What is Term: Definition and 774 Discussions

A term limit is a legal restriction that limits the number of terms an officeholder may serve in a particular elected office. When term limits are found in presidential and semi-presidential systems they act as a method of curbing the potential for monopoly, where a leader effectively becomes "president for life". This is intended to protect a republic from becoming a de facto dictatorship. Sometimes, there is an absolute or lifetime limit on the number of terms an officeholder may serve; sometimes, the restrictions are merely on the number of consecutive terms they may serve.

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  1. R

    How to simplyfy a square root term? Phonon dispersion relati

    I'm having trouble simplyfying this, I guess there's a trick but for the life of me can't remember what it is. Here is what I have so far: ##\omega ^{2} = f\left ( \frac{1}{m}+\frac{1}{M} \right )-f(( \frac{1}{m}+\frac{1}{M} \right ))^{2} - \frac{4q^{2} a^{2}}{mM})^{\frac{1}{2}}## so I divide...
  2. J

    Term to express a range of fluctuation

    I am trying to make a term for a function equipped on an image sensor. The term is to express "the upper limit of fluctuation allowance in image size which is specified in %" The value of percentage does not express the ratio of the enlarged image size compared to the original image size, so...
  3. Suraj M

    Arithmetic progression sum and nth term

    Homework Statement The ratio of sums of 2 AP for n terms each is ## \frac{3n + 8}{7n + 15}## that is $$ {\frac{s_a}{s_b}} = \frac{3n + 8}{7n + 15} $$ find the ratio of their 12th terms. $$ Required= \frac{a₁_a+(n-1)d_a}{a_b + (n-1)d_b}$$Homework Equations Tn = a + (n-1)dThe Attempt at a...
  4. D

    Fluid mechanics: intuition about the 'convective' term

    Hi, I am doing an introductory course on fluid mechanics, and I'd like some intuition (that's why I'm posting on the engineering forums and not on the math forums, even if I'm studying for a degree in math) about the concept of the total derivative and, particularly, its convective component...
  5. Suraj M

    Evolution, short term or long term adaptation?

    I had a small question, which one contributes more to evolution: 1)short term adaptation and heritable 2)long term adaptation and heritable ?
  6. J

    What is the term for this image processing?

    How do you call of the digital image processing that simplifies an image by reducing the amount of pixels? I thought of the word “thinning”. But according to ”Fundamentals of Digital Image Processing” by Anil K. Jain, “Thinning algorithm transforms an object to a set of simple digital arcs...
  7. Superposed_Cat

    Given the sum of a series and a term how would you find Tn?

    Hi all, given the sum of a series and a single term how would one find the nth term? Any help appreciated.
  8. F

    Where did this term go? - Help with Example Problem

    I'm having trouble figuring out how the term below boxed in red was eliminated on the left side of the equation as shown below. I reviewed properties of exponential functions, and still can't understand how this term was cancelled. 1. Homework Statement Homework Equations Exponential laws...
  9. S

    Leading term of a power-series solution

    Hey! I have a question: how can you find the power-series solution and its leading term of the following ODE around the point x=+-(1-b) (where b is near x): $$-(1-x^2)\frac{\partial^2 f^m_l}{\partial x^2}+2x\frac{f^m_l}{\partial x}+\frac{m^2}{1-x^2}f^m_l=l(l+1)f^m_l ,$$ and m and l are...
  10. M

    Calculating term in Virial Expansion

    Homework Statement ...For each of the temperatures...compute the second term in the virial equation ##B(T)/(V/n)##, for nitrogen at atmospheric pressure. Homework Equations ##PV = nRT(1+\frac{B(T)}{V/n}+\frac{C(T)}{(V/n)^2}+...)## The Attempt at a Solution I'm given a list of temperatures and...
  11. T

    Gauge Fixing Term and Equations of Motion

    Lets take QED just to simplify. When we are doing Path Integrals and we want to "fix the Gauge": 1 we add in the integral a delta(F) -meaning that we are going to integrate only in one representative of each class of equivalent configuration- 2 We take some factors out because they are constant...
  12. R

    Time-independent Schrodinger equation in term of the TDSE

    Homework Statement Write down the general solution of the time-dependant schrodinger equation in terms of the solutions of the time-independant Schrodinger equation. Homework Equations TDSE TISE The Attempt at a Solution I'm really not sure how to interpret this question, I could write the...
  13. chwala

