What is Terms: Definition and 1000 Discussions

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  1. S

    Sum of (n+1) terms in exponential series

    Homework Statement S = 1+ x/1! +x2/2! +x3/3! +...+xn/n! To find S in simple terms. Homework Equations None The Attempt at a Solution I tried with Taylor's expansion, coshx and sinhx expansions. But cannot see consequence.
  2. H

    Work done for isothermal process in terms of Helmholtz func

    The Helmholtz function differential form for a reversible process is: dF = -SdT - PdV, as for a reversible process δW (by system/here an (ideal) gas) = PdV and dS = δQ/T. Therefore, for a reversible isothermal process, dT = 0 and hence dF = -PdV. Therefore, the work done by the system is W =...
  3. D

    Faraday's Law--Confusion about terms in the integrals

    Hi. The induced emf is given by -d/dt ∫B.dS but when the time derivative is taken inside the integral sign this becomes -∫ ∂B /∂t.dS . Why isn't B.dS differentiated using the product rule giving an extra term inside the integral sign ? For some reason the integral sign is appearing as a small...
  4. D

    Calculus II: Convergence of Series with Positive Terms

    Homework Statement https://imgur.com/DUdOYjE The problem (#58) and its solution are posted above. Homework Equations I understand that I can approach this two different ways. The first way being the way shown in the solution, and the second way, which my professor suggested, being a Direct...
  5. Richie Smash

    ZPQM is a parallelogram, express Vector OZ in terms of u and v

    Homework Statement u and v are two vectors in the same plane. Vector OM = u+2v Vector OP = 6u+v Vector OQ = 5u +2v Vector OR =2(VecOM) +v Given that ZPQM is a parallelogram, express Vector OZ in terms of u and v.Homework EquationsThe Attempt at a Solution First they wanted me to find Vectors...
  6. mertcan

    Consistency of interpolation in terms of flux at node sides

    Hi, first of all I am aware of the fact that QUICK SCHEME used in computational fluid dynamics has consistent slope at the sides of node elements (for instance at the left side of node 3 in my attachment same slopes exist) as you can see in my picture/attachment. But I must express that I can...
  7. Y

    Scalar in terms of multiple variables, Nyquist & Bode Plot

    Homework Statement A scalar is given by It is controlled by With step time h = 0.2 s 1. Find the discrete equivalent model 2. Check the stability of closed loop (K = +1) 3. Obtain the via the Bode plot Homework EquationsThe Attempt at a Solution So for question 1. This is where I'm...
  8. D

    What is Leakage in terms of quantum computing?

    I am doing a project on stabilizer code, and I keep running into a term about qubits and leakage. What does leakage mean?
  9. K

    Derivative of a product of 3 terms

    Homework Statement Taking derivative of 3 term product. ## \frac{d}{dx} (3x^3 y^2 y'^2) ## Homework Equations I read that (abc)' = (ab)c' + (bc)a' + (ca)b' The Attempt at a Solution ## 9x^2(y^2y'^2) + 6x^3yy'^2 + 6x^3y^2y' ## is this correct ?
  10. Richie Smash

    Derive an expression for the price of a pen in terms of p

    Homework Statement Hello there are two types of pens expensive and cheap. The ratio of the prices of the two is 3:7 The total cost for 30 of the cheaper pens and 10 of the expensive pens is $1568. I am asked to derive an expression for the cost of ONE of the expensive pens which i will...
  11. A

    What is the relationship between voltage and charge in a battery?

    I'm trying to understand what exactly it means in terms of the voltage of a battery. I know that the voltage in a battery is just the potential difference between the two terminals. But, is the negative terminal used as a relative point and seen as 0? If that's the case does 12V mean that the...
  12. J

    A Physical meaning of terms in the Qi, Wu, Zhang model

    The Hamiltonian of the Qi, Wu, Zhang model is given by(in momentum space): ## H(\vec{k})=(sink_x) \sigma_{x}+(sink_y) \sigma_{y}+(m+cosk_x+cosk_y)\sigma_{z} ## . What is the physical meaning of each component of this Hamiltonian? Note: for the real space Hamiltonian(where maybe the analysis of...
  13. W

