Multiple Definition and 1000 Threads

Figure shows six identical circles inside a rectangle. The radius of each circle is 24 cm. The radius of the circles is the greatest possible radius so that the circles fit inside the rectangle. The six circles form the pattern shown in Figure so that • each circle touches at least two other...

Hello! Now what I've done is first calculate the acceleration. a = 1,962 m/s^2. Than I tried looking at the solution simply through the Newtons laws (or axioms I don't know how to say it in english). Since the elevator is moving through the air the gravitation constant has to be taken into...

In cosmology, CMB tells a lot about which cosmological model can be acceptable or not. For instance we know that, whatever the cosmological model we use ##\theta_*## parameter will be always the same. Is there any other parameters that is listed in this picture is **model-independent** ?(i.e...

Hello all I come to again seeking guidance... There is another thread but he seems to have pulled formulas from somewhere other than our learning materials to reach the conclusions. Looking at this question and I can't figure out where to start really, the examples in out learning materials...

The three events; t = 0s, x=0 t=1.3s, x=1.3 light seconds t=2.6s, 1.3 light seconds

Is Multiple Allelism and Gene Polymorphism same ?If not then why?

I cannot attempt the problem after multiple tries. Can you give me an insight to the problem.

So as the hot plasma of a universe expanded it grew colder and at "recombination" it reached a state where it isn't opaque to em radiation any more unlike dense plasma which is. So we say this is the moment the CMB started. But this got me thinking, after recombination the matter was still some...

Is it possible to put multiple accelerator grid in ion engine instead of one? So we will get higher exhaust velocity and benefit for us right? or is there any disadvantages?

I understand that the Big Bang was an explosion from an extremely tiny mass with particles and quanta traveling away into empty space (anything out there at the instant of this bang being too far to hit yet). I also understand that some ejecta from the Big Bang have been colliding since then...

Say we have a motor attached to the Earth with gear A, that drives identically sized gear B. Gear B spins on its own axis and but is also attached to ground. Torque between gears is equal. Technically each gear has equal but opposite AM right, but If I take Earth into account, how is Ang...

The Week magazine Oct 30, 2020 page 8 To be fair, it's not quite as simple-minded as that makes it sound, but it is still, to me, is a terrible idea. Another progressive education idea that is well-meaning but likely to be disastrous in practice. Here's an article with more detail...

I wish to draw a proper free-body diagram for this shaft. However, my FBD does not agree with the solutions manual. If someone could point out where I erred, that would be great. This is what I drew: From my FBD, it is clear that the maximum torque is present in section DE of the shaft. We...

I am designing a board which will have relatively high current. The options are to use heavier copper (4 oz), use two layers (2 oz), or 4 layers (1 oz). Are there any benefits to using one configuration over the others?

I draw the graph like this: For (b), I divided each force vector to e from p1 and p2 as x and y parts. I computed them and got Fx=-4.608*10^(-15)N Fy=-2.52*10^(-15)N However, I am not sure whether I did it correctly or not... I appreciate every help from all of you! Thank you!

Imagine there were two simultaneous Big Bangs, each producing an independent Universe, and well separated from each other at their formation. Presumably because each would have its own unique set of initial conditions and would follow its own development timeline, they would each have different...

i. Rearranging the equation for kinetic energy in terms of momentum; 1/2mv^2=(mv)^2/2m=p^2/2m Inputting the values given KE=1^2/2*4kg = 1/8 J Kinetic energy of a body with twice the momentum; KE=2^2/2*2kg =1 J The ratio of the kinetic energy of the first body to the second body is therefore...

1. I believe that the gravitational field strength would decrease because it is inversely proportional to the square of the distance from the centre of the Earth, g∝1/r^2. Gravitational potential energy at large distances is directly proportional to the masses and inversely proportional to the...

I took statistics in university about two years ago, but I'm rusty. I was trying to write a zero player game - except sometimes, the player can control one of the characters, and I needed to be able to compute these probabilities. That said, I almost put this in homework help, but it is not...

