Relation Definition and 1000 Threads

Homework Statement A vector r has length 21 and direction ratio's 2,-3,6. The direction cosines of r, given that r makes an obtuse angle with x-axis is given by? Homework Equations l/a = m/b =n/c ...(1) (l,m,n are direction cosines, a,b,c are direction ratios l^2 + m^2 + n^2=1...(2) The...

Homework Statement Suppose ##R## and ##S## are relations on a set ##A##. If ##R## and ##S## are transitive, is ##R \cup S## transitive? Why? Homework EquationsThe Attempt at a Solution Suppose that ##a## is an arbitrarily but particularly picked element of ##R \cup S##, then $$a \in R \...

I am studying about dielectric materials and their relaxation properties. There are several ranges of electromagnetic frequencies where different material show different kinds of resonance starting from molecular to atomic motions. Based on the frequency dependence of the imaginary part of the...

Homework Statement Show that if ##\left( \Omega f\right) ^* = -\Omega f ^* ## then ##\left< \Omega \right> = 0 ## for any real function f. where ##\Omega## is an operator Homework Equations It's a self test of the completeness relation --Molecular quantum mechanics (Atkins)-- so the equation...

Homework Statement One of the two glass panes in each window is coated with a transparent electrical conductor. Why does this coating improve the window's insulating ability? Select one: a. The transparent conductor is black in the infrared, with a low-temperature emissivity of almost 1. b...

Hi. I'm reading an introductory text that somehow seems to confuse if ##E^2-(cp)^2=const## means that the left side is invariant (under Lorentz transformations) or conserved (doesn't change in time). As far as I understand it, they only prove Lorentz invariance. Are they both true? If so...

Hi. I've read that there's no Newtonian analogue of the energy-momentum relation $$E^2-(pc)^2=(mc^2)^2\enspace .$$ Why doesn't $$E=\frac{p^2}{2m}$$ qualify as such? There's no rest energy in Newtonian physics anyway.

Hi all, I was wondering if there is a correlation between the accretion rate and time. I think it should decrease as time increases, but I can't find the right correlation

In Hebrew, one explain to me that: "Transitivity is a property (or attribute - I don't which word is correct) of property". So, (1) Which word is correct? (2) Why Transitivity is not standalone by itself? (3) Are there relations of other kind, that no standalone by themselves?

Can one explain to me the sentence: "Transitivity (or transitiveness) is a key property of both partial order relations and equivalence relations.". ...in simple words. The sentence is from Wikipedia at address: https://en.wikipedia.org/wiki/Transitive_relation

In 'Introduction to Cosmology' by Barbara Ryden, there is an argument made using the first law of thermodynamics to derive the relation T(t) ∝ a(t)-1 on pages 29 and 30. MENTOR NOTE: removed copyrighted material. I've been able to work out all the omitted details up to 2.37, which gives the...

Homework Statement I need to find the explicit formula for the following recursive sequence: ##v_n=\frac{2}{1+q^n}v_{n-1}## where ##0<q<1## is a constant Homework Equations I found the following method to solve it...

Starting from the following definition of stress-energy tensor for a perfect fluid in special relativity : $${\displaystyle T^{\mu \nu }=\left(\rho+{\frac {p}{c^{2}}}\right)\,v^{\mu }v^{\nu }-p\,\eta ^{\mu \nu }\,}\quad(1)$$ with ##v^{\nu}=\dfrac{\text{d}x^{\nu}}{\text{d}\tau}## and...

I apologize ahead of time for the simplicity of the question, but this has really been bothering me.Given the de Broglie relation, assuming natural units, where ##\hbar = 1##: \begin{equation} \begin{split} \vec{k} &= M \vec{v} \end{split} \end{equation}My question regards velocity and...

There is no sample file given in DBMS file organization chapter in my book. 1. Storing each relation in separate file 2. Storing many relation in one file. Can you please provide a sample of these files. How they look ?

A few simple questions which I am not sure about, it's about NMR. First sentence: "A magentic field B0 is applied on a sample, If the applied magnetic field B0 is stronger, the magnetisation of material is greater" . Would you say that sentence is correct? As I understood, magnetization is a...

I've found the general solution to be y(x) = C1cos(x) + C2sin(x). I've also found a recursion relation for the equation to be: An+2 = -An / (n+2)(n+1) I now need to show that this recursion relation is equivalent to the general solution. How do I go about doing this? Any help would be...

