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  1. C

    I What is the name for the "stuff" at heart of black hole?

    What is the name for the "stuff" (neither matter nor neutrons) at the heart of a black hole?
  2. FallenApple

    I Thinking about the static electric field in terms of QFT

    So according to classical electrodynamics, an electron would produce an electric field that is a physical entity in and of itself. This field has momentum so when a test charge is placed within this vicinity, it would be affected by the field itself, not the electron. But what about the QFT way...
  3. Aashish sarode

    What are different terms of flight controllers?

    can anybody please tell me terminology of flight controller and it's specifications. Also, how these specs matter, like what is the effect of increase in Magintude or Frequency of different parameters which will help me buy a flight controller for a quadcopter. I want to build a FPV for racing.
  4. Yiming Xu

    I Express power sums in terms of elementary symmetric function

    The sum of the $k$ th power of n variables $\sum_{i=1}^{i=n} x_i^k$ is a symmetric polynomial, so it can be written as a sum of the elementary symmetric polynomials. I do know about the Newton's identities, but just with the algorithm of proving the symmetric function theorem, what should we do...
  5. S

    A Weinberg angle in terms of Higgs mass

    The Weinberg angle ##\Theta_{W}## is commonly expressed as $$\cos\Theta_{W} = M_{W}/M_{Z}.$$ Can the Weinberg angle ##\Theta_{W}## be expressed in terms of the Higgs mass and the mass of the W boson as $$\sin^{2}\Theta_{W}= m_{H}/M_{W}?$$
  6. S

    A Matching interaction terms and decay processes in standard model

    I would like to consider the interaction terms in the Standard Model which allow the following decay process: The only interaction terms in the Standard Model which allow this decay process are contained in the charged current interactions: $$\mathcal{L}_{cc} =...
  7. S

    A Charge-current interaction: linear terms in a given quark

    I am trying to figure out the interaction terms in the Lagrangian which are linear in the top quark.I find that these terms can only be found in the charged-current interaction since the neutral-current interaction and the gluon-fermion couplings are quadratic in the top quark. Now, I find two...
  8. Sagant

    English Terms for Academic Scholarships

    Hey, I'm writing my CV in English right now, and because my native language is Portuguese, I got stuck on some specific terms. Two to be fair. 1) Here in my university we have a scholarship that lasts one semester (our academic year is divided into two semesters) which is given to undergraduate...
  9. davidge

    I Derivative with several terms in denominator

    Hi. I want to solve \frac{\partial x^{\nu}}{\partial x^{\mu} + \xi ^{\mu}}, knowing that \frac{\partial x^{\nu}}{\partial x^{\mu}} = \delta ^{\nu}_{\mu}. How can I do this?
  10. R

    Mathematica How to plot several terms in a Fourier series

    I was given a function that is periodic about 2π and I need to plot it. I was wondering if there is a way to input a value and have mathematica generate a new graph with the number of iterations. The function is: $$\sum_{n=1}^{N}\frac{sin(nx)}{n}$$ where n is an odd integer. I guess a better...
  11. M

    Express volume expansivity in terms of density

    Homework Statement Express volume expansivity (B) in terms of density (ρ) and its partial derivatives Homework Equations B = (1/V) (dV/dT) V = m/ρ The Attempt at a Solution I have only managed to substitute m/ρ into the expansivity equation. Don't really understand how to manipulate the...
  12. S

    A Spinor indices on Yukawa coupling terms in electroweak sector

    In the electroweak sector, we define the left-handed Weyl fields ##l## and ##\bar{e}## in the representations ##(2,-1/2)## and ##(1,+1)## of ##SU(2) \times U(1)##. Here, ##l## is an ##SU(2)## doublet: ##l = \begin{pmatrix} \nu\\ e \end{pmatrix}.## The Yukawa coupling in the electroweak sector...
  13. M

    What Are Alternative Terms for Moving a Pickoff Point in Control Engineering?

    I would like to ask about some terms of control engineering. What are other common expressions for "moving a pickoff point" which can be used as" moving a pickoff point behind of a block" or as "moving a pickoff point ahead of block." Source:Self-made Thank you.
  14. Albert1

    MHB Are At Least Two Numbers Equal in This Sum of 100 Terms?

