Term Definition and 775 Threads

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. D

    System of linear equation in term of column vector

    Hello! The following system of linear equations has been expressed in term of column vector in the following. . How can I express the system of linear equations in term of row vector? In addition, What is the field of scalars? I would request to explain it. Thanks in advance.
  2. J

    I feel like the term fundamental fields is a cop out

    Whenever I ask someone what an electromagnetic field is exactly, they say that science does how questions, not why questions (which doesn't really make sense in this context, maybe i worded my question differently). We say that there are four fundamental forces that create the universe we live...
  3. M

    Finding Coef. of x2n: An Easy Way?

    After multiplication the coef. of x2n was found which is highlighted in red in the paint document. My question is, is there an easy way of finding the coef. without actually going through the process of squaring the series given and locating the pattern for the coef. for x2n? What I tried...
  4. P

    Question about the x term in time dilation

    When I first learned time dilation I was given this equation proven using the light clock example. t = γt' However, when I looked into the topic in more detail, I was given this equation. t = γ(t' + xv/c2) If x represents the distance between 2 frames, then does x have to change...
  5. J

    Finding a Formula for the General Term of a Sequence

    Homework Statement A bored student enters the number 0.5 in her calculator, then repeatedly computes the square of the number in the display. Taking A0 = 0.5, find a formula for the general term of the sequence {An} of the numbers that appear in the display, and find the limit of the sequence...
  6. anemone

    MHB Find the nth term of the sequence.

    A sequence of positive integers is defined as follows: The first term is 1. Then take the next two even numbers 2, 4. Then take the next three odd numbers 5, 7, 9. Then take the next four even numbers 10, 12, 14, 16 and so on. Find the nth term of the sequence.
  7. A

    Dipole term in multipole expansion

    Hi. I'm having some difficult in understanding something about the dipole term in a multipole expansion. Griffiths writes the expansion as a sum of terms in Legendre polynomials, so the dipole term in the potential is writen \frac{1}{4 \pi \epsilon r^{2}}\int r^{'}cos\theta^{'}\rho dv^{'}...
  8. S

    How can there be a term called intestinal metaplasia of stomach

    How can there be a term called "intestinal metaplasia" of stomach Hello everyone, Ok Stomach's normal epithelium is simple columnar, now in intestinal type of adenocarcinoma of stomach it undergoes "intestinal metaplasia", due to gastrititis. Now intestine also has simple columnar...
  9. R

    Finding the nth Term of a Sequence: 6+13+24+39+...

    How to find nth term of the sequence 6+13+24+39+...
  10. S

    Taking three courses per term in undergrad

    I am a slow learner and I prefer to spend lots of time on few subjects rather than to distribute time over many. In addition, most of my courses will be extremely time consuming. So I probably want to take three courses per term and I will most likely attain a much higher GPA in this way, but I...
  11. J

    Inverted Pendulum on Cart: What is this term in the KE?

    I am working through an example of an inverted pendulum on a cart, exactly like this: L is the length of the massless pendulum arm. Two degrees of freedom, x and theta. If I write out the kinetic energy as three parts: translational KE from cart + translational KE from pendulum +...
  12. D

    Describing electromagnetic radiation, why is there a second sin term?

    Homework Statement Hey all, I am working through a derivation that my professor gave me to do and I am having trouble understanding one of the formulas that he gave me, namely: "EM waves can be described as: E(x, t) = Eosin(2πx/λ)*sin(2πc/λ)" The the Eo*sin(2πx/λ) term makes sense to...
  13. G

    Boundary Layer Equations: Neglecting the term for x-axis momentum

    I'm having a little difficulty in the topic 'Boundary layer Equations' in Fluid Mechanics due to my weak math skills. With reference to the figure in attachment, if we say that "we neglect \frac{∂^{2}u}{∂x^{2}}", does it mean that we will only consider the portion where \delta(x) is almost...
  14. DiracPool

    New Math: An Analysis of its Validity

    I always remember my dear departed grandmother referring to something called "New Math" when I was a youngster, but at the time I wasn't interested enough in whatever it was to look into it. However, I just read the Wiki page on it: http://en.wikipedia.org/wiki/New_Math And it looks like...
  15. D

    What is the general term of this sequence?

