What is Index: Definition and 827 Discussions

Indian Institute of Management Lucknow (abbreviated IIM Lucknow or IIM-L) is a public business school in Lucknow, Uttar Pradesh, India. It was established in 1984 as the fourth Indian Institute of Management (IIM) by the Government of India. IIM Lucknow offers post-graduate diploma, fellowship and executive programs in management. It is recognised as an "Institution of Excellence" by India's Ministry of Human Resource Development. IIM Lucknow also serves as the mentor institution for the newly established IIM Jammu, IIM Rohtak and IIM Kashipur. It also served as a mentor institute to IIM Sirmaur till 2018.The institute is on a 200-acre site in the northern outskirts of Lucknow. It also has a second campus on a 20-acre site at Noida exclusively for one year full-time MBA program (IPMX), Two-year PGP for working executive and executive education. The admission for the two-year PGP and fellowship programmes is done through Common Admission Test (CAT), while GMAT score is used for International Programme in Management for Executives, a one-year full-time residential programme equivalent to an MBA program, while admission to the Two-year PGP for working executive program is done based on GMAT score or a competitive written examination conducted by IIM Lucknow. The shortlisted candidates based on GMAT or the written examination go through the Writing Ability Test and Personal Interview (WAT & PI) to get final selection. The programs are accredited by the global accreditation body AMBA and AACSB. The institute has tie-ups with 24 leading B-schools across the world for student exchange. A number of b-competitions, cultural and sports events are organised by various clubs, academic interest groups and committees throughout the year.

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  1. S

    Calculation of the Pontryagin index

    When I read A.Zee's QFT in a Nutshell, he asked me to do the calculation of his exercise IV.4.6: (A.Zee called these the Pontryagin Index) Let g(x) be the element of a group G. The 1-form v = gdg† is known as the Cartan-Maurer form. Then tr v^N is trivially closed on an N-dimensional manifold...
  2. K

    Extracting thickness of glass and index of refraction from Cartesian Graph

    Homework Statement I made a graph in Excel which graphs (1/x^2) vs (1/cos^2 (angle of incidence)). From the graph I am supposed to analyze the slope and intercept of the straight line. I made a trendline which came out to be y=mx + b = (-0.0084)x + 5.54. From this equation I'm supposed to...
  3. O

    MHB If G is the union of 3 of its subgroups, show that they each have index 2

    Let G be a finite group and let G = H_1 \cup H_2 \cup H_3 . Show that [G: H_i] = 2 for i = 1, 2, 3. There was a hint for this question saying to first prove that at least one of the subgroups has index 2 in G. So far I am not sure how to even start this problem. I know that the orders of...
  4. J

    Gaussian Beam Width and Refractive Index

    Homework Statement I know that in free space, the width of a Gaussian beam can be written as W=W_0\sqrt{1+(\frac{z}{z_0})^{2}}. However, I was wondering if it was possible to express this width as a function of refractive index instead (since I don't believe a Gaussian beam originating in say...
  5. S

    Refractive Index of Optical Fibre Core and Cladding

    Homework Statement I need to find the refractive indexes of the core and cladding of an optical fibre by using the specs found here http://www.photonics.byu.edu/FiberOpticConnectors.parts/images/smf28.pdf Then I'm suppose to calculate the Numerical aperture and compare it with the one listed...
  6. A

    Simplifying Index Notation in Vector Calculus

    (r×∇).(r×∇)=r.∇×(r×∇) now in index notation it is written as, =xi∂jxi∂j-xi∂jxj∂i but when I tried to prove it ,it just came out twice.can anyone tell how it is correct(given is the correct form).i really mean that i was getting four terms which gave twice of above after reshuffling...
  7. S

    Index Notation Help: Solving ∫∂k(gixiεjklxl)dV

    Homework Statement ∫ ∂k(gixiεjklxl dV Can anyone make sense of this? I know I'll need to apply the chain rule when taking the derivative, but I'm not quite sure how to proceed. Also, this is part of a larger problem where g is a gravity vector existing purely in the -z direction, but I...
  8. D

    Sum of Sums over Primes that Divide the Index

    I have seen double sums, but have come across a problem involving sums over primes. However, this sum is inside a second sum, and is taken over all primes that divide the outside index, like this: \sum_{k=1}^{n} \sum_{p | k} \frac 1p for p prime. Is there any way to manipulate this...
  9. S

    Understanding Division in Index Notation

    Hello everyone, Recently I started to use index notation, but still the division is not clear for me. I'll mention just some simple examples that I'm not sure about: Does a =\frac{1}{b_i} mean that a = \sum_{i=1}^{3}\frac{1}{b_i} or a = 1 / \sum_{i = 1}^{3}b_i ? Similarly, does a_i...
  10. S

    Index Notation - Prove the following

    Homework Statement http://imgur.com/gTapO Homework Equations The Attempt at a Solution The first one is easy, just use the fact that δi = δ/δxi and it reduces to the sum from with i=1,2,3 of δxi/δxi = 1 + 1 + 1 I tried to do a similar thing with the second one, also using...
  11. O

    Derivation of complex refractive index

    Hi, Got a problem with the following derivation: Coming from the Helmholtz equation one gets: \textbf{n}^2=\muc^{2}(\epsilon+i\frac{\sigma}{\omega}) which is of course something like: \textbf{n}=n+i\kappa My question is, how do you obtain the following relations...
  12. S

    Understanding Index Notation: Allowed Combinations Explained

    I'm not sure if this is the correct place to ask this question, so please let me know if there is a better place for me to post it. I'm having trouble understanding index notation. I understand the basics, such as in the following examples: (a x b) = εijkajbk εijkεiab = δjaδkbδjbδka...
  13. A

    What is the index of refraction of the tank's walls?