The following 3 pages are extract from the book: "CALCULUS VOL II" by Tom M. Apostol My interpretation of these 3 pages is worked out in the attached PDF file. Entirely done in propositional logic language. Can anyone point out the mistakes or incorrect logical steps (if any) in the attached...

Gerd Binnig, Nobel laureate in physics in 1986, proposed in his article "The fractal structure of evolution" [1] that everything in the universe, including its laws, had changed and became what we have got today through a process which mixes some concepts from darwinian evolution and fractal...

My main issue with this question is the manipulation of the two arbitrary fields into a single one which can then be substituted into the divergence theorem and worked through to the given algebraic forms. My attempt: $$ ∇(ab) = a∇b + b∇a $$ Subsituting into the Eq. gives $$ \int dS ·...

The following link leads to a question I asked on the mathematics Stack Exchange site. https://math.stackexchange.com/questions/3790900/chain-rule-with-a-function-depending-on-functions-of-different-variables/3791017?noredirect=1#comment7809514_3791017 I want to understand how the chain rule...

I'm studying the proof of this theorem (Zorich, Mathematical Analysis II, 1st ed., pag.136): which as the main idea uses the fact that a diffeomorphism between two open sets can always be locally decomposed in a composition of elementary ones. As a remark, an elementary diffeomorphism...

In the Many Worlds Interpretation, I would formulate measurement something like this: {Cat_alive + Cat_dead}[Observer] -> {Cat_alive}[Cat_alive_observed] + {Cat_dead}[Cat_dead_observed]. So does that mean that the cat and the observer are entangled after measurement? Does this mean there are...

To get the velocity I integrate the accelaeration function and get v_0-c*(t_2-t_1)^2/2 since I think these should be the boundaries of the definite integral. Bu the correct answer is v_0-c*(t-t_1)^2/2 and they integrate from t (upper limit) to t1 (lower limit). Could you please help me to...

I attached a file with some explanations of the variables in the code and the plot that I should get. I don't know what is wrong. Any help will appreciated. from scipy.integrate import quad import numpy as np from scipy.special import gamma as gamma_function from scipy.constants import e...

I am trying to come up with a parent loss function for the following neural network model. On top of that the algorithm for processing an image would also be helpful. The quad-tree compression algorithm divides an image into ever increasingly small segments (squares) and stops in a particular...

Physicist John A Wheeler proposed the "Principle of mutability" which said that it could be the case that the universe would eventually shrink in a "Big Crunch" and the be re-born in another Big Bang. He proposed that the laws of physics (even the considered most fundamental ones) would change...

1. I have calculated the first angle using Snell's Law and with subsequent proceeding angles I am uncertain whether my workings are correct since I have used basic laws of geometry that all internal angles of a triangle add up to 180 degrees and that alternate angles are equal to find proceeding...

Hello, Please I need help to find the objective function of a linear program (attachement : example). I tried to figure it out from the formula provided in (attachement : formula) but I couldn't understand it, it's written (MIN(lambda)wj) I think it's the key to my question ! ( Full file is...

Hello PF! I would like to know how to open multiple files and print different content to each files. The problem is $line_no1,2. means, I tried to write $line_no1,2 as a different value for each of files(tmp1~4.pco) using a while and for statement. I tries like this but dosen't work... The...

Let the new engine, NE, extract heat from a certain subset of these baths, and let heat obtained from the ##i^{\rm th}## bath be denoted by ##Q_i##, and let the heat rejected to the ##j^{\rm th}## be denoted by ##Q_j##. Let the engine perform an amount of work ##W##. Now right beside this...

Dear Everyone, I am having trouble with finding a formula of the multiplication 3 formula power series. \[ \left(\sum_{n=0}^{\infty} a_nx^n \right)\left(\sum_{k=0}^{\infty} b_kx^k \right)\left(\sum_{m=0}^{\infty} c_mx^m \right) \] Work: For the constant term: $a_0b_0c_0$ For The linear...