I’m confused because there are two equations: 1) A=λN 2) A=A0exp^-(λt)If half-life increases, λ decreases, and A decreases according to 1); but, If half life increases, λ decreases, hence exp^-(λt) decreases, A should decreases according to 2)Why is this so? Where went wrong? Thanks!

Homework Statement Homework Equations Halpin Tsai equation:[/B] Voigt model: P*=VfPf+VmPm Vf= volume of fiber/ volume of composite Vm= volume of matrix / volume of composite ζ= estimated parameter Pf, Pm= fiber and matrix properties V_v=1-Vf-Vm The Attempt at a Solution Since there is no...

On the one hand, the intuitive notion of a recurrence relation is clear from examples. On the other hand, what is the precise way to define it? The first interesting technicality is why should we call it a "relation" ? Is it, in general, a "relation" and not the more specific case of a...

I am currently reading this notes by t'Hooft, and I realized that a soliton and a Goldstone boson behave in a similar way: Both of them interpolate between the vacua. Keeping in mind Soliton is described classically in the notes(atleast until first few sections in chap1), Is there a relation...

I will state the problem below. I don't quite understand what I am needing to show. Could someone point me in the right direction? I would greatly appreciate it. Problem: Let p be a natural number greater than 1, and x a real number, 0<x<1. Show that there is a sequence $(a_n)$ of integers...

Homework Statement [/B] Strap in, this one's kind of long. (This problem is from 'Six Ideas That Shaped Physics, Unit T' by Thomas A Moore, 2nd edition. Problem T6R2.) Imagine that aliens deliver into your hands two identical objects made of substances whose multiplicities increase linearly...

Bernoulli's principle states that under dynamic conditions total energy inside the fluid container remains constant. and if area is decreases then pressure decrease . and Pascal states that pressure = force/area . here if area decreases then pressure increase . I'm getting confusing...

<Moderator's note: Moved from a technical forum and thus no template.> Not sure this should be under Linear and Abstract Algebra, but regardless I need help with a question in my mathematical proofs course. Here it is: Let ∼ be a relation defined on Z by x ∼ y if and only if 5 | (2x + 3y). (a)...

From this link https://en.wikipedia.org/wiki/Baryon_acoustic_oscillations#Measured_observables_of_dark_energy , I can't get this relation : ##c\Delta z = H(z)\Delta \chi\quad\quad(1)## with ##z## redshift, ##H(z)## Hubble constant at redshift = ##z## and ##\chi## radial coordinates. One...

Homework Statement Consider the isentropic expansion of air from a fixed given reservoir (i.e. total pressure and temperature). Investigate the behaviour of the value of the Reynolds number of the flow, as a function of the Mach Number M of the expanded flow. For small values of M, the...

Hi, I'm trying to simulate the process of charged particles attenuation in matter (like this) by a montecarlo-metropolis algorithm in Python. I thought that I could use for the number of particles at thickness ##x## the formula ## N (x) = N_0 e^{-\mu x} ##, so the probability in this case will...

Hi physics folk, Thought you guys would be able to clarify something, self study learner here getting into quantum. So I've just learned about the De Broglie relation and The Photoelectric effect and am bamboozled (in a good way). The notion being that light is absorbed in packets. However I'm...

Hi everyone. I am reading through these very interesting (in terms of topics) notes: https://arxiv.org/abs/1807.05996 And so far I am at Section 5. The author gives me the impression they don't seem to fear to call what is Bayesian and what is Frequentist, making the distinction in applications...

Hello, I am encountering some confusion with the relation between the latent heat of vaporization and the temperature of a substance. I understand both the latent heat and the entropy change of vaporization are dependent on the temperature, assuming the pressure is held constant. However given...

Homework Statement Assertion- If linear momentum of particle is constant, then its angular momentum about any axis will also remain constant Reason-Linear momentum remains constant when net force is 0, angular momentum remains constant when net torque is zero which of these statements is/are...

In particle phyisics four-momentum is used and De Broglie relation is used to understand what lenghts can be "seen" in an experiment. Here (page 6) https://people.phys.ethz.ch/~pheno/PPP/PPP2.pdf it is claimed Where ##Q^2## is not actually "momentum" but its the square of the four momentum...

