Division Definition and 486 Threads

A division is a large military unit or formation, usually consisting of between 6,000 and 25,000 soldiers.
In most armies, a division is composed of several regiments or brigades; in turn, several divisions typically make up a corps. Historically, the division has been the default combined arms unit capable of independent operations. Smaller combined arms units, such as the American regimental combat team (RCT) during World War II, were used when conditions favored them. In recent times, modern Western militaries have begun adopting the smaller brigade combat team (similar to the RCT) as the default combined arms unit, with the division they belong to being less important.
While the focus of this article is on army divisions, in naval usage, "division" has a completely different meaning, referring to either an administrative/functional sub-unit of a department (e.g., fire control division of the weapons department) aboard naval and coast guard ships, shore commands, and in naval aviation units (including navy, marine corps, and coast guard aviation), to a sub-unit of several ships within a flotilla or squadron, or to two or three sections of aircraft operating under a designated division leader. Some languages, like Russian, Serbian, Croatian and Polish, also use a similar word, divizion/divizijun/dywizjon, for a battalion-size artillery or cavalry unit.

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  1. M

    MHB Is Every Non-Zero Element in a Finite Ring Invertible?

    Hey! :o Let $R$ be a finite non-trivial ring. We suppose that for each $r,s\in R$ with $rs=0$ then either $r=0$ or $s=0$. I want to show that $R$ is a division ring. Could you give me a hint how we could show that each element $x\in R\setminus \{0\}$ has an inverse? (Wondering)
  2. Docscientist

    Understanding Cell Division: Chromatin and Chromosomal Changes Explained

    During cell division there are different processes that take place like prophase,metaphase,anaphase etc...I don't understand about chromatin condensation and chromosomal condensation that happens during these processes.Can some one explain how the chromatin material changes itself in different...
  3. I

    Finding Division Equivalents of n-Digit Numbers

    Take a number r that is n-digits long where n is finite. so if r =2385813... $$r_1r_2r_3...r_n$$ $$r_1 = 2$$ $$r_2 = 3$$ $$r_3 = 8$$ etc.. I postulate (since I don't know this is true): Every such number can be expressed as a division between two other numbers, say a and b. $$r = \frac{a}{b}$$...
  4. E

    I Is long division for a non-polynomic function possible?

    My question is: suppose you have a function ##F(x)## which has an asymptote at ##x=x*##. Can you decompose ##F(x)## so that $$F(x) = G(x) + H(x)$$ where ##G(x)## is defined at ##x=x*## and ##H(x)## contains the asymptotic behaviour at ##x=x*## and goes to ##0## at plus or minus ##\inf##? This is...
  5. P

    B Divide Chocolates: Division & Fraction Homework for Kids

    I am following up my 8 years old daughter's homework, and want to show her how division and multiplication work together , such as in division by a fraction : am I right if I say " we divide chocolates by boxes and 6 chocolates divided by half a box means 6 x 2 half boxes = 12 in one box ? " or...
  6. Marcin H

    Current Division: Find Load Resistor Current for 4 Resistors

    Homework Statement Find the load resistor current for 4 different resistors. Homework Equations Current Division The Attempt at a Solution I need to use current division to find the load resistor current for 4 different resistors, but I am not sure how to apply it here. I have I_norton and...
  7. M

    How to calculate the foraging radius of a bird?

    I would love someone to verify the answer for equation 8 in this paper (bottom of page 263) http://onlinelibrary.wiley.com/doi/10.1046/j.1365-2028.2002.00368.x/epdf For the sake of clarity here is the equation is LaTeX which you can render at the following link \frac{QC + Q\lambda \sigma -...
  8. Marcin H

    Find voltages across resistors using voltage division

    Homework Statement 7a from picture Homework Equations V=IR Voltage division The Attempt at a Solution I am not sure how to apply voltage division here. It is a new concept for me and I'm not really sure how to apply it here. voltage division can only be used in series, but these resistors...
  9. B

    MHB Divide Binary: Learn & Get Tricks!

    Hello! Can you teach me how to divide a smaller binary by a bigger binary. For example, 10111÷ 1110001. If you can also share tricks for a much faster solution it would be very much appreciated.
  10. CollinsArg

    How decimal division is explain in real life?

    Okay, hello there! I'm just beggining with an electricity course, and I saw this formula to claculate the Vrms : " Vrms=Vp/√2"... I'm trying to understand the origen of this formula, I see that I have to divide Vp%1,4142... but how do you explain a division with a decimal number..I...
  11. J

    Voltage division of a 5v regulator output?

