R as \hat f(\xi) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty f(x) e^{-i\xi x}dx. Another defines it as \hat f(\xi) = \int_{-\infty}^\infty f(x)...

Here is the definition of oxide I found in a dictionary: A compound of one oxygen atom combined with another element. And here is the definition of dioxide that I found in a dictionary: An oxide containing two atoms of oxygen in each molecule; binoxide. Now my question/confusion is...

hey guys i want to know the definition of these terms & what are they but please i don't want big words because i won't understand i want to understand it simply: 1-Fermi level 2-Density of states 3-Carrier concentration & the graphs (in the attachment) 4-Mass action law 5-Charge...

Homework Statement Let X1,…,Xn denote a random sample from a population with mean μ and variance σ^2. Assume that both μ and σ^2 are finite but unknown. Let X denote the sample mean and S^2 denote the sample variance. Are the following statements true or false? A-There is no difference...

So I was reading through my textbook (specifically, Physics for Scientists and Engineers, Eighth Edition, Volume 1 by Raymond A. Serway and John W. Jewett Jr.) and I noticed that, in one of the "Pitfall Prevention" sections (which are usually quite helpful - not this time, evidently), it says...

Hi I am looking for the actual meaning of some technical/procedure words in astronomy, like: 1) Follow-up 2) Pipeline As far I know, the follow up is the observation of an object or a field for a given amount of time, isn't it? Then, if it is, what's the difference with "standard" surveys...

While making a comparative study between turbines and compressors, I noticed some differences between the way they are studied...pleasehelp me understand why these differences exist... 1. Efficiency for a turbine = (actual work/ideal work) whereas for compressors, it is (ideal work/actual...

There seem to be two definitions for a regular representation of a group, with respect to a field k. In particular, one definition is that the regular representation is just left multiplication on the group algebra kG, while the other is defined on the set of all functions f: G \to k . I do not...

Hi I was trying to solve the following problem from Kenneth Ross's Elementary Analysis book. here is the problem. Let S be a bounded nonempty subset of \mathbb{R} and suppose that \mbox{sup }S\notin S. Prove that there is a non decreasing sequence (s_n) of points in S such that \lim...

Correct me if I am wrong but as far as I know, force is generally defined in three ways ways: 1) F = \frac{d p}{d t} 2) F = m\dot v 3) F = ma This is all well in good usually...until the case arises when mass is variable. Then two contradictory cases arise: If we take definition 1...we...

Can anyone help me to find out the definition of "carrier swing"&"deviation ratio"? The definitions which i found on surfing the net is too vague.Can someone help me with this?

i've seen in some texts they use sin(pi t)/pi t = sinc(t) and in some they've used just sin(t)/t = sinc(t) each gives different answer for example if i want to find FT of rect(t/tow) using former one gives sinc(w tow/2 pi) and if i use former one i get sinc (w tow / 2) so how...

i remember the French came up with metric meter by measuring the distance between equator and north pole and then divided by an integer to come up meter. it that still the defintion for meter? also, it seems now that a second is defined by the integer number of oscillation of atomic clock...

Hi! I want to learn a course of "general relativity". For this, I've realized that I have to master the differential geometry. So, I've chosen Lee's book called " introduction to smooth manifolds". In the appendix of the book, some required knowledege of integrations on an euclidean space...

With the study of logic, lots of words get thrown around that I don't really understand their complete meaning. With a deductive argument the conclusion is true if the premises are true, and an argument is valid if all the inferences (and the conclusion) follow logically from the axioms. These...

In classical mechanics, if we consider the motion of a particle of mass m, then The mass m is constant The vector \vec{c} can be: \ldots or \vec{r} or \vec{v} or \vec{a} or \vec{j} or \ldots \vec{c}_1 = d\vec{c} / {dt} \vec{c}_2 = d^2 \, \vec{c} / {dt^2} Definition of...

In classical mechanics, if we consider the motion of a particle of mass m, then m=constant\vec{v}=d\vec{r}/dt\vec{a}=d\vec{v}/dt\vec{j}=d\vec{a}/dt\ldots Definition of Momentum (\vec{M}) \vec{M} \; = \int_a^b m \, \vec{a} \, dt \; = \int_a^b m \,d\vec{v} \; = \Delta \; m \, \vec{v} If...

I had an interesting challenge earlier this year in physics class, and I got a good grade on my answer, but I'd like to see what other people think about this. Energy is defined in the dictionary as being the ability to do work, while work is defined as the application of energy (roughly...

A Newtonian inertial frame is one where objects obey Newton's first law. Schutz (A first course in general relativity) says an inertial frame cannot be constructed in a gravitational field because it's then impossible to synchronize the frame's clocks? For the same reason an inertial frame...

I feel that a lot of the misunderstaing in quantum physics arises from the misinterpretations of terms used by physicists. I think that the forum should have a page where all the quantum terms are explained in a precise technical manner to avoid confusion. I will state pop culture's...

Homework Statement Show that 2.1.1 is equivalent to the totality of 2.1.2 and 2.1.3.Homework Equations The Attempt at a Solution aTx + bTy = aT(x) + bT(y) = T(ax) + T(by) = T(ax + by) ?

What are the definitions of source difference, path difference and reflection difference. Thanks!

Hi, I am studying PDEs and I am confused by the definition of Sobolev spaces as they are different in two books. I'll write the definitions and mention the points of difference which I see despite which I still can't see the difference in definitions. 1) PDEs by Lawrence Evans Let U be...

(Is this thread in the right place?) A few questions on vectors: 1. I was wondering if anyone could explain in conceptual terms what the dot product and cross products represent. (I understand how these are calculated, but why are they important?) 2. Also, would it be accurate to describe a...

I think the FAQ on proofs would be improved if it emphasized the use of defintions. It says that theorems and axioms are used in proofs, but many many textbook type proofs hinge on "parsing" definitions correctly. As alluded to in the FAQs related to "is .999.. = 1?", many difficulties that...