What is Terms: Definition and 1000 Discussions

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  1. 24forChromium

    Compressing arrays and various number of terms

    Behold this array of numbers: 3, 5, 11, 4 Sometimes, the programming limits the number of things that can be recorded in one location to a single number, such as 93240, but sometimes I also need to record an array of numbers such as the one shown above. An example of such platforms include the...
  2. E

    I Why do those two terms add here?

    In complex manifold, one writes $$ds^2=g_{ab}dz^adz^b\hspace{3cm}(1)$$ $$ds^2=2g_{\alpha\bar{\beta}}dz^{\alpha}d\bar{z}^{\bar{\beta}}+g_{\alpha\beta}dz^{\alpha\beta}dz^{\alpha}dz^{\beta}+g_{\bar{\alpha}\bar{\beta}}d\bar{z}^{\bar{\alpha}}d\bar{z}^{\bar{\beta}}\hspace{3cm}(2)$$ My question is...
  3. N

    Understanding 'Observe' in Physics: Definitions and Explanations

    When I read any physics articles online I always end up receiving the wrong message. especially in terms such as 'observe'. what does this term mean when its used to describe exeperiments such as the double slit
  4. H

    How to find the vo in terms of v1 and v2?

    Homework Statement The problem is upload below. Homework EquationsThe Attempt at a Solution I was stuck at finding the voltage between the 100k resistor and 200k resistor. Is the voltage zero since the node below there is zero and there is no resistor between them? But if the node voltage is...
  5. I

    Infinite series with all negative terms

    Hello, I have been reviewing my textbook lately, and I came across a rather paradoxical statements. all of the convergence tests in my book state that the terms of the series has to be positive. However, when I solved this power series ∑(-1)n-1(xn/n), I found that it converges for -1<x≤1, but...
  6. L

    Affine Connection Γ in Terms of Tetrad: Help Needed

    Hi, some one know the expression of the affine connection Γ in terms of tetrad formalism? I would like also some references if it's possible, i found a hit but i think that is wrong... please help me it's so important!
  7. B

    Maxwellian CCD equations having potential terms

    I wasn't sure whether to post this in the classical forum or the quantum forum. In "SU(3) Maxwell equations and the Classical Chromodynamics" by Sanchez Monroy, he gives four field equations for CCD similar to Maxwell's four field equations for EM fields. However, unlike Maxwell's equations...
  8. A

    Cauchy's equation in terms of material acceleration

    Does anyone know which formula is used or how to arrive at the righthand side of the equation below, which is the dot product of del and rho*a 2nd order tensor(V V). . represents dot product and X a vector quantity This problem is in connection with transforming cauchy's equation in terms of...
  9. D

    MHB Solving Equations with High-Power Terms

    What steps can be taken to solve an equation with a relatively higher power on one side such as: 6977x/1200 = (1 + x/12)60 - 1
  10. T

    Integration of sin terms

    Homework Statement (This is a part of the entire problem. I'm just struggling with going to the next step since it involves solving this integral.) Integrate: $$ \int \frac {1}{\sin \theta \sqrt {R^2\sin ^2 \theta - a^2} } d\theta $$ Homework Equations R and a are simply constants. Only $$...
  11. D

    Characterization of a gauge theory in terms of observables

    Although I have a good understanding of how to do calculations in gauge field theory, I am still dissatisfied with my understanding of why we use them in the first place. From a philosophical point, it should be possible to characterize a gauge theory in terms of observables only. I suppose one...
  12. S

    What are generic terms for integration/summation parameters?

    This is not only a question strictly about mathematics, but in science or any other quantitative field in which there is an integration - or a summation that is like a discrete integration. [ A ] the parameter that is considered the input variable for the integration/summati - i.e., the x of dx...
  13. SquidgyGuff

    Finding relativistic force in terms of acceleration

    Homework Statement The instantaneous force F acting on a particle, as measured in frame S, is Use the formula for the linear momentum () in and the definition of the acceleration a to show that The Attempt at a Solution The professor said that this required use of programs such...
  14. G

