What is Terms: Definition and 1000 Discussions

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  1. binbagsss

    Maple Maple- simplifing an expression in terms of pre-defined variables?

    I have some dimensionless numbers commonly used in fluid mechanics and I want to express a certain expression in terms of these dimensionless numbes If I, after defining my dimensionless numbers, enter the command : simplify(*expression*) where the expression is a function of variables that...
  2. K

    B Explaining Spaghettification w/ Spacetime Curvature

    I enjoy explaining spacetime curvature to people with a rank-beginner understanding of GR. But someone asked about that favorite concept in pop-sci, spaghettification. I'm having a hard time with it. If you fell into a black hole, there's no reference frame within which you could describe...
  3. Arman777

    A What is the jerk parameter in terms of the Density parameters?

    In cosmology the deceleration parameter defined as the $$q_0 = \frac{1}{2}\sum_i\Omega_{i,0}(1+3w_i)$$ Is there a similar expression for the jerk parameter (##j_0##) ?
  4. S

    Find the middle terms of this binomial expansion

    I know how to expand it. My question is: the expansion has 8 terms so what would be the middle term? Will the answer be "the expansion has no middle term"? Or maybe seeing the phrase of the question (middle terms), there will be two answers (the 4th and 5th term)? Thanks
  5. steve1763

    A Exploring Free and Interaction Terms of L in Quantum Field Theory

    With free part L=-½(∂Φ)^2 -½m^2 Φ^2 and interaction term L=½gΦ^2Any help would be appreciated, thank you.
  6. SamRoss

    B Simple forces described in terms of fundamental forces

    My first question is actually, what happens when any two objects get near each other? This question is often phrased as "Why can't you really touch anything?" or "Why can't you walk through walls?" I have heard two answers: 1. the repulsion between electrons 2. the Pauli exclusion principle...
  7. S

    Find minimum value of f(x) in terms of variable a

    (1) For ##x>a## ##f(x)=x^2+x-a+1 \rightarrow## minimum value obtained when ##x=-\frac{1}{2}## Minimum value of ##f(x)=\frac{3}{4} -a## (2) For ##x<a## ##f(x)=x^2-x+a+1 \rightarrow## minimum value obtained when ##x=\frac{1}{2}## Minimum value of ##f(x)=\frac{3}{4}+a## But the teacher said...
  8. BohmianRealist

    I Is the phrase "discrete spectrum" in rule #5 a contradiction in terms?

    When conversing informally about QM, there is often wonder about the apparently acausal nature of processes that we may call "quantum leaps" between physical states. It is often said that the purely mathematical foundations of QM give no reason for such wonderment, i.e., that the math, in...
  9. J

    Express this trajectory in terms of proper time

    The object moves solely on the $x$-axis, hence I calculated its speed to be $v_x = \frac{dx}{dt} = \frac{c \kappa t}{\sqrt(1+\kappa ^{2} t^2$ Because its speed is not constant, I suppose the Lorentz factor $\gamma = \gamma (t)$, and by plugging in the velocity, I obtain $\gamma = \sqrt(1+ \kappa...
  10. A

    Angular velocity in terms of Euler angles

    In Chapter 4, derivation 15 of Goldstein reads: "Show that the components of the angular velocity along the space set of axes are given in terms of the Euler angles by $$\omega_x = \dot{\theta} \cos \phi + \dot{\psi} \sin \theta \sin \phi, \omega_y = \dot{\theta} \sin \phi - \dot{\psi} \sin...
  11. Athenian

    I Transforming Cartesian Coordinates in terms of Spherical Harmonics

    As the subject title states, I am wondering how would one go about transforming Cartesian coordinates in terms of spherical harmonics. To my understanding, cartesian coordinates can be transformed into spherical coordinates as shown below. $$x=\rho \sin \phi \cos \theta$$ $$y= \rho \sin \phi...
  12. nomadreid

    I Ratio of a real value to the max theoretical value: what term to use?