    So here's my problem. I have a pair of noise-cancelling in-ear headphones, and they require a AAA battery. Batteries are expensive so I only use rechargeable ones, but those have a lower capacity (700 maH) and don't last long. I want to make it last longer by putting several of them together...
  12. stungheld

    Finding Solutions for Polynomial Division: Where to Begin?

    Homework Statement How many pairs of solutions make x^4 + px^2 + q = 0 divisable by x^2 + px + q = 0 Homework Equations x1 + x2 = -p x1*x2= q[/B] The Attempt at a Solution I tried making z = x^2 and replacing but got nowhere. I figure 0,1,-1 are 3 numbers that fit but I am not sure what's...
  13. J

    Polynomial Division (continued from osnarf's problem)

    Hello, My problem is the same as osnarf's problem in thread "Polynomial division proof", https://www.physicsforums.com/threads/polynomial-division-proof.451991/ But, I would like some further help. The problem: Prove that for any polynomial function f, and any number a, there is a polynomial...
  14. C

    Why do we use division when we use per something?

    Why do we use division/fractions to represent per something?
  15. Sirsh

    Complex Number Division and Addition

    Homework Statement This is not for a mathematics unit but is part of an electrical question I'm trying to solve but I cannot solve this equation. The complex numbers Zp and Zr are both real and imaginary, whereas Xm is purely imaginary. Homework Equations Zp = (Xm*Zr)/(Xm+Zr) Zp =...
  16. Anukriti C.

    Theory behind long division method

    our maths teacher asked us that we all use the long division method to find square roots or cube roots. The question is, why do we do it that way, i.e. taking one or two nos. from the starting, doubling the divisor and all the steps(i guess everyone knows that). can anyone please help me and...
  17. gracy

    Solve the Mystery of Equational Division in Cell Division

    Homework Statement First question of this particular page http://www.hourlybook.com/ncert-questions-pmts-cell-cycle-cell-division/ Homework Equations the answer is given as C. The Attempt at a Solution But i didn't understand because in last phase i.e D dna content is again reduced to 2c.But...
  18. arivero

    Furey models with Division Algebras

    Just noticed a new article of C Furey not arxived, but readable in SCOAP Phys.Lett. B742 (2015) http://inspirehep.net/record/1342971?ln=es Charge quantization from a number operator Well, it is not new but I have not found a thread mentioning it. It seems to continue the quest from her...
  19. HaLAA

    Show that Q_F is not a division ring.

    Homework Statement Let F be a finite field of characteristic p∈{2,3,5}. Consider the quaternionic ring, Q_F={a_1+a_i i+a_j j+a_k k|a_1,a_i,a_j,a_k ∈ F}. Prove that Q_F is not a division ring. Homework EquationsThe Attempt at a Solution Let α=1+i,β=1+i+j∈QF. Then...
  20. amor_mundi

    Upper division (300/400 level) vs lower division classes

    In community college right now and Physics 3 (electricity and magnetism) has crushed my physics GPA. Phys 1/2 was a 3.9/3.8 and this quarter is likely to be a 3.5. I could have studied harder and I could have done more to get a higher grade, but I should probably say the class average on...
  21. B

    High Resolution Upper Division Undergrad Math lecture videos

    I'm interested in watching videos of Real Analysis lectures etc. in good quality resolution. Those Harvey Mudd College lectures are valuable but annoying re video quality. Thanks. - Blue
  22. G

    Langrange interpolation polynomial and Euclidian division

    Homework Statement Let ##x_1,...,x_n## be distinct real numbers, and ## P = \prod_{i=1}^n(X-x_i)##. If for ##i=1...n ##, ##L_i = \frac{\prod_{j \neq i}^n(X-x_j)}{\prod_{j\neq i}(x_i-x_j)}##, show that for any polynomial A (single variable and real coefs), the rest of the euclidian division of A...
  23. V

    Any place to take upper division physics classes online?

    Looking for accredited upper division physics [undergraduate] classes online/correspondence. Anyone know of any? My searches are failing me. Also, before someone says that it's impossible, upper div physics classes rarely have labs and are mostly math, so it is possible to do via correspondence...
  24. M

    MHB What is the Remainder When \(121^{103}\) is Divided by 101?

    What is the remainder of the division number $121^{103}$ by 101
  25. S

    MHB How Does Modular Arithmetic Simplify Integer Divisibility Proofs?