    Finding the nth term of a sequence

    Find the nth term of the sequence; ## 2, 5, 10, 17,26......## this is how i did it: 2, 5, 10, 17, 26 can form a difference of 3,5, 7,9... whose nth term is 1 + 2n. now how can apply this to the original sequence to get the nth term?
  14. J

    Solving a PDE in spherical with source term

    Homework Statement I have a PDE and I need to solve it in spherical domain: $$\frac{dF(r,t)}{dt}=\alpha \frac{1}{r^2} \frac{d}{dr} r^2 \frac{dF(r,t)}{dr} +g(r,t) $$ I have BC's: $$ \frac{dF}{dr} = 0, r =0$$ $$ \frac{dF}{dr} = 0, r =R$$ Homework Equations So, in spherical coord. First...
  15. G

    Einstein's Regret: Penrose Asserts on Relativity

    In the following program http://www.bbc.co.uk/programmes/b02144gl Penrose asserts that Einstein regretted the term relativity because it gave ammunition to those who assert that there is not one truth or that reality is a social construct. Does anyone have exact quotes from Einstein asserting...
  16. D

    Derivative of first term in Lagrangian density for real K-G theory

    Hey guys, This is really confusing me cos its allowing me to create factors of 2 from nowhere! Basically, the first term in the Lagrangian for a real Klein-Gordon theory is \frac{1}{2}(\partial_{\mu}\phi)(\partial^{\mu}\phi). Now let's say I wana differentiate this by applying the...
  17. bearcharge

    Pointless in talking about atomic term for a certain micro-state?

    I'm a chemist trying to understand atomic term symbol. If we list all the micro-states of certain multi-electron configuration, these micro-states can be grouped into several certain terms characterized by L and S. In other words, when we compute the ML and MS for each of the micro-state, they...
  18. A

    How to teach yourself programming for the long term?

    No, I'm not asking what language to learn, etc. I started learning python last year and i was wrapping my head around the basic concepts and even making some nifty programs. However, one day I just got frustrated and gave up. I know frustration is common but I felt very stupid while...
  19. B

    Can You Define "Term" and "Expression" in Math?

    I have heard different things and want to get a "professional" opinion on this. It seems like the words "term" and "expression" are technical terms with specific definitions in math and I want to know what they technically refer to (not just the personal slang or informal definitions someone...
  20. S

    MHB Find Nth Term of Sequence: (-1)^n

    I have been trying to find the nth term of the following sequence: -1, 5, -17, 65... I am thinking that the nth term has (-1) ^n . It doesn't appear to be a geometric or arithmetic sequence. I am stymied.
  21. S

    Runge Kutta question, equation has dx/dt in it and non linear term ?

    How does one set up the Runge Kutta for \frac {d^2y} {dt} m = b(\frac {dy} {dt} - \frac {dx} {dt}) + k (y-x) ? Set up the substitution variables: a = \frac {d^2y}{dt} v = \frac{dy} {dt} Then what ? Is there a way to get \frac{dx} {dt} out of the equation ? If not, I have to...
  22. M

    Differential Equation with Noise term

    Homework Statement (\partial_t - A\nabla^2 + B)f(x) = \eta(x, t) So I have a homogeneous linear differential equation except for an added noise term ##\eta(t) ##. The noise is uncorrelated between times and has a Gaussian distribution with zero mean. That is we have Gaussian white noise...
  23. G

    Struggling with Math Homework? E(t) Term Got You Stuck?

    Homework Statement Please see the attached file. Homework EquationsThe Attempt at a Solution If my math is right so far, I am basically stuck as to what to do with the E(t) term. [/B]
  24. JohnPrior3

    Forgetting a Term: Country Expands Borders on Religious Beliefs

    I know this is physics forums and I am a physicist. I figure the people out here are well read beyond the realm of physics. I am trying to remember the term that describes a country should expand its borders based on religious belief. I am writing a paper, and I cannot come up with the name of...
  25. D

    What Do You Call Singing Without Words?

    When a singer is performing a song, and they're singing syllables which are not words or have any meaning, but only have some aesthetic quality. For example, "la la la" or here in this song from about 2:25-2:50 What is the term or word for this?
  26. evinda

    MHB What is the dominant term of a function and its complexity?

