What is Multiple: Definition and 1000 Discussions

A multiple-unit train or simply multiple unit (MU) is a self-propelled train composed of one or more carriages joined together, which when coupled to another multiple unit can be controlled by a single driver, with multiple-unit train control.
Although multiple units consist of several carriages, single self-propelled carriages - also called railcars, rail motor coaches or railbuses - are in fact multiple-units when two or more of them are working connected through multiple-unit train control (regardless if passengers can walk between the units or not).
The term multiple unit does not denote locomotives using multiple-unit train control.

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  1. W

    I Inner Product Between States of Multiple Particles

    $$<p_1 p_2|p_A p_B> = \sqrt{2E_1 2E_2 2E_A 2E_B}<0|a_1 a_2 a_{A}^{\dagger} a_{B}^{\dagger} |0>$$ $$=2E_A2E_B(2\pi)^6(\delta^{(3)}(p_A-p_1)\delta{(3)}(p_B-p_2) + \delta^{(3)}(p_A-p_2)\delta^{(3)}(p_B-p_1))$$ The identity above seemed easy, until I tried to prove it. I figured I could work this...
  2. user15197573

    I Order of summation in series with multiple indices

    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...
  3. T

    Finite quantum well, multiple choice question

    Homework Statement:: Consider an electron trapped in a one-dimensional finite well of width L. What is the minimum possible kinetic energy of the electron? A) 0 B) Between 0 and h^2/8mL^2 C) ≈h^2/8mL^2, but it is not possible to find the exact value because of the uncertainty principle D)...
  4. olgerm

    I Summation Convention in Einstein Notation

    I got another basic question: should the summation in einstein notation start from first occurance of index or in beginning of equation? For eampledoes this equation ##R_{\alpha \beta }={R^{\rho }}_{\alpha \rho \beta }=\partial _{\rho }{\Gamma ^{\rho }}_{\beta\alpha }-\partial _{\beta }{\Gamma...
  5. karush

    MHB 9.1.317 AP calculus exam multiple choice derivatives of sin wave

    ok just posted an image due to macros in the overleaf doc this of course looks like a sin or cos wave and flips back and forth by taking derivatives looks like a period of 12 and an amplitude of 3 so... but to start I was not able to duplicate this on desmos altho I think by observation alone...
  6. S

    MHB Multiple Transformations of Functions

    I have to transform the first function which is f(x)=x^3 to the second function. First, I have to find each shift then combine those to make a new function equation. I've used desmos and I know that there is a horizontal shift 3 units to the right. There is a vertical shift up but I don't know...
  7. Amartansh

    Understanding the Multiple scattering effect

    What does it mean by induced source in multiple Electromagnetic scattering by large scatterer? While solving volume source integral to model multiple scattering by large scatterers, do we consider each discrete small region as induced dipole or a point source? Why it is a rule that these small...
  8. P

    B Correct way to write multiple argument functions

    Hi, This is on the wikipedia entry for the Euler Lagrange equation. Here is a link. https://en.wikipedia.org/wiki/Calculus_of_variations#Euler%E2%80%93Lagrange_equation The notation I am confused about is this: Aren't the y(x) and the y'(x) unnecessary to list as arguments when x is...
  9. Beelzedad

    I Multiple integral Jacobian confusion

    Consider a continuous charge distribution in volume ##V'##. Draw a closed surface ##S## inside the volume ##V'##. ___________________________________________________________________________ Consider the following multiple integral: ##\displaystyle B= \iint_S \Biggl( \iiint_{V'}...
  10. Pencilvester

    LaTeX Trying to display an equation spanning multiple columns in table

    I’ll just paste in all of the packages I’m using and the relevant code. The line in this sample that is giving me errors is line 24. (Errors below) \documentclass[10pt]{article} \pagenumbering{gobble} \usepackage[english]{babel} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb}...
  11. I

    Weight Distribution Across Multiple Points

    Thanks in advance to anyone that can help me solve this problem, its causing me a real headache. I need to transport a rather large frame that supports a large heavy item. The weight is not evenly distributed along its length. I know the various distances between the supports, the total weight...
  12. I like Serena

    MHB Multiple consists of only 6's and 7's

    Given a number that does not end in 0 or 5, prove that it has a multiple that consists of only 6's and 7's. For instance 12 has the multiple 7776.
  13. I like Serena

    MHB Can a number that ends in 3 have a multiple consisting of only 1's?