    Mean of the square of a sum of exponential terms

    Homework Statement [/B] Calculate \widehat{Y^{2}} (i.e., the mean of the square of Y. Homework Equations Y=\sum_{k=0}^{N-1}y_{k} where y_{k}=e^{-\gamma t}e^{\gamma \tau k}G_{k} and t=N\tau The quantities y_{k} (or G_{k}) are statistically independent. The Attempt at a Solution...
  15. W

    Affine independence in terms of linear independence

    This question mostly pertains to how looking at affine independence entirely in terms of linear independence between different families of vectors. I understand there are quite a few questions already online pertaining to the affine/linear independence relationship, but I'm not quite able to...
  16. J

    How can I find the first few terms of the Laurent series for

    Homework Statement For each of the following functions find the first few terms of each of the Laurent series about the origin, that is, one series for each annular ring between singular points. Find the residue of each function at the origin. The function is... 1/(z*(z-1)(z-2)^2) Homework...
  17. F

    Python How can I input a polynomial equation of infinite terms in P

    I have been given a task to create an interpolating/extrapolating programme. I have completed the programme for linear interpolation (2 points) but now must make it usable for 3 or more points, ie a polynomial of n points. I think I have the equation in general for a polynomial as it is an...
  18. D

    Solve the following differential equation (by regrouping terms)

    Homework Statement (4x^3y^3-2xy)dx+(3x^4y^2-x^2)dy=0[/B]Homework Equations (4x^3y^3-2xy)dx+(3x^4y^2-x^2)dy=0 The Attempt at a Solution i expanded it as 4x^3y^3dx-2xydx+3x^4y^2dy-x^2dy=0 next we have to take the common such that there will be m(X)(xdy+ydx)[/B] m(x) is the common onee
  19. MexChemE

    Heat and mass transfer -- Boundary conditions & balance terms

    Hello, PF! Recently, while reading chapter 10 (microscopic energy balances) of the second edition of BSL, I found a minor discrepancy which is confusing me, especially when considering the mathematical analogies of heat and mass transfer. In section 10.1, the authors introduce Newton's law of...
  20. C

    Energy loss in terms of beam momentum change

    1. Homework Statement Express the beam energy loss in the accelerator in terms of the change in the beam momentum. It is taken from one paper, where \begin{equation} \Delta T = \left( \frac{1+\gamma}{\gamma}\right) \frac{T_0 \Delta p}{p_0} \end{equation}expression is used for transition from...
  21. phoenixthoth

    Terms of Service & Ownership of Forum Posts: Legal Considerations

    I was wondering if anyone knows of what type of law is involved with the terms of service of internet discussion forums. Is it possible through terms of service for a discussion forum to legally own poster's posts? Thanks!
  22. O

    Derivative of Force in terms of distance?

    Hi, Suppose I have a function on a graph with a vertical axis is Force and the horizontal axis is distance. Then the area under the curve is given by F*d = Work = Energy, correct? If so, then what would the slope of the curve represent? F/d = ? Thank you.
  23. A

    Help with consensus terms in k-map solution

    Homework Statement Find consensus (redundant) terms for the minimal SOP solution for the following function (inputs A,B,C,D and output F): Σm(1,3,4,5,7,10,11,12,14,15) Homework Equations n/a The Attempt at a Solution I find the minimal SOP solution is F=A'D + AC + BC'D' Then it seems like...
  24. D

    MHB Power Series: Find First 5 Terms of x^2/(1-5x) - Help Needed

    For this function f(x)=x^2/(1-5x). The interval of convergence is (-1/5) < x < (1/5). I tried to differentiate, but got it wrong. Could someone please help?
  25. B

    Integrals log x in terms of dilogarithm

    Hi members,see attached PdF file.Have you any idea to prove thes integrals Thank you
  26. J

    Why is the nominal capacity of power plants given in terms of power, not energy?

    Why is the nominal capacity of power plants given in terms of power and not in terms of energy?
  27. B

    Expressing Vector R in Terms of A, B, C, & D

    Homework Statement Express the vector R in terms of A, B, C, D (VIEW IMAGE ATTACHED) Homework EquationsThe Attempt at a Solution R=B-D OR R=A+C In this problem, I figured that because of the way the arrows are pointing R+D=B which you can then simplify to R=B-D. However, this is not an answer...
  28. Mr Davis 97

    Justification for cancelling terms in limits?