    If the Summary is not clear, the following is an example translated from: https://telecombloger.ru/7335 '... air conditioning systems. For example, the efficiency of a compressor is about 85%. The remaining 15% is spent on friction, oil movement, overflows, heating, etc. The efficiency of the...
  13. J

    MHB Diff-in-Diff Regression: 6 Var, Interaction Terms & Estimate

    I am doing a difference-in-difference analysis on a set of survey data for a health education program and I need to find statistical significance for the difference-in-difference estimate. I know that I find this using a regression. I need to use a regression in a mixed logistic model including...
  14. M

    Partial derivative of Vxx w.r.t. r in terms of Vxx

    Can anyone please help me to write partial derivative of Vxx w.r.t. r in terms of Vxx as shown in the hand written box at the end.
  15. T

    I Can someone explain to me a flop transition in laymen's terms?

    Can someone explain a flop transition to me in laymen terms? And what consequences does it have on the universe? Thanks
  16. Diracobama2181

    Calculating Terms in $\bra{P'}\phi^4\ket{P}$

    From this, I find $$\bra{P'} \phi^4 \ket{P} = \int \frac {d^3 k_1 d^3 k_2 d^3 k_3 d^3 k_4} {16 \omega_{k_1}\omega_{k_2}\omega_{k_3}\omega_{k_4} (2\pi)^{12} }\bra{0} a_{P'}(a_{k_1} a_{k_2} a_{k_3}a_{k_4}e^{i(k_1+k_2+k_3+k_4)x}+...)a^{\dagger}_{P}\ket{0}$$ (a total of 16 different terms) Right...
  17. brotherbobby

    Vector potential ##\vec A## in terms of magnetic field ##\vec B##

    My solution is making an analogy of the ##\text{Relevant equations}## as shown above, starting from the equation ##\vec \omega = \frac{1}{2} \vec \nabla \times \vec v##. We have ##\vec B = \vec \nabla \times \vec A = \frac{1}{2} \vec \nabla \times 2\vec A \Rightarrow 2\vec A = \vec B \times...
  18. Uchida

    Minimium diameter of an electromagnetic beam in terms of wavelength

    Is there a limit on the minimum diameter that a collimated electromagnetic beam must have (lasers or masers), in terms of its wavelength, or it is possible to create a beam with its diameter smaller than its wavelength? I'm considering a colimated planar wave directly from the source, and not...
  19. K

    I Rotation and Boost of Tensor Components: Meaning?

    If two coordinate systems are related by a rotation or a boost, does it make sense to say the tensors components are rotated or boosted with respect to their components in the original coordinates? For vectors, I think it is standard to say that, but what about general tensors?
  20. K

    I Differential equation with two terms

    I'm trying to solve a differential equation of the form $$\frac{A'(x)}{A(x)}f(x,y) = \frac{B'(y)}{B(y)}$$ where prime denotes differentiation. I know that for the case ##f(x,y) = \text{constant}## we just equal each side to a same constant. Can I do that also for the case where ##f(x,y)## is not...
  21. Saracen Rue

    I Find the value of this definite integral in terms of t, s and alpha

    One of the maths groups I'm apart of on Facebook posts (usually) daily maths challenges. Typically they act as small brain teaser for when I wake up and I can solve them without much trouble. However, today's was more challenging: (Note: blue indicates a variable and red indicates a constant)...
  22. JorgeM

    I How to calculate this Bessel's terms limit?

    $$ \lim_{x \to 0} [ \frac{J_{p}(x)}{Y_{p}(x)} ] $$
  23. E

    A How to understand when surface terms go to zero

    Hi all, I'm trying to understand when surface terms go to zero. I'm not really getting a connection other than many textbooks just saying surface terms go to zero. I have added a photo of Liboff's Kinetic Theory page 3 on Lagrange's equations. Before equation 1.7, he says the surface terms go...
  24. D

    I Logarithmic terms in a system of equations

    (I hope this is not a double posting) I want to solve this system of equations, containing logarithmic terms: ##7\ln(a/b)+A = 7\ln(d/e)+D = 7\ln(g/h)+G## ##7\ln(a/c)+B = 7\ln(d/f)+E = 7\ln(g/i)+H## ##7\ln(b/c)+C = 7\ln(e/f)+F = 7\ln(h/i)+I## ##a\phi_1+d\phi_2+g\phi_3=X##...
  25. T