Hello everybody, I have to find the amplitudes of a wave that goes through 4 different mediums in terms of ##E_0##, suffering reflection in the first three but not the last one. I calculated the corresponding reflection indexes of the three mediums (all of them real). Following calculations, I...

Hey everyone! Had an attempt at this circuit question, but wanted to check if I got the set up right in order to find the current in the 3rd wire? Here is what I have done Thanks!

Hi PF! How can I run two bash scripts run1.sh run2.sh simultaneously (having two separate terminals, one for each run.sh, is fine but I'd like to execute the python script from a single terminal)? Won't the below execute run1.sh and then when it's finished execute run2.sh...

Summary:: How to combine two formulas to find the material index Attached is the problem I am having trouble understanding. I have been able to do the first two combinations by transposing for A in the mass equation then subsituting into the stress equation. The next combinations (in red box)...

Struggling to see if I am doing this right or not from a section of a question I have been given I have drawn out a sketch of the circuit again, and labelled as to what my 1st and 2nd closed loop to be to then apply Kirchhoff's 2nd law I get a negative I_2 current which just indicates that...

Suppose ##\alpha=0##. Then ##\alpha f=0##, the zero map. Hence, the distance between the images of any two ##x_1,x_2 \in D## through ##f##, that is to say, the absolute difference of ##(\alpha f)(x_1)=0## and ##(\alpha f)(x_2)=0##, is less than any ##\epsilon>0## regardless of the choice of...

The Euler Lagrange equation finds functions ##x_i(t)## which optimizes the definite integral ##\int L(x_i(t),\dot x_i(t))dt## Is there any extensions of this to multiple integrals? How do we optimize ##\int \int \int L(x(t,u,v),\dot x(t,u,v))dtdudv## ? In particular I was curious to try to...

Suppose we have a region R in the x-y plane and divide the region into small rectangles of area dxdy. If the integrand or the limits of integration were to be simplified with the introduction of new variables u and v instead of x and y, how can I supply the area element in the u-v system in the...

Afternoon all, Hopefully somebody can help me, I'm doing my final year project and it's looking at the effect of heat treatment on in17, when I run an XRD scan I found that I all the phases sort of hid behind the matrix and so can't really make them out. So I've been looking at using the SEM...

Hi all; This goes under the heading of experimental predictions... gone awry. Let me say from the start that I think I've got something wrong, and would have no problem having it pointed out to me. I'm a newbie, and I've been boning up on basic quantum physics phenomena on Youtube, and...

The Lerch Transcendent identity from my paper which may or may not be true, for ##N\in\mathbb{Z}^+##, and I forget the domain of z and y, here it goes $$\Phi (z,N,y) :=\sum_{q=0}^{\infty}\frac{z^q}{(q+y)^N}$$ $$=\int_{0}^{1}\int_{0}^{1}\cdots \int_{0}^{1}\prod_{k=1}^{N}\left(...

Hi all, Let me give some background to my question. In computational neuroscience it's now fashionable to train recurrent neural networks (RNNs) to solve some task (working memory for example). We do so by defining some cost function and training the model weights to minimize it (using...

Hi I need to create a electricity generator, I've got plenty of car alternators and car batteries, all are 12v. I know how connecting batteries in parallel / series, basically i could connect like 20 car batteries to have a 12v massive amperage power bank which would cause an issue with wire...

$$<p_1 p_2|p_A p_B> = \sqrt{2E_1 2E_2 2E_A 2E_B}<0|a_1 a_2 a_{A}^{\dagger} a_{B}^{\dagger} |0>$$ $$=2E_A2E_B(2\pi)^6(\delta^{(3)}(p_A-p_1)\delta{(3)}(p_B-p_2) + \delta^{(3)}(p_A-p_2)\delta^{(3)}(p_B-p_1))$$ The identity above seemed easy, until I tried to prove it. I figured I could work this...

Can someone help me understand why what I wrote is correct? That is: If I have a sequence with double indices and if the summation of the elements modules of this sequence converges (less than infinite) than it does not matter how I make this sum (second line) they are going to be always the...