    Could you help me to find the general term of the sequence: ## 1 , \frac{5}{3} , 1 , \frac{15}{17} , 1 , \frac{37}{35} , 1 , \frac{63}{65} ,... ## Thank you!
  16. Lebombo

    Sequence formula [itex]a_{n}[/itex]=((last term) - (n-1)(common diff))

    Calc 2 will require some basic knowledge of sequences and series. Since this topic has never been covered in any of my past math classes, I am currently learning about sequences and series from scratch. On youtube, I found a video that contains an explanation of the General Term of the...
  17. D

    Is Big Bang a Misleading Term for Describing the Early Universe?

    I'm new to this forum, so I apologize if this has been raised/discussed before, or if this does not make much sense... I've been watching numerous debates about the Big Bang and the origins of the universe, and I can't help but think that Big Bang is not a good term for describing the early...
  18. T

    Find the explicit formula for the nth term of the sequence?

    Homework Statement Consider the sequence n1, n2, n3, ... that satisfies the recurrence relation nk = nk-1 / k + 1 for all integers k ≥ 2 with the initial condition that n1 = 1. Find the explicit formula nk for the nth term of the sequence? 2. The attempt at a solution I calculated...
  19. C

    Evaluating a double integral with an e^(x^2) term

    Homework Statement Evaluate ∫(0-1)∫(sqrt(y)-1) (ye^(x^2))/x^3 dx dy Homework Equations The Attempt at a Solution First, factor out the y for the inner integral, making ∫(0-1) y∫(sqrt(y)-1) (e^(x^2))/x^3 dx dy And evaluating the inner integral first: y∫(sqrt(y)-1)...
  20. W

    How Do I Adjust a Formula to Alternate Sequence Terms?

    Homework Statement I am trying to solve this problem and need help with one aspect.Homework Equations sequence: 0,-1,0,1 -- repeated.The Attempt at a Solution How do I make every 4th term of the sequence a negative number? for instance i have: (1 + (-1)^n)/2 but i don't know how to...
  21. V

    DoubtProve the term is irrational

    Homework Statement Prove that any number with zeroes standing in all decimal places numbered 10^n and only in these places is irrational?(yeah,its the easiet question in my list,but I am still not sure about it) Homework Equations The Attempt at a Solution when i think about...
  22. anemone

    MHB Find the 100th term of a given sequence.

    The increasing sequence 1, 3, 4, 9, 10, 12, 13 ... consists of all those positive integers which are powers of 3 or sum of distinct powers of 3. Find the 100th term of this sequence.
  23. W

    Divided by highest term in numerator limit

    Homework Statement evaluate.Homework Equations lim\displaystyle _{x->∞} \frac{2^x - 3^x}{3^x + 4^x}The Attempt at a Solution i tried diving by highest term in denominator (4^x), but got me no where. the solution manual has: (divided by highest term in numerator.)with the answer is zero which i...
  24. G

    Nth term of alternating series with two positive terms at beginning

    (I hope this is the right subforum) I'm talking about the series 1, 1, -1, 1, -1, 1, -1... I thought about it for a long time but I have no idea. If that first term were gone it would just be (-1)^(n+1), but...it's there...
  25. J

    Why does the enthelpy equation include work (PV term) twice?

