Let ## x\geq 2 ##.

Then ## \frac{d}{dt}(\frac{ \log {t}}{t^3})=\frac{1-3\log {t}}{t^4} ##.

By Euler's summation formula, we have that

## \sum_{n\leq x}\frac{ \log {n}}{n^3}=\int_{1}^{x} \frac{\log {t}}{t^3}dt+\int_{1}^{x} (t-[t])(\frac{1-3\log {t}}{t^4})dt+(x-[x])\frac{log {x}}{x^3} ##...

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I need to figure out the definition of the oft-called "Standard" action of the circle ##S^1 ## ( as a Topological/Lie group) ,on ##S^n##, the n-sphere ( I guess seen as ##\{z : |z|=1\}## in Euclidean n-space). My searches returned an action of ##S^1## on ##S^3 ## given by ##A(z_1...

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The rules:

1) https://www.nytimes.com/games/wordle/index.html

2) Post your result.

3) Do not spoil the answer.]]>

So, I was wondering, the Biot-savart show us a magnetic field created by a constant electric current. Initially I thought that an example would be biological systems with a nervous system that works on the basis of electrical discharges, but I don't think it's a valid example...

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I have a pulse generator (this one) and I want to test it with a low voltage for now. I have a bench power supply (something like this). I am confused about how to make the connections. For...

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I just read this article about how electrical transformers work and have some questions.

https://www.dfliq.net/blog/the-basics-of-electrical-transformers/#:~:text=The%20three%20important%20components%20of,magnetic%20flux%20is%20initially%20produced.

i). What exactly is...

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I tried Updating the NVIDIA drivers from 470 to 510 and then to 515, but in vain...

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A test here. (chose size 10)

A test here. (chose size 18)]]>

http://www.npr.org/blogs/thetwo-way...-exchange-mt-gox-goes-dark-after-theft-report

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I really despite that it is automatically added when replying or quoting the OP. I always delete it.

But the summary of this thread really shows the little added value of a summary: It is, word for word, the entire post!]]>

My issue arises from the premise that I learned; Integrals and derivatives are based on steps of a fixed constant...

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Hopefully I'm not alone in this hobby here :)]]>

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##\int_{-\infty}^{\infty} (xa^3 e^{-x^2} + ab e^{-x^2}) dx##

a and b are both constants.

From what I found

##\int_{-\infty}^{\infty} d e^{-u^2} dx = \sqrt{\pi}##, where d is a constant

and...

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I have researched the internet but can't find a reason why this relationship exists.

Is it somehow a consequence of some type of gravitational balance, if not is there some other mechanical reason?

Thanks

Martyn]]>

As prompted in https://www.physicsforums.com/threads/how-to-become-a-successful-physicist.1045728/post-6803003 I ask my question as new topic:

How or what do successful scientists or engineers do BEFORE ever reaching university? I...

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I try to better understand how and when I can apply the Born rigidity condition.

So, for the following example:

We've two space probes (P

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Here is the last page of part 5.

https://www.physicsforums.com/threads/random-thoughts-part-5.851969/page-134]]>

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Note: Please read what she is talking about before commenting.]]>

The first flight of the Space Launch System will launch...

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1. If the potential energy where a particle moves is of the form

##V(x) = c_2 x^2 + c_4 x^4 + c_6 x^6 + \dots##

or

##V(x) = c_2 x^2 + c_3 |x|^3 + c_4 x^4 + c_5 |x|^5 + c_6 x^6 + \dots##

with ##c_j \geq 0##...

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*

Her current "signal" is to simply pace back and forth from the foyer to the dining room. Unfortunately, this is pretty normal behavior for her (because she's highly intelligent and therefore gets bored)...

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I understand that a vector is a physical object

I understand that it is the underlying basis that determines how the components transform.

However, I encounter this:

https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors

The fifth paragraph has this...

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An event is shown as a point on a spacetime diagram

Another frame has coordinates of space and time as:

##\begin{aligned} c t^{\prime} &=(\cosh \theta)(c t)-(\sinh \theta) x \\ x^{\prime}...

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If possible, what is the most efficient method of achieving it ?]]>

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A K shell electron is ejected from a tungsten atom. The result of this is the emission of a characteristic x-ray proton. (The binding energy of the K shell in tungsten is 69.5keV. The binding energy of the L shell in a tungsten atoms is 10.5 keV).

a) If the vacancy in...

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(I drew motion in the opposite direction so the object would rotate trigonometrically but it should be the same thing)

I have just finished the Kinetic Energy and Work chapter in my course and this is the last problem from the problem set. I have not worked many...

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Is TiCl4 more covalent because it has more cation than TiBr3 correct ?

(sorry im not good at english)]]>

The general definition of the four-current density is ##j^{\mu} = (\rho, \vec j)##, where ##\rho## is the charge density and ##\vec j## is the three-current density. This vector may be timelike, lightlike, or spacelike, because both positive and negative charges may be involved with...

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I accept that a proper Lagrangian for Dynamics is "Kinetic minus potential" energy.