    Given a number that ends in 3, prove that it has a multiple that consists of only 1's. For instance 13 has the multiple 111111.
  14. Buzz Bloom

    I A variation of the Multiple World Interpretation

    The multiple worlds are not real, but instead they are contingent. This mean that each of the various possible combinations of all of the possible future measurements or relevant interactions that change the probabilities, that could possibly happen according the wave function of everything...
  15. ChrisXenon

    B Do multiple WiFi devices create areas of high EMR?

    I'm thinking in a typical house or office, areas of constructive interference may exist which aggregate the fields of maybe 10 WiFi devices. Wouldn't this mean the safe power levels stipulated for any single device would be routinely be exceeded? And if so, do we care?
  16. P

    Fortran Program to plot multiple datasets on a single graph in Fortran95

    PROGRAM Test IMPLICIT NONE REAL, PARAMETER :: Omega_m0 = 0.27, Omega_rel0 = 8.24E-5, Omega_L0 = 0.73, Omega_0 = 1.02 REAL :: z_max, z, dz REAL :: I, g_z, g_zplus, S REAL :: d_p0, d_L, d_A, d_nr, d_r INTEGER :: n = 100000 OPEN(UNIT = 10) z_max = 0 DO WHILE (z_max <= 4.001) dz = z_max/n...
  17. S

    Did Paul Dirac believe in multiple universes?

    Prominent physicist Paul Dirac proposed a hypothesis that indicated that constants and laws of physics would evolve with time into different constants and laws of nature (https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis) This hypothesis was used by Robert Dicke...
  18. P

    Admissions Including multiple areas of interest in my SoP for PhD Applications

    I'm starting to write my statement of purpose for Physics and Astronomy graduate schools, but I'm not yet dead set on which field I want to specialize in. Considering this, is it ok for me to write something along the lines of, "I want to either do field 1 with professor I or do field 2 with...
  19. christang_1023

    I What is the addition law for probability with multiple elements?

    The additional law with two elements can be expressed $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$, while the law with three elements can be $$P(A\cup B\cup C)=P(A)+P(B)+P(C)-P(A\cap B)-P(B\cap C)-P(A\cap C)+P(A\cap B\cap C)$$ Now I wonder if there is the more general form of addition law, which applies...
  20. Wrichik Basu

    Python Question about a function call with multiple arguments

    Recently in college, we have started learning python. I found that the print statement can accept multiple variables. For example, if I have variables x1, x2 and x3, I can write print(x1, x2, x3) in python. Something similar exists in Matlab as well. I have learned Java for nearly four years...
  21. M

    MATLAB How can I import multiple .csv files into MATLAB using a loop?

    Hi PF! I'm trying to import multiple .csv files into MATLAB. Since the first row of the .csv is titles, I'm using the readtable function. This process works when I don't use a loop, but when I try to loop through several files I get the error "Error using readtable (line 198) The file extension...
  22. R

    B Multiple Histories theory by Richard Feynman

    Summary: There is some thing i did not get about Multiple History theory Summary: There is some thing i did not get about Multiple History theory I am reading big answers to the big questions from Stephan Hawking. He has mentioned very little about Multiple History theory. I could not...
  23. J

    Static Analysis of Bolts on Multiple Surfaces

    I am trying to analyze if the bolts in my design are sufficient to support the load on a shaft. Unfortunately, the bolts are not all located on one face, and though I know how to analyze each face by itself, but I would like to be able to combine them all into one problem. I have attached a...
  24. L

    Can you charge multiple capacitors simultaneously?