    $a_1,a_2,...,a_{100}\in \begin{Bmatrix} 1,2,3,-----,100 \end{Bmatrix}$ $S=\dfrac{1}{\sqrt{a_1}}+\dfrac{1}{\sqrt{a_2}}+\cdots+\dfrac{1}{\sqrt{a_{100}}}=12.5$. Prove that at least two of the numbers are equal
  15. anemone

    MHB Find the sum of three trigonometric terms

    Evaluate \tan^4 10^\circ+\tan^4 50^\circ+\tan^4 70^\circ without the help of a calculator.
  16. nomadreid

    I Odd use of terms (“stationary stochastic process”., etc.)

    I am trying to make sense of a Russian author’s use of terms (I have to translate his article). I have three questions, but please don't think you need to answer all three before answering. Thanks for any insights! [1] He uses the term “probability density distribution” ρ(ξ) of a stationary...
  17. anemone

    MHB Sum of 100 Terms: Prove At Least 2 Numbers Equal

    The natural numbers $a_1,\,a_2,\,\cdots,\,a_{100}$ are such that $\dfrac{1}{\sqrt{a_1}}+\dfrac{1}{\sqrt{a_1}}+\cdots+\dfrac{1}{\sqrt{a_1}}=20$. Prove that at least two of the numbers are equal.
  18. M

    MHB Sum of First 20 Terms of Arithmetic Progression with Even Terms Removed

    First term of the progression is 3 & the common difference is 4 Find the sum of the first 20 terms of the progression that is obtained by removing the terms in the even positions of the given progressions, such as the second term,fourh term, sixth term. Formula preferences For the sum of an...
  19. K

    If acceleration is stated is terms of velocity....

    Homework Statement This is not a particular problem but a generic one. If one has acceleration stated in terms of velocity (or position) such as a=v, how do we convert these values into time? Homework Equations ads=vdv ad(theta)=wdw And of course, the usual time-based derivative relations...
  20. S

    Tresca criterion in terms of invariants

    Hi, The Tresca Critrion is given in the form of non continuous equations: Max(½|σ1-σ2|,½|σ2-σ3|,½|σ3-σ1|) = k How did they come up with the invarient equation f(J2,θ) = 2√J2 * sin(θ+⅓π)-2k, θ from (0 to 60)
  21. Z

    Avg of two terms & largest possible value

    Homework Statement If the average (arithmetic mean) of 3a and 4b is less than 50, and a is twice b, what is the largest possible integer value of a? Homework Equations Avg of two variables is: (a+b)/2 The Attempt at a Solution (3a + 4b)/2 < 50 3a + 4b <100 Now try out values such a = 2b I) a=...
  22. S

    I Vector Calculus: What do these terms mean?

    In our section on path independence, we were asked to find the potential function given a vector field. Our teacher says to use only line integrals to find the potential function, and not any other method. Like if we have ##F=\left< M,N,P \right> ## The first step is to determine if the domain...
  23. binbagsss

    QFT Wicks theorem contraction -- different fields terms of propagation

    Homework Statement I am trying to express ##T(\phi(x1)\Phi(x2)\phi(x3)\Phi(x4)\Phi(x5)\Phi(x6))## in terms of the Feynman propagators ##G_F^{\phi}(x-y)## and ##G_F^{\Phi}(x-y)## where ##G_F^{\phi}(x-y) =\int \frac{d^{4}k}{(2\pi)^{4}}e^{ik(x-y)} \frac{ih}{-k.k - m^2 -i\epsilon} ## and...
  24. vktsn0303

    I Express x in terms of the constants

    I have the expression, A(Bx + 1) = C*d^(2x) where A,B,C and d are constants. How to arrive at an expression for x in terms of A,B,C and d? I have tried doing this: Log [A(Bx + 1)/C] = Log [d^(2x)] 2xLog(d) = Log[A(Bx + 1)/C] but I'm unable to arrive at an explicit expression of x in terms...
  25. L

    Why are there two terms of both mutal and self inductance

    Homework Statement Given two inductors, connected in parallel connected to a battery, why do the following emf relations hold? $$\mathcal{E}_1 = - N_2 A \frac{d B}{d t} = -M\frac{d I_1}{d t } \\ \mathcal{E}_2 = -L_2 \frac{dI_2}{dt}- M \frac{dI_1}{dt}$$ See attachment ! Homework Equations...
  26. karush

    MHB 206.11.3.27 first three nonzero terms of the Taylor series

    $\textsf{a. Find the first three nonzero terms of the Taylor series $a=\frac{3\pi}{4}$}$ \begin{align} \displaystyle f^0(x)&=\sin{x} &\therefore \ \ f^0(a)&=\sin{x} \\ f^1(x)&=\cos{x} &\therefore \ \ f^1(a)&= -\frac{\sqrt{2}}{2}\\ f^2(x)&=- \sin{x}&\therefore \ \ f^2(a)&=\frac{\sqrt{2}}{2} \\...
  27. karush