    Hey again! (Smile) I want to find the complexity of $g(n)=10 \cdot \log (n^{30}+30)+2 $. We will find that $g(n)=\Theta(\log n)$, right? (Thinking) What can I say at the beginning? Which is the dominant term of the function? (Thinking)
  27. C

    Analytically solve second-order coupled ODE (damping term coupled)

    Homework Statement I need to (analytically) solve a system of coupled second-order ODEs: (A) \frac{du}{dt} - fv = \Omega^2x (B) \frac{dv}{dt} + fu = \Omega^2y where u = \frac{dx}{dt} v = \frac{dy}{dt} subject to the initial conditions u(t=0) = U and v(t=0) = 0. Homework Equations --- The...
  28. 22990atinesh

    What is the meaning of term "Framework" in Programming Environment ?

    Hello, What is the meaning of term "Framework" (Programming Environment). I've usually keep hearing this term, But didn't understand the meaning. Suppose we we say .NET Framework, then what actually does it refers.
  29. 9

    Simple regression: not including the intercept term

    Homework Statement The simple regression model is y = α + βx + u, where u is the error term. If you don't include α, when is β unbiased? Homework Equations y = α + βx + u The Attempt at a Solution Not including α doesn't affect whether β is unbiased because α is a constant.
  30. S

    Finding the General Term of a Series

    Homework Statement Find the general term and test the nature of the series: Homework Equations 1+1*4+1*4*7+... The Attempt at a Solution Term N = Term (N-1) * 3N-2 Hence,3(N-1)-2 * 3N-2 which simplifies to (3N-5)(3N-1) = 9N^2 - 18N + 5 Is this correct?
  31. S

    Finding the general term of the series

    Homework Statement Find the general term and test the nature(convergent/divergent) of: 1/3 + 2/15 + 2/35 + ... The Attempt at a Solution If I simplify I get , 1/3 + (1)(2)/(3)(5) + (1)(2)(3)/(3)(5)(7) +.... I found that, TERM(N) = TERM(N-1)((N)/(2N+1) After this I am struck.
  32. U

    Find the expansion of this term

    Homework Statement IF e^{m \arctan x}=a_0 + a_1x + a_2x^2 + a_3x^3...+a_nx^n+... prove that (n+1)a_{n+1} + (n-1)a_{n-1}=ma_n and hence obtain the expansion of e^{m \arctan x} . Homework Equations The Attempt at a Solution $$e^{m \arctan x} = 1+m \arctan x + (m \arctan x)^2/2! + (m...
  33. basheer uddin

    How do we get the n th term of the sequence?

    Homework Statement how do we get the n th term of a sequence if it is given in form of ##x_{ n+1 }=f({ x }_{ n })## and the p th term is given Homework Equations I figured we may get it if we get it in the form of ##x_{ n+1 }-{ x }_{ n }## but how?can we even get it?if yes,under...
  34. P

    Finding general term of a sequence

    Homework Statement Find the general term of 0, 4, 22, 118, 718, 5038, 40318 if a1 = 0, a2 = 4 and so on. The Attempt at a Solution I have tried getting the differences between them, even going 4 levels deep, but that isn't working obviously, I tried seeing if the ratios are the...
  35. I

    Parabolic pde with additional term

    Homework Statement Solve \frac{\partial v}{\partial t} = k\frac{\partial^2 v}{\partial x^2} - v 0\leq x \leq L t > 0 Homework Equations v(x,0) = f(x), v(0,t)=0, \frac{\partial v}{\partial x}(L,t) = -v(L,t) The Attempt at a Solution I've already attempted to solve...
  36. H

    Laplacian term in Navier-Stokes equation

    I am trying to derive part of the navier-stokes equations. Consider the following link: http://www.gps.caltech.edu/~cdp/Desktop/Navier-Stokes%20Eqn.pdf Equation 1, without the lambda term, is given in vector form in Equation 3 as \eta\nabla^2\mathbf{u}. However, when I try to get this from...
  37. F

    MHB Did I misinterpret the sign attached to a term when factoring?

    I wanted to factor xy+x-2y-2 I got x(y+1)-2(y-1) and got stuck I tried somethings out and noticed (x-2)(y+1)=xy+x-2y-2 so how come I did get stuck? Did I extract the 2 incorrectly with the sign? For example should I have interpreted it at -2y-2 not 2y-2?
  38. T

    Exploring Complex Roots of Underdamped Systems: Why the Sine Term?