    What if you put two RC circuits in parallel?
  25. M

    B Can I keep multiple clocks in sync after a ride on a roller coaster?

    Suppose there are 6 cars on a roller coaster and I synchronize 6 clocks at rest with respect to each other in a box with no wiggle room on the space station. The bottom of the box has the same shape as the curvature of the earth, and the box is always kept "top side up" with respect to the...
  26. S

    Calculate combined friction on multiple different surfaces?

    Hello, I have a cuboid on two different surfaces. I am applying a changeable force F to it, but it should stay on the same point / in static friction. I now want to calculate the combined (static) friction coefficient μ_combined out of the two known coefficients of cuboid to surface 1 μ_1 and...
  27. B

    Voltmeter problem from (OCR paper) multiple choice

    As you can see when the switch is open it measures the voltage across the battery or emf I am assuming when calculating the internal resistance when the switch is closed voltage is 6 right so the internal resistance is 6/2 =3 which is not correct. answer is A Does this mean when the switch is...
  28. B

    Potential at a point multiple choice question ( aqa)

    I understand how they arrived at the answer of 2Q , but i have a couple of questions on this. If one of the charges were negative for example how would the resultant potential be found then? at the middle point would i add the positive charges and subtracted the negative ? Also what would the...
  29. NP04

    Simple kinematics multiple choice question

    I selected A, because the ball is merely in motion due to the force of gravity (after applied force). My teacher has not concerned us with air resistance so can someone please explain why the correct answer is C? I reasoned that gravity was always accelerating the ball at -9.8 m/s^2...
  30. Grinkle

    B Can superposition be attained for multiple states at once?

    I hope my articulation makes sense. Can I prepare a particle so that it has >1 states in superposition and resolve them at different times? I will make up states to try and illustrate my question better. Prepare a particle so that spin up and spin down are in a state of superposition. Also...
  31. F

    Running multiple studies in COMSOL

    Hi. Can anyone help me to figure out how to run multiple studies in COMSOL? I want to first compute the displacement of a membrane using temperature load and then find the capacitance between two electrodes using electrostatics. The idea is that as the membrane moves upwards the capacitance will...
  32. O

    Looking for an app to demonstrate motion via multiple exposure images

    I am introducing uniform and accelerated motion in a 6th grade. To demonstrate the difference I would like to use multiple exposure photography (like in the image below) in the classroom. There are many apps to make serial shoots and other apps to overlay them artfully. I am looking for an App...
  33. D

    MHB Appropriate graph to illustrate multiple differences in measurement?

    I have two groups (expert & novice) that were tested on walking with stilts and without. The results were: walking velocity (cm/s) cadence (steps/min) stride length (cm) What would be the appropriate graph to run with RStudio to account for the three different measurements? Thanks, Dants
  34. D

    MHB Require assistance with possible multiple regression analysis

    I am interested in determining more efficient ways of determining individuals' body fat percentage. To do this, I measure the circumference of a number of segments (10 of them) of the body and determine the person's percentage body fat through underwater weighing. I have done this for 252 total...
  35. Rasias

    How to calculate what a voltmeter measures with multiple resistors?

    I tried to solve it by removing the voltmeter and simplifying it to just one resistor, then calculate the individual volts and then the deltaV, but still didn't found the answer, can you guys help me?
  36. Comeback City

    B Finding Multiple Ways to Integrate

    Hello everyone! Today in my BC Calculus (calc 2) class, we spent time trying to find ways to integrate the same function (all methods we're fluent with, but are reviewing for the upcoming AP test)... (I apologize in advance that I do not know how to use LaTex, but am trying to learn) f(x) =...
  37. R

    A The Oberth effect and multiple orbits

    Hi all, I've been following the launch of the first commercial lunar lander, SpaceIL. Because of its small size, there is not enough fuel for a more direct approach to the moon, so the path they are taking is multiple orbits around the Earth with impulses at the perigee, at each orbit. As I...
  38. J