    MHB 206.11.3.27 Tayor series 3 terms

    $\textsf{a. Find the first four nonzero terms of the Taylor series $a=1$}$ \begin{align} \displaystyle f^0(x)&=6^{x} &\therefore \ \ f^0(a)&= 6 \\ f^1(x)&=6^{x}\ln(6) &\therefore \ \ f^1(a)&= 6\ln(6) \\ f^2(x)&={6^{x}\ln(6)^2} &\therefore \ \ f^2(a)&= {12\ln(6)} \\ f^3(x)&={6^{x}\ln(6)^3}...
  28. karush

    MHB 206.11.3.39 Find the first four nonzero terms of the Taylor series

    $\tiny{206.11.3.39}$ $\textsf{a. Find the first four nonzero terms of the Taylor series $a=0$}$ \begin{align} \displaystyle f^0(x)&=(1+x)^{-2} &\therefore \ \ f^0(a)&= 1 \\ f^1(x)&=\frac{-2}{(x+1)^3} &\therefore \ \ f^1(a)&= -2 \\ f^2(x)&=\frac{6}{(x+1)^4} &\therefore \ \ f^2(a)&= 6 \\...
  29. karush

    MHB 206.11.3.11 Find the first four nozero terms of the Maciaurin series

    $\textsf{a. Find the first four nozero terms of the Maciaurin series for the given function} \\$ \begin{align} a&=0 \\ f(x)&=(-5+x^2)^{-1} \\ \\ f^0(x)&=(-5+x^2)^{-1}\therefore f^0(a) = 1 \\ f^1(x)&=\frac{-2x}{(x^2-5)^2} \therefore f^1(a) = 0 \\ f^2(x)&=\frac{2(3x^3+5)}{(x^2-5)^3} \therefore...
  30. Z

    I Help please -- Seeking clear definition of fundamental terms

    I've tried repeatedly to get clear, succinct definitions of the following terms over and over again, but invariably the definitions provided clash, and I'd like to put an end to that. The terms I am trying to define clearly are: - Relation - Definition (Mathematical definition) - Function -...
  31. 10Exahertz

    Orbital Potential Energy to find r and phi in terms of t.

    Homework Statement A particle in central force field has the orbit r=cφ^2, c is a constant. Find the potential energy, Find r and phi in terms of t. I get how to find the potential energy and found it to be U=-l^2/mu (2c/r^3+l/2r^2) l is angular momentum and mu is the reduced mass But how do I...
  32. D

    Expressing one Vector in terms of others

    Homework Statement I am very rusty on my mathematics and I am wondering if there is a way to express Rs in terms of r1 and r2. The positions of the bodies are all relative to the origin 0 (C.o.M between m1 and m2). Basically I'm trying to express the two vectors coming from m3 in terms of the...
  33. WeeChumlee

    Solving Transimpedance Circuit: Find k in Terms of R1, R2, and Rf

    Homework Statement The circuit of FIGURE 2 is known as a transimpedance circuit used for the measurement of very small currents. Derive the relationship between the output voltage V and the input current I; i.e. if V = kI find k in terms of R1, R2 and Rf. Homework EquationsThe Attempt at a...
  34. W

    Can anyone explain this sun reflection in terms of angles?

    I'm trying to understand the physics of reflection to better draw objects. Normally, you see the reflection of a light source on metallic surfaces where the angle of incidence can equal the angle of reflection. This should reflect an image of the source that is approximately equal in size to how...
  35. G

    I Differential form of Gauss' law: All three terms the same value?

    Hi. Is the Maxwell equation $$\nabla\cdot\vec{E}=\frac{\rho}{\varepsilon_0}$$ even true in the stronger form $$\frac{\partial E_i}{\partial x_i}=\frac{\rho}{3\cdot\varepsilon_0}\enspace ?$$ I guess not, since I haven't found a source suggesting this. But shouldn't the isotropic electric field...
  36. J

    Terms Allowed in Spectroscopic Structure of Calcium

    Homework Statement Why can't we have 4s^2 3S1 calcium? I've looked up a table of terms and this is never given, so I guess we can't have it. Why can't the spins of each of the outer electrons add to give S = 1, J = 1, and a degeneracy of 3? I guess the answer must be pretty basic since nobody...
  37. karush

    MHB -z78 first four terms of the sequence of 𝑎_(𝑛+1)=𝑎_𝑛+𝑛,𝑎_1=−1.