    Expressing the magnetic vector potential A-field in terms of the B-field

    We have a retarded magnetic vector potential ##\mathbf{A}(\mathbf{r},t) = \dfrac{\mu_0}{4\pi} \int \dfrac{\mathbf{J}(\mathbf{r}',t_r)}{|\mathbf{r}-\mathbf{r}'|} \mathrm{d}^3 \mathbf{r}'## And its curl, ##\mathbf{B}(\mathbf{r}, t) = \frac{\mu_0}{4 \pi} \int \left[\frac{\mathbf{J}(\mathbf{r}'...
  26. T

    Engineering I can't figure out what's going on with these sqrt[3] terms (3-Phase AC Mains question)

    In this example I am thoroughly confused on why Is is divided by sqrt(3). My understanding is that the transformer supplies 3 phase (which is always described in line to line or Y connected). So the current in the winding should be 120[KVA]/230[V] then multiplied by sqrt(3) to convert it to...
  27. C

    I How is this product of terms calculated?

    ##\prod_{j \neq i}^{6} (\lambda_{i}-\lambda_{j})##
  28. Physicsphysics

    Finding t and x in terms of proper time?

    I tried finding a.a (four vector inner product) and I got to γ4{(v.a)2(1-γ4v.v - 2γ2) - a.a}, where again a and v are three vectors on the rhs (sorry to be confusing). a.a = g2 since it's a constant. I have no idea where to go from here to find the time and position. Please help!
  29. Adrian555

    A Geodesics of the 2-sphere in terms of the arc length

    I'm trying to evaluate the arc length between two points on a 2-sphere. The geodesic equation of a 2-sphere is: $$\cot(\theta)=\sqrt{\frac{1-K^2}{K^2}}\cdot \sin(\phi-\phi_{0})$$ According to this article:http://vixra.org/pdf/1404.0016v1.pdfthe arc length parameterization of the 2-sphere...
  30. P

    Constant Pressure Specific Heat in terms of Entropy and Enthelpy

    If ##N## is constant (per the partial derivatives definitions/ the subscripts after the derivatives) then ##G## is constant ##H - TS = constant## Taking the derivative of both sides with respect to ##T## while holding ##N,P## constant we get the following with the use of the product rule...
  31. A

    Expressing an Integral as a sum of terms

    e.g Can we write it as $$f(a)+f(a+dx)+f(2a+dx)+f(3a+dx)+...f(b)=\int^b_a f(x)dx$$...(?) Although $$\int f(x)dx$$ given the area tracked by thr function with the x-axis between a and b Thanks.
  32. currently

    Schrodinger's Equation in terms of vacuum permittivity?

    Summary:: How can Schrodinger's Equation be written relative to vacuum permittivity I am wondering why a particular problem uses this equation: It is stated to be Schrodinger's equation. Where does the potential come in, as well as the e^2/r ? An explanation would be greatly appreciated. Thanks.
  33. K

    I Question regarding notation when omitting terms

    If we want to expand a function ##f(x)## up to first order around ##x = 0## say, we usually write ##f(x) = f(0) + (df/dx)|_0 x + \mathcal O(x^2)##. But what if I want to expand ##f(x)## in the whole series, and showing only the first order term in x? What notation do you use for that? (Aside...
  34. G

    A Fermion mass terms in Peskin and Schroeder's book

    I'm currently looking at how fermion masses are produced via the Higgs mechanism in "An Introduction to Quantum Field Theory" by Peskin and Schroeder. It all makes a lot of sense and I've been fine with it so far, but I ended up getting stuck on something that's driving me nuts. I feel silly...
  35. W

    Getting the Answer in terms of Input()

    Hi, I have this mini-program and I am being lazy. Wherever I post this they make me go through a grinder reviewing basics . I just need a small hint. We are asking for the name of the user in "name =input()". I would like the line immediately after name 'x' is inputed to print 'Hi, x '. Instead...
  36. 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...
  37. S

    MHB Dominant Terms in Calculus Limits

    Hello, I am having issues finding the dominant terms in the following expression: lim [(x^7)-9(e^x)] / [sqrt(10x-1)+8*ln(x)] x->infinity Prompt: Find the limit and the dominant term in the numerator and denominator.
  38. T

    A Derivatives of Lagrangian Terms: Why We Lower?