I understand it is a principle, the same way F=ma is a law (something one cannot prove, but which works)

Still... what do you say to students who say "I...

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I am happy with the answer (I love this group).

But the answer opened up a deeper question.

Many elasticity textbook posit the existence of a strain energy function:

And they make an additional assumption about...

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I am currently planning on self studying math analysis with MIT ocw courses, but I cannot find the analysis course. I have found on the web that analysis and ODE are the same thing. If I want to get a good introduction to analysis, is the MIT ODE course fit for such a use?

Thanks]]>

A 2.70 kg box is moving to the right with speed 9.50 m/s on a horizontal, frictionless surface. At t = 0 a horizontal force is applied to the box. The force is directed to the left and has magnitude F(t)=( 6.00 N/s2 )t2

What distance does the box move from its position...

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Prove that ##a(a+b) \le 2##.]]>

My answer is (1) only but my teacher said (3) is also correct. I don't understand why, I think when the wave is moving to the left both Q and R will be moving upwards, no?

Thanks]]>

I have a little problem understanding Young's slit experiment with single photons :

I have understood for a long time that each photon impact on the screen corresponds to a photon sent by the source, and that, if we don't try to find out by which path the photon has passed, of course...

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Simplified, Class A (and several other classes and instances of classes) has a string that stores the tooltip text and updates it every frame.

Class B contains the logic to generate the...

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For anyone interested in graduate-level study galactic dynamics, Jo Bovy (Assoc Prof in the Astrophysics Dept at U. Toronto) is in the process of constructing an interactive textbook on the subject, which you can check out at...

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Doing some math here - if the local mass density is significantly higher in the inner 10-15% of the galaxy, and then lower and gradually thinning outwards in the disk, we will...

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Couldn't it be like this:

Let F(x) = ##\int f(x)dx## so ##\int_{a}^{x} f(x)dx## = F(x) - F(a)

Thanks]]>

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If the goal of the fundamental forces (in a heavily generalized sense) is to bring particles to a lower state of energy, how is the strong force participating to this?

Could it be due to atoms being a very stable configuration?

If this is the...

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https://www.kron4.com/health/corona...rs-discover-why-some-people-are-asymptomatic/

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I am reading something on wave function in quantum mechanics. I am thinking a situation if we have particles distributed over a periodic potential such that the wave function is periodic as well. For example, it could be a superposition of a series of equal-amplitude plane waves with...

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$$\displaystyle f \left(t \right) \, = \, \frac{\lambda ~e^{-\frac{\lambda ~t }{k }}}{k }, \, 0 < t, \, 0< \lambda, \, k = 1, 2, 3, \dots$$

It seems that this distribution is a limiting case of another distribution. The question is what...

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I would like to search and prepare me...

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in Section 1.9 we read the following:

I need some help to confidently interpret and...

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[Submitted on 22 Sep 2022]

A.J. Krasznahorkay, A. Krasznahorkay, M. Begala, M. Csatlós...

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A frictionless puck is slid horizontally off the top of an infinite set of stairs with a speed of 3m/s. The steps are standard size: 20cm high and 20 cm wide. Which step will the puck strike first?

Since the pluck will not get faster on the x-axis, these are my...

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In our music system, the fundamental frequencies of the different notes on a musical instrument such as the piano or the guitar are related to each other in such a way as to allow...

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STAGE 1:

I have a c6-7 rocket motor which provides 10N-s of impulse, and...

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I have often read on the internet that it would be caused by the weight of the water above the water at the base...

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My research experience during undergrad has primarily been about...

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Prove: that if H and K are sets and p is a limit point of H ∪ K,then p is a limit point of H or p is a limit point of K

In this...

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Any opinions?]]>

It provided an easy-to-understand mechanism for tracking the effects of adding information to a fictional universe. The example they gave for...

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The thing is, I know the torque in the wheels from the torque the electric motor I designed do provide, multiplied by the gearbox ratio. I also know the...

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If

To prove this we take the Hermitian conjugate of

U

⇒

My question is -...

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We watched all the

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So what’s your favorite theory?]]>

Universally, the gear icon symbolizes settings, and this is true across different OS and desktop or...

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But I want to introduce and consider a slight and...

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Maybe I've just not found the right source. Google seems obsessed with...

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## w\equiv d+[(2.6)m-0.2]-2c+y+[\frac{c}{4}]+[\frac{y}{4}]\pmod {7} ## provided that March is taken as the first month of the year and January and February are assumed to...

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Hello! I'm trying to understand how this pendulum works. I found this video that explains how to calculate the T force from the rope.

He uses the preservation of kinetic and potential energy in order to find the magnitude of the velocity and then using Newton's second law, he...

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I an clear on how the modulo operator ##%##, also called the remainder operator, is used in programming. It gives the remainder of the integer division. For example, ##5 % 2 = 1## because the divisor 2 fits 2 wholly times into the dividend 5 leaving behind a reminder of 1.

## 6% 3 =0##...

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When...

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https://www.nature.com/articles/s41567-022-01766-x]]>