Terminology Definition and 170 Threads

This is not only a question strictly about mathematics, but in science or any other quantitative field in which there is an integration - or a summation that is like a discrete integration. [ A ] the parameter that is considered the input variable for the integration/summati - i.e., the x of dx...

Now I am starting to learn Quantum Mechanics. In the class I am taught about operators, postulates and all other basic stuff. I understand operators to be +, -, /, etc; but quantum mechanical operators are entirely different; to understand them, I think, I need to know the historical...

I thought I had these, but then I get to Sturm-Liouville and my confidence wavers ...please confirm / correct / supplement: 1) An Adjoint operator is written $ A^† = (A^T )^*≡(A^* )^T $ We can identify an operator A as adjoint $ (A^† ),iff <ψ_1 |Aψ_2> = <Aψ_1 | ψ_2> $ An adjoint operator...

In mathematical parlance, we say "take the derivative of a function f" to indicate that we are computing a new function, which maps slopes, that derives from f. However, in physics, we say "take the derivative of velocity". However, velocity is a quantity, not a function. What does it mean to...

I hope someone with a deep conceptual understanding of terminologies would help me out here. I am having starting problems in understanding the approach of gauge theories. I have read suggested threads and I am still at a loss. I am an experimental physicist and know basics of electrodynamics...

In a geometric mean equation, say 2 x 8 = 16, or a x b = c, what are the words we would use to describe the numbers or terms? Specifically, if you know 'a' and 'c', what do you call 'b'? For example, in a normal multiplication, a x b = c, 'a' is the multiplicand, 'b' is the multiplier, and 'c'...

I have attached an image of a function that I fit to a scatter plot, and I would like to know if there is a term for the point on the function at which the slope transitions from being less than -1 to greater than -1. I have highlighted this point approximately in yellow...

I think its correct to state that: "Kinetic energy is a property of a moving object." But would it be correct to state that: "Kinetic energy is carried by a moving object"? If not is there a better alternative terminology to use? Thank you.

Homework Statement How to explain, and distinguish among (or build up from initial definitions) the terms electric field, electric potential, electric potential energy, voltage, difference in voltage. The usage in various sources is casual or insufficiently specific. Homework EquationsThe...

First, I would like to clear up notation and the definition for sequences. What exactly is a sequence? I read somewhere that it is defined as a function ##f: \mathbb{N} \to \mathbb{R}##. But if this is the case, why do we only define functions based on the range of the function, e.g., ##\left \{...

Hi guys, Can someone explain - as simply as possible - what the following terms mean? 1) Lorentz observer 2) Lorentz frame 3) spacelike vector Thanks guys!

Consider the following two calculations: (1) d(x\cos x)=(\cos x-x\sin x)dx (2) \frac{d}{dx}(x\cos x)=(\cos x-x\sin x) I would describe these both as differentiation. Is there a standard terminology that allows one to make the distinction between the two, if desired? The best I could come up...

Hello, My professor wrote something on the board the other day and I forgot to ask after class. $$\lim_{{x}\to{c}} f(x)$$ = L <=>$$\lim_{{x}\to{c^+}} f(x)$$ = L && $$\lim_{{x}\to{c^-}} f(x)$$ = L What does mean by L and what does <=> mean?

Meter sticks laid out around the rim of a rotating disk will foreshorten by the Lorentz factor. This means more of them will fit around the disk in the reference frame of an observer on the moving rim. Q: In physics, what name is given to the longer measured length by a foreshortened meter...

I am attempting to write a page concerning exponentiation and logarithms for my website www.1728.com Basically I'd like to know the precise terminology. In the equation 2³ = 8 we can say that "2" is the base, "3" is the exponent but what exactly is the "8" called? I have seen it referred...

So, I was trying to type something like dy/dx or dt/dy or a^(n)dy/dx But the problem is: I can't write subscripts on word or nth order derivatives. For my math club, I can't use ^ symbol or dx/dx (must be fraction form). I also need to know how to write the subscripts for y1, y2, y(n-1), y(n)...