    In Lagrangians we often take derivatives (##\frac{\partial}{\partial (\partial_{\mu}\phi)}##) of terms like ##(\partial_{\nu}\phi \partial^{\nu}\phi)##. We lower the ##\partial^{\nu}## term with the metric and do the usual product rule. My question is why do we do this? Isn't...
  39. M

    Engineering Best career option in terms of time, demand and money?

    Hi everyone, I’m a student in Ireland and I’m still in high school and the teachers were saying that its finally time for us to choose what paths we should take in terms of choosing subjects for our final high school years. Now my main question is that should I become an astrophysicist...
  40. binbagsss

    A QHE: rotational invariance, no terms linear in E or B

    'Let’s first see what all of this means in the context of d = 3 + 1 dimensions. If we have rotational invariance then we can’t write down any terms linear in E or B. The first terms that we can write down are instead ...' Why is this? I don't understnad . My thoughts would be pictruing the set...
  41. P

    A Christoffel Symbols in terms of a Change in Basis

    Hi All Given that the Riemann Curvature Tensor may be derived from the parallel Transport of a Vector around a closed loop, and if that vector is a covariant vector Having contravariant basis The calculation gives the result Now: Given that the Christoffel Symbols represent the...
  42. ColoradoGrrrl

    Circular Motion: Write expression for the period in terms of r and g

    I'm not sure if I'm doing this right as far as coming up with the equation they are asking for. I feel the question is poorly worded and the formatting makes their equation notation difficult to understand. Any insight would be very helpful. This is my work so far:
  43. NightHaWk

    Understanding Exponential Terms in Quantum Mechanics Problem

    So I am trying to understand and solve the problem mentioned in the title.I found a solution online: https://physics.bgu.ac.il/COURSES/QuantumMechCohen/ExercisesPool/EXERCISES/ex_9011_sol_Y09.pdf The problem is, I can't understand this step : I relly can't find out how the two expontential...
  44. looseleaf

    A Extra terms in the Action in Zee chapter 1.3?

    Hi, could someone please explain where the tau and sigma terms come from in this expression: I see the kinetic energy and quadratic "mattress" potential terms, but the tau and sigma kinda come out of nowhere. Where are they from?
  45. T

    I Number of Terms for Harmonic Series to Reach a Sum of 100

    I am reading an interesting book by Julian Havil called:" Gamma-Exploring Euler's Constant." Much of the book is devoted to the harmonic series,a slowly diverging series that tends toward infinity.However,one paragraph puzzles me. On p. 23 he says: " In 1968 John W. Wrench Jr calculated the...
  46. D

    I Binomial theorem with more than 2 terms

    Hi. Is the binomial theorem ##(1+x)^n = 1+nx+(n(n-1)/2)x^2 + ….## valid for x replaced by an infinite series such as ##x+x^2+x^3+...## with every x in the formula replaced by the infinite series ? If so , does the modulus of the infinite series have to be less than one for the series to...
  47. S

    How to decide which component is best in terms of stress and deformation?

    Summary: In terms of stress, strain & deformation, what is better for a given component. 1) low stress or high stress 2) less strain or large strain 3) less deformation or large deformation? Some dimensional changes were made in an existing component to study how these changes effect the...
  48. DaTario

    Zero Limit of Sum of Squares of Terms with Bounded Range

    I don't know how to show that this limit is zero. It seems that ##\sum_{i=1}^N a_{i,N} /N = 1## and the fact that ## 0 < a_{i,N} < M > 1## implies that some ##a_{i,N}## are less than one. Another conclusion I guess is correct to draw is that ##\lim_{N \to \infty} \sum_{i=1}^N a_{i,N}^2 /N < 1##.
  49. geoelectronics

    Please define a few atomic/nuclear terms for me? Thank you.

    I think a ray is electromagnetic, is mass-less, and could be described as a photon. A ray must travel at the same speed as "c" in the same medium. I think the term particle is used in atomic studies as a physical piece of matter, one that has mass and could hold a charge or be neutral. Being...
  50. TOUHID11

    Calculate Induced EMF in Circular Loop: Cylindrical Coordinates

    In order to calculate for the curl of the induced electric field for a loop moving in a uniform magnetic field, and using the cylindrical coordinate system for a curl, it's my understanding that since the B field is in the 𝑧̂ direction, then so is the partial time derivative of B, and therefore...
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