    I am confused about the algebraic process of finding a limit. Let us take ##\frac{x^2 -1}{x - 1}##. In trying to find ##\lim_{x\rightarrow 1}\frac{x^2 -1}{x - 1}##we do the following: ##\displaystyle\lim_{x\rightarrow 1}\frac{(x+1)(x-1)}{x - 1}## ##\displaystyle\lim_{x\rightarrow 1}x+1##...
  29. K

    Maple Partially Factor Lengthy Expression w/ Maple - Positive Real Numbers

    I need to show that the following expression, $$a^3b-a^3c+a^3z+a^3x+a^3y-a^2bx+a^2by+a^2cx-a^2cy-a^2zx+a^2zy-a^2x^2+a^2y^2-abcz-abcx-aczx-acx^2+b^2c^2+2bc^2x+c^2x^2-b^2c-2bcx-cx^2,$$ is positive given that: $1.$ $\ a,b,c,x,y,z$ are positive real numbers $2. \ \ a>b+x$ $3. \ \ c<b+y$ I...
  30. P

    Write Torsion Tensor: Definition, Metric Tensor & Equation

    Would it be possible to write the torsion tensor in terms of the metric? I know that a symmetric Christoffel Symbol can be written in terms of the partial derivatives of the metric. This definition of the christoffel symbols does not apply if they are not symmetric. Is it possible to write a...
  31. T

    Expanding a function in terms of a vector

    Homework Statement ## L (v^2 + 2 \pmb{v} \cdot \pmb{ \epsilon } ~ + \pmb{ \epsilon} ^2)##, where ## \pmb{\epsilon}## is infinitesimal and ##\pmb{v}## is a constant vector (## v^2 ## here means ## \pmb{v} \cdot \pmb{v} ## ), must be expanded in terms of powers of ## \pmb{\epsilon} ## to give...
  32. M

    What is dynamic equilibrium in laymen's terms?

    I was receiving help for the following problem... The 2.0 kg wood box in the figureslides down a vertical wood wall while you push on it at a 45 ∘ angle. The coefficient of kinetic friction of wood on wood is μk = 0.200. What magnitude of force should you apply to cause the box to slide down at...
  33. avito009

    Lagrangian and Hamiltonian. What are these in layman terms?

    All I know is that Lagrangian is kinetic energy- potential energy and Hamiltonian is kinetic energy + Potential energy. Why do we calculate the lagrangian or hamiltonian?
  34. D

    MHB Determining Terms in $\sum_{n=-N}^{N}|e^{J\frac{\pi}{4}n}|^2$

    I just want to know how do I determine the number of terms will be in this summation. The answer to this 2N+1 terms. I can only arrive at preliminary steps of solving this. can you tell why 2N+1 is the number of terms? I know that the magnitude of complex exponential function squared would...
  35. RJLiberator

    General Understanding of Terms [ Complex Analysis ]

    Hi all, I was unsure where to put this thread as I read the main topic title in the topology/analysis forums and decided to post it here. I am looking for a chart/graph/website that helps me understand the basic terms such as: -neighborhoods -Boundary points -Singularity points - "Function is...
  36. J

    Is a math major a jack-of-all-trades in terms of marketable

    skills? If you got a B.S. in Math, you probably know some programming, but not enough to qualify you for a software engineering job; some statistics, but not enough to qualify you to be an actuary; and some data science-type stuff, but not enough to qualify you for a data analysis or database...
  37. N

    Is there any difference between these 2 terms?

    Homework Statement Is there any difference between these 2 terms, if yes how are they different? \begin{align}(\nabla\cdot\nabla\vec A)\vec B &= (\nabla\vec A\cdot\nabla)\vec B\end{align} Homework Equations From what i know about dot product, it is commutative, so does this property apply here?
  38. 1

    What is saturation in terms of wavelength?

    could it be possible, to make a, for example, and lens that has a special texture, or colour and putting it on would make the pictures more saturated? or maybe make a pair of glasses for people who can't produce as much cones as others? my questions is because i can't really think of it, but...
  39. B

    Curl in terms of "fractional" notation

    See these equations: \left | \frac{d \vec{f}}{d \vec{r}} \right | = \left | \frac{d(f_1,f_2)}{d(x,y)} \right | = \frac{\partial f_1 \wedge \partial f_2}{\partial x \wedge \partial y} = \left | \begin{bmatrix} \frac{\partial f_1}{\partial x} & \frac{\partial f_1}{\partial y} \\ \frac{\partial...
  40. Christian Grey

    Which book is better in terms of Depth?