    Writing integrals in terms of the error function

    Homework Statement I have the following integral, $$\frac{1}{\sigma \sqrt{2\pi} t} \int_{-\infty}^{0} \exp[\frac{-1}{2\sigma ^2} (\frac{x-x_0}{t} - p_0)^2]dx$$ that I wish to write in terms of the error function, $$erf(x) = \frac{2}{\sqrt{\pi}} \int_{0}^{x} e^{-g^2}dg$$ However, I can't seem...
  14. T

    B Understanding A Middle Ordinate In Terms Of Geometry

    Hello community I was hoping someone could help me with the following problem. I am trying to understand what a middle Ordinate is in terms of geometry (I know it has a versine along a chord).Given the diagram below:- The Blue line is an arc of some radius. AB & CB are both tangent to...
  15. M

    Limitation of the number of search terms in search engines

    Why does Google limit its searches with 32 terms? I think other search engines seems to not limit but adding more terms for some reasons such as filtering does not work, for example in Yahoo. Thank you.
  16. G

    I How 'big' is the present moment in terms of time?

    Time can be divided three ways Time in the future Time in the present Time in the past We are living in the 'present'. My question: how 'big' is this present time? It might help if you think of a pen placed on a white sheet of paper. The pen represents our present time. The white space above...
  17. Kushwoho44

    Carnot Theorem: Understand Terms & Impossibility of Heat Engines

    Hi there, I hold an engineering degree and I was just reviewing a page on Wikipedia. This image specifically demonstrates the impossibility of two theoretical heat engines having different efficiencies between two heat reservoirs. The full Wikipedia page can be found...
  18. R

    Definition of Momentum in terms of a partial derivative

    Dear Members, I was going through some video lecture (Quantum Mechanics) when I encountered a definition of momentum as shown in the attached picture. I do not understand how iota and ħ is ignored ? There are some negligible terms after plus sign. What are those ? In short how they have...
  19. K

    Cartesian unit vectors in terms of cylindrical vectors

    How do I express ex,ey,ez in terms er,eθ,eZ? r=(x^2+y^2)^1/2,θ=arctan(y/x),Z=z A(r,θ,z) ∂A/∂x=x/(x^2+y^2)^1/2er+(-y)/(x^2+y^2)eθ=cosθer-(sinθ/r)eθ ex=(∂A/∂x)/|∂A/∂x| I should get ex as cosθer-sinθeθ, but I don't get ex correctly. am i doing this wrong?
  20. S

    I Terms canceling out in unitarily evolving state

    The Hong-Ou-Mandel experiment is one of many examples where the amplitudes associated with two histories cancel out, leaving us with a reduced range of possible outcomes. Obviously, the total probability of those outcomes has to be unity. My question relates to the fact that these processes are...
  21. A

    Establish Taylor series using Taylor's Theorem in terms of h

    Homework Statement Find the Taylor series for: ln[(x - h2) / (x + h2)] Homework Equations f(x+h) =∑nk=0 f(k)(x) * hk / k! + En + 1 where En + 1 = f(n + 1)(ξ) * hn + 1 / (n + 1)! The Attempt at a Solution ln[(x - h2) / (x + h2)] = ln(x-h2) - ln(x + h2) This is as far as I have been able to...
  22. DeathbyGreen

    I Infinite series of trigonometric terms

    I'm trying to make an approximation to a series I'm generating; the series is constructed as follows: Term 1: \left[\frac{cos(x/2)}{cos(y/2)}\right] Term 2: \left[\frac{cos(x/2)}{cos(y/2)}-\frac{sin(x/2)}{sin(y/2)}\right] I'm not sure yet if the series repeats itself or forms a pattern...
  23. D

    Adding "annihilating terms" to factor

    Not a homework problem, just something I came across in my book that makes sense but not fully. Homework Statement Factor: ##a^4-b^4## Homework EquationsThe Attempt at a Solution [/B] The book's solution: ##a^4-b^4## ##=a^4-a^3b+a^3b-a^2b^2+a^2b^2-ab^3+ab^3-b^4##...
  24. D

    Finding an expression for max distance in terms of theta

    Homework Statement Basic projectile motion if you throw from ground level, to obtain a max distance in the x you'd want to throw at a 45° angle right? So as your initial height increases, your throwing angle will decrease and my guess is as your initial velocity increases your angle increases...
  25. P

    I TIR (total internal reflection) in terms of quantum world

    how total internal reflection of light takes place in terms of quantum world?
  26. J

    Can force be understood in terms of time/speed?