A lot of textbooks give the definition of an S-matrix element as: \langle \beta_{out}| \alpha_{in}\rangle = \langle \beta_{in}| S| \alpha_{in} \rangle=\langle \beta_{out}| S| \alpha_{out} \rangle=S_{\beta \alpha} and that S|\alpha_{out} \rangle =|\alpha_{in} \rangle I don't...

I am very mixed-up with the terms perturbation, anisotropy and ripple. What is the relation or difference between them?

Are the quantum mechanical terms "probability amplitude" and "probability density" used interchangeably?

I'm just looking for the right words to use to talk about something like the "bijective correspondence" between the class of groups defined as pairs and the class of groups defined as 4-tuples. I'm talking about the "map" ##(G,\star,i,e)\mapsto (G,\star)##. It seems to me that it shouldn't be...

In my book is says the electric flux density D is equal to εE if the medium is linear and isotropic, where E is the electric field and permittivity ε is a scalar. I have no idea what they mean by a linear and isotropic medium.. How am I suppose to know if the medium is linear or isotropic?

Tensors can be of type (n, m), denoting n covariant and m contravariant indicies. Rank is a concept that comes from matrix rank and is basically the number of "simple" terms it takes to write out a tensor. Sometimes, however, I recall seeing or hearing things like "the metric tensor is a rank 2...

I am reading the draft of a paper written by someone whose native language was not English and so who might not have been using the same abbreviations that I am familiar with, or maybe he was using standard ones and I am simply not familiar with the abbreviations involved. I can't ask him, as he...

Hello, I am confused about the terminology moment, specifically that there is a 1st moment and 2nd moment. What does moment even mean, and why does it have numbers associated with them?

So if we imagine a rectangle. The aspect ratio is width/height. What if you want the ratio of the parallel sides? Is there a terminnology for that ratio?

For anyone who has taken discreet math are there any easy ways of remembering all the terms for the condition statement? I added the terms in the paint doc.

Hello, Just wondering if any of you have encountered a term for a particular type of graph. It is like a graph that allows for loops, but for loops, instead of joining a vertex to itself, it joins a vertex to nothing. I just want to be consistent with existing terminology, if there are none...

My language is not English and i have got some problem in terminology . In physics , what's the meaning of "convert" ? Somewhere like Wikipedia claims that mass is not converted to energy since mass and energy can not be destroyed but Elsewhere claims that Energy can be converted into matter...

Lets say if there was an experiment in which: A toy car with modelling clay attached to it, and a pellet is fired at it, the pellet sticks into the clay and the toy car moves forward. Now if it is replaced with a metal plate attached to the toy car instead of the clay, the pellet rebounds...

So in finding a pattern for the nth derivative for y = x-1 the book wrote y(n)(x) = (-1)nn!x-n-1 What does the exclamation mark mean? I know != means not equal to.

Definitions like this one are common in books: For all ##k,l\in\mathbb N##, a multilinear map $$T:\underbrace{V^*\times\cdots\times V^*}_{k\text{ factors}}\times \underbrace{V\times\cdots\times V}_{l\text{ factors}}\to\mathbb R$$ is said to be a tensor of type ##(k,l)## on ##V##. Lee calls this...

I'm just beginning to learn general chemistry, and I'm reading my textbook's chapter on aqueous solutions. My question is, why do we term a solution of an ionic compound (like NaCl) like this: NaCl(aq) instead of: Na+(aq) + Cl-(aq) ? Technically, when the sodium chloride is...

Ok, I am a fusion physicist, but I still don't know what the strict criterion is for calling a nuclear reaction a fusion reaction. Yes, it's a collision between two nuclei that results in a bigger nucleus. But, then ^{11}B + ^{1}H \rightarrow 3 \alpha is usually called a fusion reaction. Isn't...