    Hello. I am a thermodynamics novice trying to gain a better understanding of state functions, particularly enthalpy. I understand that enthalpy is defined as "A measure of the total energy of a thermodynamic system, including internal energy, which is the energy required to create a...
  26. Petrus

    MHB Constant term in a binomial expansion

    Decide constant term in \left(3\cdot x^3+\left(\frac{-4}{x} \right) \right)^{20}. I have problem with this one, I can't find any example about this one in my book, any advice would be great:)
  27. P

    Question about the Majorana mass term

    The Majorana mass term is expressed from a single Weyl spinor. But I am a little confused by the expression. For example, see Eq. (2) in http://arxiv.org/pdf/hep-ph/0410370v2.pdf \mathcal{L}=\frac{1}{2}m(\chi^T\epsilon \chi+h.c.) Here \chi is the Weyl spinor and \epsilon = i\sigma^2 is...
  28. R

    Is there a special term for refractive indices when 1 is subtracted?

    I have been doing a bit of studying for my optics course and I have often come across refractive indices or materials being presented as n-1 (which often makes a lot of sense). I was just wondering if there was a special term like for this format or if we still call it just the "refractive...
  29. P

    Finding the Minimum of the Scalar Potential in F-Term SUSY Breaking

    In F term SUSY breaking, is the minimum of V just: V=\sum^{N}_{i}|F_i|^2
  30. S

    Taylor polynomial remainder term

    Homework Statement Consider the followign function f(x) = x^-5 a=1 n=2 0.8 \leq x \leq 1.2 a) Approximate f with a tayloy polynomial of nth degree at the number a = 1 b) use taylor's inequality to estimate the accuracy of approximation f(x) ≈ T_{n}(x) when x lies in the interval...
  31. D

    Exploring the Darwin Term in Hydrogen Fine Structure

    I'm trying to do a HW involving the Darwin Term in the fine structure of hydrogen. I'm given that the perturbation from the Darwin term is equal to (times a constant factor which I'll ignore), V_D = [p_i,[p_i, \frac{e^2}{r}]] = e^2\vec{p}^2\frac{1}{r} -2e^2\vec{p}\frac{1}{r}\vec{p} +...
  32. P

    Identifying term and level (Atomic Physics)

    Homework Statement Consider the beryllium (Be) atom. What are the possible terms and levels of the ground configuration 1s22s2 and the excited configuration 1s3p? Indicate any allowed transition between the levels. Homework Equations Transitions allowed if ΔS = 0 (change in total...
  33. K

    I discovered a formula for the nth term of any sequence of numbers

    Hi there, I recently discovered a formula for the nth term that works for any finite sequence of numbers. I was just wondering whether a formula has already been discovered, and if not, how and where I should publish it. To give you an example of what i mean: one formula for the nth...
  34. U

    Boltzmann equation with collision term

    Homework Statement Solve the Boltzmann equation for a homogeneous plasma with not external forces present when the collision term is \frac{\partial f(v,t)}{\partial t} = -\nu (f(v,t) - f_0(v)), where \nu and f_0 are constants. Homework Equations Boltzmann equation \frac{\partial...
  35. I

    Find the limit of sequence (trig term)

    Homework Statement find the limit of this sequence 1) An = \frac{\sqrt{n} sin (n! e^{n})}{n+1} 2) An = 4n^{3} sin\frac{1}{n^{3}} Homework Equations The Attempt at a Solution (1) |sin n! e^n)| ≤1 |An| ≤ \frac{ \sqrt{n} }{n+1} |An| ≤ \frac{ \sqrt{n}/n...
  36. Greg Bernhardt

    News Energy Secretary Steven Chu Not to Serve a Second Term

    http://energy.gov/articles/letter-secretary-steven-chu-energy-department-employees-announcing-his-decision-not-serve Hopefully the next SoE will also have a strong scientific background.
  37. Fredrik

    Orthochorous? Don't think I've heard that term before

    An arbitrary Lorentz transformation ##\Lambda## in 1+1 dimensions can be written as \begin{align} \Lambda=\frac{\sigma}{\sqrt{1-v^2}} \begin{pmatrix}1 & -v\\ -\rho v & \rho\end{pmatrix}. \end{align} Here ##\sigma=\operatorname{sgn}\Lambda_{00}## and ##\rho=\det\Lambda##. I learned today that...
  38. B

    Simple Sinx Expansion (General Term Help)