    If there is a massive object floating in space and I tap the side of it with a relatively small force it will move said object a very small amount. If I tried the same thing on Earth the object would not move because of gravity. I'm inferring (perhaps erroneously) that this means the object is...
  27. Graeme M

    Resolution of the human visual system in physical terms

    I've often wondered at the "resolution" of the human visual system but it's not at all clear from what I've read whether this question even makes sense. As a sort of general position, many of the articles I've read suggest that the human eye, over the full field of vision, delivers around...
  28. D

    Genetics double recombination counted twice in terms of RF

    When mapping out re-combinations of a crossed trihybrid you have to account for the proportion of the offspring who do not share parental genotypes. Of the 8 possible genotypes stemming from this mating, 6 will be recombinant and two will be of parental genotypes. Your idea is to Map out the...
  29. Saracen Rue

    B Second derivative differential equations in terms of y?

    Firstly I know how to do this with first derivatives in differential equations - for example say we had ##\frac{dy}{dx}=4y^2-y##, and we're also told that ##y=1## when ##x=0##. ##\frac{dy}{dx}=4y^2-y## ##\frac{dx}{dy}=\frac{1}{4y^2-y}=\frac{1}{y\left(4y-1\right)}=\frac{4}{4y-1}-\frac{1}{y}##...
  30. P

    Expressing series in terms of a Power Series

    Hello and thank you for trying to help. In spite of the fact that this seems a very simple problem, I do not find myself able to get a solution. Here it goes: Let $$f(x)=\displaystyle \sum_{k=3}^\infty a_k \frac{x^k}{k(k-1)(k-2)}$$ and $$g(x)=\displaystyle \sum_{k=0}^\infty a_k x^k$$. Express...
  31. M

    I Potential terms in SE & Quantum Chemistry

    I bought this book "Idiot's Guide to Quantum Physics" I bought it because I know I am an idiot in quantum physics. Now I have a question about the contents. It says that: "The four fundamental forces in nature (gravity, electromagnetism, plus two more that we'll formally introduce in Chapter...
  32. B

    Moment Equilibrium in terms of box weight

    Homework Statement The board shown below is being held in equilibrium in the vertical plane by three smooth rods at A, B, and C Determine the magnitudes of forces at A, B, and C in terms of the weight of the body, W. Homework Equations Moment = f*r Here's a diagram The Attempt at a...
  33. FallenApple

    A Interpreting Models with Multiple Interaction Terms: Gender, Weight, and Height

    If there are two interaction terms in a single model, does that mess up the interpretation of it? For example, Gender*Weight and Gender*Height. Say the model is Y~Weight+Height +Gender +Gender*Weight+Gender*Height. Would I simply interpret it as usual? That is, "The difference in mean...
  34. pairofstrings

    B Names of elements of any equation

    Hello. I came across a Quadratic Equation that looks like this. 5x2 + 4x + 9 = 0. The '5' in the above equation is called Quadratic Coefficient. The '4' in the above equation is called Linear Coefficient. The '9' in the above equation is called Constant. The 'x' in the above equation is called...
  35. A

    Pronunciation of terms

    Hey guys, this is a rather silly question, but does anyone know how to pronounce 1. Kac in Kac-Moody algebras 2. Henneaux in Brown Henneaux central charge? Don't want to make a fool of myself when talking to people.
  36. M

    MHB How to Factor Cubic Terms in Algebraic Expressions?

    Factor the expression. (a - a^2)^3 + (a^2 - 1)^3 + (1 - a)^3 (a - a^2)(a - a^2)(a - a^2) + (a^2 - 1)(a^2 - 1)(a^2 - 1) + (1 - a)(1 - a)(1 -a) Is this the right approach thus far?
  37. Bunny-chan

    Epsilon distance between two terms

    Homework Statement How close is x to x_0 (x_0 \neq 0) so that 2. Homework Equations The Attempt at a Solution I tried to use absolute value properties:- \epsilon \lt \frac{\sqrt{x_0^2+1}}{x_0^3} - \frac{\sqrt{x^2+1}}{x^3} \lt \epsilonBy adding in the three sides, we...
  38. B

    MHB [Series] State the first four terms and find the nth term

    What is the procedure for finding the unknown term(end value in this scenario) in a series? For example \sum_{r=1}^{n}{2r+3} My Attempt was to simply state the first four terms and then simply add the nth term as it is: 2(1)+3=5 2(2)+3=7 2(3)+3=9 2(4)+3=11 2(n)+3=2n+3...
  39. F

    I Show me how terms with Q disappear

    The general Ampere force law equation given by Maxwell is: According to Maxwell, all terms containing function ##Q(r)## will vanish after closed integration w.r.t. ##s'## because they will get reduced to functions of ##r## and the upper and lower integration limits will be same since the...
  40. EthanVandals

    Gravitational Force in terms of Density?