    Comp Sci C++ program to read an input file with multiple headers

    Homework Statement Write a program that can read an input file with a simple header. The Attempt at a Solution #include <iostream> #include <fstream> using namespace std; int main() { ifstream inFile; inFile.open("Data"); //Check for error if (inFile.fail()) { cout...
  39. E

    Combining Multiple Rules for Error Propagation

    Homework Statement An object of mass m=2.3±0.1kg moves at a speed of v=1.25±0.03m/s. Calculate the kinetic energy (K=1/2mv2) of the object and estimate the uncertainty δK? Homework Equations - Addition error propagation--> z = x + y and the Limit error--> δz = δx + δy -...
  40. Mr Davis 97

    First multiple of 2019 with last digits 2018

    Homework Statement What positive integer is the first multiple of ##2019## such that the last four digits of this numbers are ##2018##? Homework EquationsThe Attempt at a Solution I was thinking just take multiples of 2019 mod 10000 and look for a pattern, but this didn't really seem to work...
  41. StarWarsNerd

    Collisions Between Two Bodies Undergoing Multiple Transformations

    I have been searching for an answer to this for a really long time and I have not found any definitive answers as of yet. What I am trying to do is determine if and when two bodies collided between the times t0 and t1. Calculating this is much more straight forward if each body is only either...
  42. M

    Mathematica Plotting Multiple values on different domains

    Hi PF! I have a list of numbers, and I'm trying to plot each constant value on a 1-unit long interval. What I'm trying is this a = Table[i, {i, 2, 8}]; For[i = 1, i < 5, i++, Plot[a[[i]], {x, i - 1, i}] // Print] but that generates plots that are not on the same axes. Any help?
  43. R

    I Multiple hypothesis testing for radar tracking in clutter

    Hello All, The goal is to formulate a multiple hypothesis test for a radar tracking problem when false alarms are occurring and to apply a particle filter on this update step, however I first need to come to/understand the multiple hypothesis formulation in this problem. Say we are interested...
  44. A

    Eigenfrequencies of a multiple DOF system

    I am confused with this concept. So if a system possesses multiple possible eigenfrequencies (and therefore modes), how does the system "know" which eigenfrequency will it want to vibrate on? Does that depend on the initial condition you give the system? Is there any mathematical relation...
  45. S

    MHB Converse, Contrapositive and Negation for multiple Quantifiers

    If every printer is busy then there is a job in the queue. where B(p) = Printer p is busy and Q(j) = Print job j is queued. When it's translated to symbol, we'll have (∀pB(p)) → (∃jQ(j)). I'm trying to translate this statement to both English and symbol forms for Converse, Contrapositive and...
  46. G

    A Fraunhofer's multiple slits versus atomic scatteres (diffraction theory)

    Hey, I am currently busy with studying solid state physics and looking at diffraction theory. Following link explains Frauenhofer diffraction pretty good: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/mulslid.html#c3 Let's assume a N=6 multiple slits. Its diffraction pattern depends on slit...
  47. Bobman

    Courses Multiple physics and maths courses at the same time?

    So we are to choose electives (this is all undergrad) for the spring in about a month or so, and i am having doubts if i might end up taking one "math heavy" or "concept heavy" course too many. My uni splits one semester into two periods, meaning the spring semester is based on two periods...
  48. H

    A Metal or Insulator: Examining Resistance in Multiple Directions

    Generally, a material is metal or insulator is simply determined by the gap. But if we view it in another way, to measure the resistance in different direction, says x and y, and there are usually different. And then measure the resistance change with temperature. Usually, the resistances goes...
  49. B

    Transformer: single primary coil and multiple secondary coils

    If I have a coil with 10 turns and a primary voltage $$V_p$$ and primary current $$I_p$$ and a single secondary coil with 10 turns, I understand the power in the secondary will be $$P=V_pI_P$$ and hence voltage and current in the secondary coil will be the same. If I now bring a 3rd coil with...
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