I'm trying to learn some physics on my own, using the internet as my main source of information. Now, I'm a bit confused about some terminology, and I can't find anything about it... Distance vs displacement in rotational kinematics! Is there a similar difference as in linear kinematics...

In lecture, we are beginning to learn about waves and periodic motion under simple harmonic motion. We were given the equations: x=Acosθ and θ=ωt+\phi -- Substituting, we get x=Acos(ωt+\phi). This is simple enough; however what is Phi? All I was told is that "phi is a constant that allows us...

Is there a specific mathematical term, which refers to this expression? A * B ------ A - B

For the formula for getting voltage difference V_b-V_a=-\int _a^{b} Edl how do we know where the limit a and b go? In the equation it goes from a to b but why not b to a? For example , in this question I am given a non uniform charge density where charge density increases with radius r for a...

A temperature activated phenomenon/process, K, is said to be Arrhenius if dlog(K)/d(1/T) is constant where T is the absolute temperature. Now suppose a process exhibits two constant slopes (m1,m2) when plotted versus (1/T), say m1 governs the low T behavior and m2 governs the high T...

Hello all. I recently read something that has me a bit confused. Consider a single-phase 100kVA transformer that supplies a 40kW heating load at unity power factor. What is meant by "how much additional kW of inductive load at 0.8 power factor can the transformer carry" mean? Is it asking how...

Homework Statement I am some trouble understanding the surfaces required to integrate over in the following questions. I can tackle them, I just don't understand some terminology. Q1) A circle C is cut on the surface of the sphere ##x^2 +y^2 +z^2 = 25## by the plane ##z=3##. The direction...

We talked about AC circuits and phase shifts were discussed. Voltage changes "lag behind" current changes so that's how we get phase shifts. It's like a sinusoid so fine. Then we talked about impedance. There's a real and "imaginary" component to impedance, graphed on x-axis and y-axis...

Hi, 9 is a perfect Square, 27 is a perfect Cube 81 is a perfect ?? 243 is a perfect ? Is there terminology for such things? -Diffy

I'm learning about how Gaussian works and I'm reading about potential energy surfaces which Gaussian uses to calculate very properties of a molecule. Right now I'm reading about optimisations, I understand the concept that to optimise the structure of a molecule, it needs to find the global...

I'm a physicist trying to learn some chemistry for my research (on-surface reactions and assembly) but am having some trouble with getting the meaning of some of the terms straight. Often one source seems to contradict another, in my reading of it at least. Specifically, the meaning of the...

Müller's law seems to differ from the modern statement of the law in one key way. Müller attributed the quality of an experience to some specific quality of the energy in the nerves. For example, the visual experience from light shining into the eye, or from a poke in the eye, arises from some...

hello english is not my native language and the few programming literature I have read in my language, is so badly translated from english, that makes it more difficult to comprehend I understand that almost all programming languages share some terms, like class, function, command, object...

I am new to non linear dynamics, I am reading some papers and there are terms that I am finding every which I still have no idea about their meaning. What is: 1. Inhibitory coupling 2. An attractor Any explanation or reference is warmly welcome Thanks

I'm looking at the diagram (Figure 1) at http://en.wikipedia.org/wiki/Supercritical_fluid I get that the region in which both the temperature & pressure are higher than the critical point is called a supercritical fluid, which really means it is both a gas & a liquid, thermodynamically...

Hello, 1. What is the technical term for two things (concepts/ideas/phenomena) that depend on one another and cannot be reduced further? I was going to use this in relation to "Physical Evidence and Reasoned Logic" as neither seems more fundamental than the other. Without logic, evidence...

The relation between two terminology "cusp" (group & algebraic curve) Dear Folks: I come across the word "cusp" in two different fields and I think they are related. Could anyone specify their relationship for me?? Many thanks! the cusp of an algebraic curve: for example: (0,0)...