    The Theoretical Minimum: Quantum Mechanics - https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20 Sakurai Modern Quantum Mechanics - http://www.amazon.com/dp/0201539292/?tag=pfamazon01-20 I want to know, which book covers more in depth? And Sakurai's book is more advanced than Leonard...
  41. liometopum

    Terms in a geometric mean equation

    In a geometric mean equation, say 2 x 8 = 16, or a x b = c, what are the words we would use to describe the numbers or terms? Specifically, if you know 'a' and 'c', what do you call 'b'? For example, in a normal multiplication, a x b = c, 'a' is the multiplicand, 'b' is the multiplier, and 'c'...
  42. can12345

    First and second order terms in pressure measurement

    Hello everyone, What does it means first and second order of pressure measurement value? Whats the main difference?
  43. B

    Group algebra terms or phrases

    (Again, I am sorry for the simplicity of these questions. I am a mechanical engineer learning this stuff late in life.) I have read the following terms or phrases: group algebra group algebra the algebra of a group an algebra group an algebraic group a group of algebras So... could someone...
  44. Square1

    Formula for the number of terms being compounded

    Ran out of room for my title - not sure how to say it concisely, or if there is a better place to put this question...lets say this is "financial engineering"... I am looking for a formula what will give me the number of terms that will be compounded in a given length of time. Say: Principle =...
  45. F

    Which of the SEMF terms account for low A binding energy?

    Homework Statement Which of the semi-empirical mass formula terms accounts for a drop in stability at low A and why? Homework Equations B = avA - asA\frac{2}{3} -acZ(Z-1)A\frac{-1}{3} -aa(A-2Z)2A-1 ± apA\frac{3}{4} The Attempt at a Solution I'm struggling getting my head around this one. The...
  46. goonking

    Ideal gas law in terms of density

    Homework Statement Homework Equations PV=nRT The Attempt at a Solution not sure if this is the right approach plugging into -ρg gives us -PMg/RT = dP/dy now we have to integrate both sides to find P?
  47. C

    Rational functions: combine and simplify terms

    Homework Statement (4a/a+4)+(a+2/2a) Homework Equations Just combine and then factor out The Attempt at a Solution It's actually fairly simple, but I'm having difficulty at the end. /multiply each term by opposite denominator 4a(2a)/a+4(2a) + a+2(a+4)/2a(a+4) /combine 4a(2a)+(a+2)(a+4) /...
  48. Jaco Viljoen

    Suppose x-2, x and x+6 where are sequential terms in a geometric sequence

    Homework Statement Suppose x-2,x and x+6, where x is an integer, are consecutive terms in a geometric sequence S Determine x Homework Equations r=x/(x-2)=(x+6)/x The Attempt at a Solution x/(x-2)=(x+6)/x cross multiply x(x)=(x-2)(x+6) x^2=x^2+4x-12 x^2-x^2+4x-12/4=0 4x=12 x=3
  49. 1

    Debye's T^3 Law: Specific heat, Latice and Electronic terms

    Homework Statement QUESTION ADDED AS ATTACHMENT AS NEED TO SEE GRAPH. Homework Equations C = (12NkBπ4/5)(T/θD)3 for T<<θD C = 3NkB for T>>θD The Attempt at a Solution a.)[/B] So I assume the expression for the specific heat as a function of temperature that the question must want: C =...
  50. T

    Trig functions in terms of x,y, and r?

    I work a good deal better when the equation is in x and y form, is it possible to set up a trig expression like 5Cos(x)/(Sin(x)-1)and substitute the proper x or y equivalent so long as I remember to replace the trig identities later when the problem is finished? Or can you just not solve these...
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