    Homework Statement expand sinx about the point x=pi/4 Homework Equations The Attempt at a Solution I know how to find each individual terms but how do I got about finding the general term for this series?
  39. M

    Constant term in the adiabatic equation

    Hi there! I am working on a project that requires some idea of adiabatic processes. I know the basics of the said topic and I'm currently stuck with the reversible adiabatic equation PV^(gamma)=constant.. and want to know what is the constant term i.e. on what parameters it depends and what is...
  40. T

    Einstein-Hilbert term and mass, gravity

    It is said that the Einstein-Hilbert term in the following couple mass and gravity. Lagrangian = R/(16*pi*GN) [Einstein-Hilbert term] + L (nongravitational) How is the above derived? Is it enough to prove that there should be a theory of quantum gravity since mass and gravity are coupled...
  41. Z

    Determine the term containing (Binomial Theorom)

    Determine the term containing... (Binomial Theorom) Homework Statement Determine the term containing x^11 in the expansion (X^2 - 1/x)^10 Homework Equations T(k+1) = nC(k)*A^(n-k)*b^KThe Attempt at a Solution x^11 = 10Ck * (x^2)^(10-k)*(-X^-1)^k (taking out the (-) from the x^-1 b/c it...
  42. G

    What are some potential long-term physics projects for a high school student?

    Hi all. Next year for school, we have a huge, year-long research project. I'm really excited, but I'm not really sure what I should do yet... It can be on pretty much anything (and I'm doing it on something physics-related, hopefully), as long as the teachers approve it. It should be a long-term...
  43. S

    Where do external photon terms go in Feynman diagram term ordering?

    I'm reading something which highlights the Feynman rules for QED, and it talks about what happens if you go along a fermionic line. For example this picture: http://wikipremed.com/image_science_archive_68/010601_68/170750_298px-ComptonScattering-u.svg_68.jpg According to these notes, there...
  44. K

    Prove that the rᵗʰ term in the nᵗʰ row of Pascal's triangle is nCr.

    Prove that the rᵗʰ term in the nᵗʰ row of Pascal's triangle is nCr. nCr formula: n!/r!(n-r)! I've tried everything I can but I don't know how to approach this question.
  45. C

    Long term genetic outcome of one time very harsh unnatural selection on humans

    A few topics ago I asked about possibilities concerning maintaining contemporary tech level with seriously reduced population. Now I will ask a question for the same story. There is a standard, generic incoming doom. The general population is already roughly aware how nasty the situation is...
  46. A

    Term Symbol of np3 & np2: What Are They?

    For np3, there is a term symbol: 4S I think it is because l are -1,0 and 1 So, L value=-1+0+1=0 However, for np2 , there is not a term symbol: 3S (I assume l are -1 and 1) I know I misunderstand something, but what are they?
  47. S

    Identifying the expression for the constant term in a power relationship

    I need to know how to identify the expression for the constant term in a power relationship. The power relationship is a relationship I imagined on a graph. On the graph both the values on the x and y axis's would be increasing. The power relationship is between square of rotational frequency...
  48. M

    How to find the nth term of this Series.

    Homework Statement 1. First, calculate the Taylor polynomial of degree 4 for f(x)=sin(3x) about x=0. 2. Then find the 156th term of the infinite Taylor Series for g(x)=sin(3x) Homework Equations My Taylor polynomial ended up being -4.5x3+3. The Attempt at a Solution I...
  49. W

    Taylor series error term - graphical representation

    Hello all, Recently I've found something very interesting concerning Taylor series. It's a graphical representation of a second order error bound of the series. Here is the link: http://www.karlscalculus.org/l8_4-1.html My question is: is it possible to represent higher order error bounds...
  50. M

    Find the Best Optimization Method for Creating Test Groups - Mike

    I am looking for a term to describe a sort of "optimization" that I am trying to do. Hi everybody, I am a college student who unfortunately is not smart enough to be a math major. But nonetheless I am obsessed with statistics and numbers. I have a question: I need help figuring out a term...
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