    I'm trying to do some refreshing of differential equations featuring damped systems. Specifically, I have a question regarding the differential equation solution to an under damped system involving complex roots. Referring to the attached pdf, an under damped system will yield a complex...
  39. KleZMeR

    Angular Momentum Term Equals Zero?

    Hi All, This is from a classical mechanics problem, and I already 'solved' the problem, but I'm interested in why a certain term is set to zero. I think I understand the concept but just want to clarify. The problem is a table with a hole in it and two masses on a string, one mass is...
  40. J

    I don't understand the term "load angle" of the syncrhonous generator

    I am studying the behavior of the magnetic fields between the rotor field and stator field(armature reaction) in a synchronous generator . I understand that the stator magnetic flux will vary depending on the power factor of the load (leading, lagging or resistive). If the load is resistive, the...
  41. S

    Formula of nth term of a pattern

    Homework Statement Find the formula for nth term of: ... , -450 , -270 , -180 , -90 , 90 , 180 , 270 , 450 , ... Homework Equations Arithmetic and geometric series Recursive The Attempt at a Solution Usually when finding the formula of Un, n starts from 1. But since the pattern...
  42. D

    Where did this 1/4*ln(C) term come from when integrating?

    Homework Statement The givenequation is this: \frac{1}{4} \frac {du}{(2-u)} \ + \ \frac{1}{4} \frac{du}{(2+u)} \ = \frac{dx}{x} My book says that when integrated, the above equation becomes \frac{-1}{4} \ln (2-u) \ + \ \frac{1}{4} \ln (2+u) \ = \ln (x) + \frac{1}{4} \ln (c) I...
  43. mesa

    Is the use of the term 'general form' correct for variable functions?

    For certain types of functions I have been using the term 'general form' as a way of stating that some function of some variable(s) is true for more than one value of the variable (usually an infinite number). Here is a simple example, 1=cos(2∏x) There have been (at times) where the use of...
  44. P

    Did Rindler coin the term "Event Horizon"?

    I'm looking for proof that Wolfgang Rindler coined the term Event Horizon. I believe that it was Rindler because that's what I've heard from reliable sources, e.g. http://www.mathpages.com/home/kmath339/kmath339.htm Thank you in advance.
  45. H

    What is the significance of using pseudorapidity in HEP experiments?

    I read some of the articles related to particle physics experiment and don't know the meaning of it. 1. minimum bias event 2. pile up Also, η (pseudo-rapidity) is used instead of θ to describes the angular distribution, but why ? Can someone explains to me ?
  46. J

    Euler-lagrange, positivity of second order term

    For twice differentiable path x:[t_A,t_B]\to\mathbb{R}^N the action is defined as S(x) = \int\limits_{t_A}^{t_B} L\big(t,x(t),\dot{x}(t)\big) dt For a small real parameter \delta and some path \eta:[t_A,t_B]\to\mathbb{R}^N such that \eta(t_A)=0 and \eta(t_B)=0 the action for...
  47. S

    Why the topological term F\til{F} is scale independent?

    why the topological term in gauge theory, ε_{\mu\nu ρσ}F^{\mu \nu} F^{ρσ} ,is scale-independent?
  48. ChrisVer

    How can I calculate the F-terms for chiral superfields in a no-scale model?

    In case you have the Kahler and super- potential K,W: K(T,S,C) = -log (S +S^{*}) -3 log ( T+ T^{*} - C C^{*}) W(T,S,C)= C^{3} + d e^{-aS} +b with T,S,C chiral super fields, b,d complex numbers and a>0. I tried to calculate the local F-terms arising from this. The local F-terms for the i-th...
  49. A

    Coulomb term in Potential of ions in a Penning Trap,Green's Function

    How do you write out the potential of an ion in a Penning trap? Specifically, how does the inter-ionic Coulomb interaction come to be written as a Green's function? I found it here : http://journals.aps.org/rmp/pdf/10.1103/RevModPhys.71.87 They do say something about interactions with image...
  50. X

    How do I find the General Term of a Sequence?

    1. Write down the general term of each of the following sequences in simplest form: So far I have been using guess and check to find the solutions, but it doesn't seem much use when you get to a sequence more complicated like this: 1, -4, 7, -10, 13, ... I really need to find an equation that I...
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