    Let $a$, $b$, and $c$ be integers, where a $\ne$ 0. Then $$ $$ (i) if $a$ | $b$ and $a$ | $c$, then $a$ | ($b+c$) $$ $$ (ii) if $a$ | $b$ and $a$|$bc$ for all integers $c$; $$ $$ (iii) if $a$ |$b$ and $b$|$c$, then $a$|$c$. **Prove that if $a$|$b$ and $b$|$c$ then $a$|$c$ using a column proof...
  26. PsychonautQQ

    Proving the Divisibility of p^2 - q^2 by 24 for Primes p and q

    Homework Statement If p and q are both greater than or equal to 5, prove that 24|p^2 - q^2 Homework Equations none The Attempt at a Solution 24 = 2^3 * 3. If p = q = 5, then 24|0. If p = 7, q = 5, then 24|24. Any other combination, p^2 - q^2 will be greater than 24. I want to show that p^2 -...
  27. U

    Fourier's method, division by zero

    Homework Statement Solve the BVP for a vibrating string with Separation of Variables/Fourier's method. \frac{\partial ^2}{\partial ^2 t} u(x,t) = c^2 \frac{\partial ^2}{\partial ^2 x} u(x,t) The string is of length L with each end fixed, ie u(0,t) = u(L,t) = 0 The Attempt at a Solution I...
  28. N

    What is the 2015th decimal number in the division 2015 by 7

    What is the 2015th decimal number in the division 2015 by 7? This is how I did it but is there an simpler way of showing this... I did 2015/7 = 287.857142 857142 857142 857142 ... As we have a recurring decimal for the numbers 857142, I divided 2015 by 6 which gives me a non finite answer so...
  29. M

    Polynomial Long Division for Limit Calculation

    Homework Statement \frac{x^5-a^5}{x^2-a^2}, where a is some constant. Homework EquationsThe Attempt at a Solution I can't figure out how to do this with long division. With synthetic, I can get to \frac{a^4+a^3 x+a^2 x^2+a x^3+x^4}{a+x} x^3+xa^2+...
  30. B

    Voltage/Current Division with central Voltage Source

    Homework Statement Find V0 using voltage/current division Homework Equations V=(VsR)/Req I=(IsIeq)/I The Attempt at a Solution I used general circuit rules (parallel and series) to get the total resistance as 14.775 ohms{?}. And I'm stuck with what to do next . . .
  31. Eclair_de_XII

    How does synthetic division produce the results it does?

    Homework Statement f(x) = x^3 Find f(-2) f(-2) = -8 The text says that by dividing a function [x^3] by [x minus a given input (-2)] using synthetic division, I'll be able to produce the correct output (-8). I want to know why this happens. Homework Equations (x^3)/(x-(-2)) = -8The Attempt at a...
  32. S

    Divide by Zero Error: Solving Pendulum Radius

    I have data from a pendulum and I am using it to work out the radius of the pendulum. I have acceleration in the x and y directions and so thought this would be easy enough. Simply I determine the (velocity in the x direction)^2/acceleration in the y direction. However when I use python to give...
  33. P

    Division with Einstein summation convention

    Homework Statement I have the following equation Aab= c ua ub Where Aab is a rank 2 tensor and ua is a vector and c is a scalar and a,b = {0,1,2,3}. I know both Aab , ua and ua I want to find c explicitly but I don't know how to interpret or calculate c = Aab / ( ua ub ) Does anyone...
  34. Mr Davis 97

    Representing ratios with division

    This might seem like a silly question, but why do we use division to compare two quantities, i.e., a ratio? I've always taken for granted that dividing two physical quantities tells how many of one quantity there is for the other quantity, but why exactly does this work? Why don't we define some...
  35. PsychonautQQ

    Number Theory Division Algorithm interesting problem

    Homework Statement Not actually for homework, but i didn't know where to post this. Problem: Show that any integer to the fourth power can be expressed as either 5k or 5k+1 where k is an integer. Homework Equations None. The Attempt at a Solution My starting point is to consider that all...
  36. anemone

    MHB Is the Remainder of Polynomial $f(x)$ the Same for Two Different Divisors?

    Show that the remainder of the polynomial $f(x)=2008+2007x+2006x^2+\cdots+3x^{2005}+2x^{2006}+x^{2007}$ is the same upon division by $x(x+1)$ as upon division by $x(x+1)^2$.
  37. Logan Rudd

    Upper division physics lab -- Project ideas

    As an experimentalist, I am very excited to be taking my first upper division physics lab next semester! The course covers basic electronics (filters, diodes, transistors, op-amps, analog & digital circuits, D/A conversion, and LabView Programming, etc.) and measurement techniques with an...
  38. 159753x

    Calculating voltage division for an AC circuit?