Homework Statement If mole fraction, pressure fraction and volume fraction are denoted by Xmol , Xp, XV respectively, of a gaseous component, then what is the relation between them? Homework Equations mole fraction = mole of component / total moles pressure fraction = pressure of component /...

Hello! In this paper https://pdfs.semanticscholar.org/e8a2/02f25555cd8c4f947bbbdff5a61a0ea0efd2.pdf the authors use VASP to determine MgSiO3 viscosity using the Green-Kubo relation ## \eta = \frac{V}{3k_{\rm{B}}T}\int_{0} \left<\sum_\limits{i<j}\sigma_{ij}(t+t_{0}).\sigma_{ij}(t_{0})\right>dt##...

Well, I obviously know the Euler's relation: eπi+1=0 But what I finally understood is that this is not a relation between those numbers. It is just the result of the function exp(z) when you extend the exponential function to the complex numbers and you supose analyticity (I don´t know if that...

Hey guys , my lecturer introduced a new concept with reference to the commutation of two operators.He claimed that if two commutators commute then they can be simultaneously measured.I can clearly see how this works.He then went on and state if they don't commute they can't simultaneously be...

1- Let’s say we have 1,000 hydrogen atoms in empty space. 2- And for this case only, let’s say 1,000 atoms is the point of fusion under their own gravity. 3- Fusion will create energy. 4- And it will continue until the star explodes or collapses, so in this case it will...

so i have been trying to calculate boltsmann constant by assuming the fact that for an ideal gas the equation : PV=nRT is true. i assume that for containing each molecule the wall needs to apply a force. now here is where it get's a little weird. each molocule should be only deflected in the...

I am getting ready for exams and I have encountered this problem on the exam paper: In AC circuit there is a condensator and a inductive coil, At first XL=XC, how does the relation change when the frequency doubles? The answer says XL=4XC Can someone explain me how they come to this conclusion...

Hi Physics Forums, I am stuck on the following nonlinear recurrence relation $$a_{n+1}a_n^2 = a_0,$$ for ##n\geq0##. Any ideas on how to defeat this innocent looking monster? I have re-edited the recurrence relation

For Schwarzschild geomery $$ds^2=-(1-\frac{2GM}{r})dt^2+(1-\frac{2GM}{r})^{-1}dr^2+r^2d\Omega^2$$ For a Schwarzschild observer , the proper time and coordinate time are related by $$d\tau=(1-\frac{2GM}{r})^{1/2}dt$$ There is a often used relation between proper time and coordinate time $$d\tau...

Homework Statement Match the following Given : Processes do not include chemical reactions. Assume CP,m and CV,m are independent of temperature for given substance and consider only pressure-volume work in given all processes. Homework Equations ΔU = Q - W ΔH = ΔU +...

Homework Statement So I have got the question below. I am asked to find the phase difference between the electric field and magnetic field of electromagnetic waves traveling in a plasma, using the electrical conductivity expression. Now I have found the frequency of the waves and I know that...

Homework Statement Homework Equations log(y) = mlog(x)+log(k) y=kxm The Attempt at a Solution Determine the exponent m and coefficient k of the power law that best fits your data. Is the acceleration directly or inversely proportional? Taking some points on the graph to get the slope (0.78 -...

Hi, I want to know the relation between the point spread function (PSF) and the morphological index (Sharp, Sround, Ground). what does the PSF represent? and what is it's importance in the detection of astrophysical objects (quasars, galaxies)? Thanks

Homework Statement a relation R⊆ℝ2 It is defined if and only if a2+b2=c2+d2 where (a,b) ∧ (c,d)∈ℝ2 Find all equivalence classes Homework EquationsThe Attempt at a Solution I said that the following set defines an equivalence class for the above problem: [/B] [(a,b)] = {(c,d)∈ℝ2 ...

I'm a complete rookie in this field so please correct me where I go wrong, I just really want a better understanding of this subject. So as far as I am aware, mass causes the space surrounding it to curve or bend. What I want to know is how much does it bend the space? is the bending of space...

I'm curious if the readers of this astronomy forum, at this point, have come to understand that the mass-luminosity relation has little to do with the physics of nuclear burning. The reason I ask this is that it is, unfortunately, still common to find textbooks and course websites that say it...

I have a pair of correlated datasets that I collected in the lab for temperature and conductivity of a solution vs time. I want to determine the functional relation between the two. (see attached plot-an interesting lead/lag in the phase difference). If I were trying to determine this...