    Write out the first four terms of the sequence defined by the recursion n_(n+1)=n_1+1,n_1=−1 $\text{Write out the first four terms of the sequence defined by the recursion}$ $$\displaystyle a_{n+1}=a_1+1,a_1=−1$$. $\text{so then}$ $$\displaystyle a_{0+1}=-1+0=-1$$ $\text{stuck!}$
  38. Aswin Sasikumar 1729

    I Is there any operator for momentum in terms of t?

    Since there is an energy operator interms of t and a momentum operator interms of x as expected.For energy there is a hamiltanion operator interms of t which is unexpected for me.Similarly whether there is any operator interms of t for momentum also?
  39. M

    MHB Find the value in terms of p and q

    If $log_a 2 = P $ & $ log_a 3 = q$ find $log_a 72 $ in terms of $p$ & $q $ I'm not sure on how to begin this may be convert the logarithms to decimals :confused: Many Thanks :)
  40. M

    MHB Shaded region in terms of set notation

    I'm having trouble in expressing the shaded region in set notation (Thinking) Many Thanks :)
  41. M

    MHB State the angles in terms of x , Circle theorems

    Problem O is the center of the circle and AB is the diameter of this circle , C & D are points on this circle , If $\angle CDB=x^\circ$ ,State the following angles in terms of $x$ $\angle CAB$ $\angle CBA$ Workings & what is known $OC=OB=OA$ radii of the same circle $\therefore \angle...
  42. M

    MHB Ratio of the area of triangle in terms of another triangle

    :D I have trouble in determining the ratio of the area of $\triangle PST$ in terms of $\triangle PQR$ In the triangle PQR $QT=TR$, $PS=1 cm$ , $SQ=2 cm$ , How should I be writing the area of $\triangle PST$ in terms of $\triangle PQR $ What is known by me : Since...
  43. R

    MHB Find the Volume of Mt. Vesuvius After 79AD in Terms of pi

    Mt. Vesuvius in Pompeii was a conic volcano with a height from its base 7950 feet and a base radius of 2300 feet. In 79 AD, the volcano erupted, reducing its height to 4200 feet . Find the volume of the volcano after 79 AD in terms of pi. WORK: Volume of Volcano(Before 79AD)= \pi *r^2*h/3...
  44. P

    B Why can't sin(x^2) be expressed in terms of sin(x)?

    I've read explanations on the internet that the product of two angles is not something fundamentally important. So, the sin of product of two angles cannot be expressed in terms of sin of individual angles. But in calculus, we often come across these functions, we deal with functions involving...
  45. Drakkith

    Writing an Expression for dρ in Terms of ρ and dT.

    Homework Statement The coefficient, β, of thermal expansion of a liquid relates the change in the volume V (in m3) of a fixed quantity of a liquid to an increase in its temperature T (in °C): dV = βV dT (a) Let ρ be the density (in kg/m3) of water as a function of temperature. (For a mass m of...
  46. Vivan Vatsa

    Difference between many chemically related terms?

    In chemistry, chemical bonding is a very important topic. What I can't really understand is the interrelation of different theories which explains the same kind of thing, like for structure of any compound there are theories like Valence bond theory or VSEPR or molecular orbital theory. I am...
  47. moenste

    Reaction on the particle in terms of angular velocity

    Homework Statement A particle is attached by means of a light inextensible string to a point 0.4 m above a smooth horizontal table. The particle moves on the table in a circle of radius 0.3 m with angular velocity ω. Find the reaction on the particle in terms of ω. Hence find the maximum...
  48. Combining like terms introduction | Introduction to algebra | Algebra I | Khan Academy

    Combining like terms introduction | Introduction to algebra | Algebra I | Khan Academy

    In simple addition we learned to add all the numbers together to get a sum. In algebra, numbers are sometimes attached to variables and we need to make sure ...
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  49. How to simplify an expression by combining like terms and the distributive property | Khan Academy - YouTube

    How to simplify an expression by combining like terms and the distributive property | Khan Academy - YouTube

    We've learned about order of operations and combining like terms. Let's layer the distributive property on top of this. Practice this lesson yourself on Khan...
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  50. Combining like terms, but more complicated | Introduction to algebra | Algebra I | Khan Academy

    Combining like terms, but more complicated | Introduction to algebra | Algebra I | Khan Academy

    This example of combining like terms in an expression gets a little hairy. Listen closely. Practice this lesson yourself on KhanAcademy.org right now: https:...
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