    Homework Statement A series RL circuit is connected to a 110-V ac source. If the voltage across the resistor is 85 V, find the voltage across the inductor. Homework Equations V = IR The Attempt at a Solution How does one go about solving this? My intuition tells me that KVL must be...
  39. T

    MHB Function Long division question

    So, I am wondering if there is a way to long divide $x+2 $ / $x -1$. My result is $1 + \frac{4}{x -2}$ but does $[1 + \frac{4}{x -2} ] * [ x - 2]$ = $x +2$ Thanks
  40. PsychonautQQ

    Division Algorithm for Polynomials in R[x] confusing me

    I will be using /= to mean 'does not equal'. From my textbook: Division Algorithm: Let R be any ring and let f(x) and g(x) be polynomials in R[x]. Assume that f(x) /= 0 and that the leading coefficient of f(x) is a unit in R. then unique determined polynomials q(x) and r(x) exist such that 1)...
  41. Math Amateur

    MHB Help with Paul E. Bland's Division Rings and IBN-rings Prop 2.2.10 Proof

    I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Section 2.2 on free modules and need help with the proof of Proposition 2.2.10. Proposition 2.2.10 and its proof read as follows:My question/problem is concerned with Bland's proof of Proposition 2.2.10...
  42. I

    How about Why does the Landau notation for division work when h approaches 0?

    Why is it that, ## \frac{a+\mathcal{O}(h^2)}{b+\mathcal{O}(h^2)} = \frac{a}{b}+\mathcal{O}(h^2) ## as ##h\rightarrow 0##? It seems like the ##\mathcal{O}(h^2)## term should become ##\mathcal{O}(1)##.
  43. J

    I don't understand polynomial division

    At first he shows 2x+4 / 2 and you just divide both 2x and 4 by 2. But then in the next example he is dividing x^2+3x+6 by x+1 and he doesn't divide x^2 by x+1, 3x by x+1 and 6 by x+1. I do not understand how he does the problem.
  44. L

    Mathematica Division of sequences in Wolfram Mathematica

    How to divide two sequences in Wolfam Mathematica? For example f_n=\frac{1}{n}=1,\frac{1}{2},\frac{1}{3},... and g_n=n^2=1,4,9,... I want to get h_n=1,\frac{1}{8},\frac{1}{27}...=\frac{f_n}{g_n} How to do that in Wolfram Mathematica?
  45. RabbitWho

    Supression ratio in classical conditioning

    I think that if you're good at maths you'll be able to help me without having heard of this before, assuming you know about classical conditioning it's explained here; http://brembs.net/classical/suppress.html The measure of the extent to which the CS suppresses responding is called the...
  46. matineesuxxx

    Runtime of Seemingly Unpredictable Division Algorithm

    Last week on my computer science assignment I had to write a division algorithm using only addition and subtraction to tackle a problem. My first attempt was the simple and naive repeated subtraction, although I quickly discovered it was not nearly efficient enough for how I needed to use it, So...
  47. M

    Inverse laplace transform (polynomial division? Complex roots?)

    Homework Statement Decide the inverse laplace transform of the problem below: F(s)= \frac{4s-5}{s^2-4s+8} You're allowed to use s shifting. Homework Equations The Attempt at a Solution By looking at the denominator, I see that it might be factorized easily, so I try that...
  48. B

    Does Associative Property Apply to Subtraction and Division Too?

    I show that the assoc. property applies to addition and multiplication in my book: (a+b)+c = a+(b+c) (ab)c = a(bc) But what about subtraction and division?
  49. B

    Problems Understanding Division of Fractions

    This is frustrating me. The formula for division of fractions in my Pre-Calculus book is a/b = a x 1/b. However, when you apply this to an actual problem, it doesn't make sense. For example: 3/4 divided by (sorry, I don't see a divisor sign in the list of symbols we can choose from) 6/11...
  50. chwala

    Does Division of Polynomials Follow a Pattern of Degree Decrease?

    When you have a polynomial say ax^4+bx^3+cx^2+dx+e where a,b,c,d and e are constants and divide this by a polynomial say ax+b it follows that the quotient will be a cubic polynomial. Assuming that a remainder exists, then the remainder will be a constant because in my reasoning, the remainder...
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