    Homework Statement Express the gravitational force equation in terms of density. Homework Equations F(Gravity) = ((GravitationalConstant)(Mass1)(Mass2))/radius^2 Density = mass/volume The Attempt at a Solution Based on the original equation for gravitational force, there are two masses...
  41. F

    I Higher order terms in perturbation theory (QFT)

    I'm fairly new to QFT and I'm currently trying to understand perturbation theory on this context. As I understand it, when one does a perturbative expansion of the S-matrix and subsequently calculates the transition amplitude between two asymptotic states, each order in the perturbative...
  42. S

    I Distinguishable Terms in a State

    Let's say we have a proposition (or state, if we prefer) ##P\equiv \psi \equiv AB^\perp + e^{j \theta} A^\perp B## where, e.g., ##A^{\perp}## indicates some ket that is orthogonal to ##A##. We also have an operator ##\hat{O}## . Without reference to a physical context, is there a test to say...
  43. L

    Hamiltonian in terms of creation/annihilation operators

    Homework Statement Consider the free real scalar field \phi(x) satisfying the Klein-Gordon equation, write the Hamiltonian in terms of the creation/annihilation operators. Homework Equations Possibly the definition of the free real scalar field in terms of creation/annihilation operators...
  44. ShayanJ

    A Integral in terms of Gamma functions

    Does anyone know how I can prove the following equation? ##\displaystyle \frac 1 {d-1}-\int_0^1 \frac{dy}{y^d} \left( \frac 1 {\sqrt{1-y^{2d}} }-1\right)=-\frac{\sqrt \pi \ \Gamma(\frac{1-d}{2d})}{2d \ \Gamma(\frac 1 {2d})} ## Thanks
  45. Mind----Blown

    Significance of terms of acceleration in polar coordinates

    How do i get an idea, or a 'feel' of the components of the acceleration in polar coordinates which constitute the component in the eθ direction? from what i know, a= (r¨−rθ˙^2) er + (rθ¨+ 2r˙θ˙) eθ ; (where er and eθ are unit vectors in the radial direction and the direction of increase of the...
  46. A

    Mathematica How to use Switch with variable number of terms?

    Hi, I'd like to use Switch with an integer partition of a number. For example, if n=4, then I define the partition as: monodromyTypes = IntegerPartitions[n]; this gives: monodromyTypes={{4}, {3, 1}, {2, 2}, {2, 1, 1}, {1, 1, 1, 1}}. I'd then like to set up a Switch depending on what the...
  47. throneoo

    I Defining exchange statistics of anyons in terms of Berry phase

    In 2D, if we define exchange statistics in terms of the phase change of the wavefunction of two identical particles when there are exchanged via adiabatic transport (https://arxiv.org/abs/1610.09260), we would discover that this phase can be arbitrary due to the topology of relative...
  48. HOLALO

    B Taylor Polynomials and decreasing terms

    Hi, I have a question about taylor polynomials. https://wikimedia.org/api/rest_v1/media/math/render/svg/09523585d1633ee9c48750c11b60d82c82b315bfI was looking for proof that why every lagrange remainder is decreasing as the order of lagnrange remainder increases. so on wikipedia, it says, for a...
  49. jim mcnamara

    Names for groups of animals - terms of venery

    https://en.wikipedia.org/wiki/List_of_English_terms_of_venery,_by_animal Lists lots of animals. Clearly people made up some of these things when it was clear nobody really knew if it was correct or not. Heck, we can do that! So let's see what we can come of with: How about a slime of...
  50. Eclair_de_XII

    How to prove that two exponential terms are congruent to 7?

    Homework Statement "Prove: ##∀n∈ℕ,7|[3^{4n+1}-5^{2n-1}]##" Homework EquationsThe Attempt at a Solution (1) "We take the trivial case: ##n=1##, and notice that ##3^5-5=238## and ##7|238## because ##7⋅(34)=238##." (2) "Now let ##n=k## for some ##1<k∈ℕ##. Then we assume that...
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