    1. A particular fish tank filled with fresh water (n = 1.33) has a coral reef sticker stuck to the exterior wall outside the fish tank. The tank's walls are 2 cm thick, but a goldfish inside the tank sees the sticker 0.6 cm away from the water-wall interface. What is the index of refraction of...
  14. S

    QFT Index Question Homework: Solving Euler-Lagrange Equations w/ F_{mu,nu}

    Homework Statement I'm learning QFT and trying to do a basic problem finding the equations of motion from the Euler-Lagrange equation given a lagrangian. The lagrangian is in terms of: F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu} so then my issue comes in with this part of the...
  15. C

    Understanding Index Sets and Unions in Set Theory: Real Analysis Explained

    Homework Statement I'm reading through the introductory pages of my real analysis book and for some reason I can't wrap my head around this seemingly simple concept. The book is talking about collections of sets and something new to me called the "index set". I apologize ahead of time...
  16. X

    Help with conversion to index notation

    Homework Statement Use index notation to calculate the following: Let R = u x (d/du) hint: R_i = epsilon_ijk u_j (d/du_k) R . (u x [T . u]) where T is a traceless (T_ii = 0), symmetric, and constant (i.e, independant of u) second order tensor. Convert your final result to Gibbs'...
  17. O

    Raman transition - Index of refraction

    When one calculate the real part of the index of refraction for a specific multilevel atom one would use the following formula: Re(n(\Delta))=1+\frac{N e^2}{8\pi \epsilon_0 m\omega} \sum_i \frac{\Delta_i}{\Delta_i^2+(\gamma/2)^2}K_i Where K_i is the C-G coefficient. My question is as...
  18. A

    Young's double slit experiment with one slit covered with block of refractive index

    Homework Statement The interference pattern formed is given by I(θ)=4I0cos2(∏dsin(θ)/λ). For d=1×10-5m and λ=500nm plot the intensity pattern as a function of θ for small θ. How would this change if a block of material of thickness 500nm and refractive index n=1.5 were placed over one slit...
  19. caffeinemachine

    MHB Chromatic number vs chromatic index

    My friend gave me a question as a challenge. The question is: Let $G$ be a non-complete simple graph. Prove that $\chi (G) \leq \chi (L(G))$. Here $L(G)$ is the line graph of $G$ and $\chi (G)$ represents the chromatic number of $G$ and $\chi (L(G))$ is the chromatic number of $L(G)$ a.k.a...
  20. B

    Evaluate this index Integral containing Trig

    Homework Statement Folks Evaluate ##B_{11}## given ##\displaystyle B_{ij}=\int_0^1 (1+x) \frac{d \phi_i}{dx} \frac{ d\phi_j}{dx} dx## where ##\phi_i= sin i \pi x## and ##\phi_j=sin j \pi x## Homework Equations The Attempt at a Solution I calculate ##\displaystyle B_{ij}=\int_0^1...
  21. M

    How Can I Calculate Index Time Based On Distance Using Kinematic Equations?

    Hi All, I need to calculate the index time of the following: Max Velocity = 2700mm/s Accel = 4000mm/s/s Decel = 4000mm/s/s Index Distance = x What Equations do I need to utilize in order to calculate the total index time for a specified distance?
  22. Jim Kata

    Property of the index of a function

    Hi, I'm working through a paper and I am quite stupid so some things that maybe obvious are not obvious to me. Say you have some have some complex analytic function that is defined on some simply closed curve, and the index of this function defined on this curve is zero, \int_C...
  23. stripes

    VERY simple: String index out of bounds exception

    Homework Statement I am making a very, very simple program that takes in the date (of type string) from the user in the form DD/MM/YYYY. It then confirms whether or not the date is legitimate or not. For example, 09/07/2012 is valid, but 09/17/2012 is not valid. My program compiles...
  24. R

    Complex term in refractive index , in context to rayleigh scattering

    I was studying Rayleigh Scattering. The theory says that Rayleigh Scattering is approximated to x<<1 where x=(2*pi*r)/lambda where r is the radius of the particle scattering light and lambda is relative scattering wavelength of light. lambda = wavelength of light / refractive index of...
  25. J

    Refractive index and its effect upon conduction/insulation

    Dear All, thank you for taking the time to view my post. I am a Biologist and I have come across a curious characteristic of proteins that are structural constituents of Nerve cell sheaths (These proteins in addition to lipids surround nerve axons). In general, they seem to have a high...
  26. C

    GR - Trying to grasp index notation (Levi Civita)

    Homework Statement I'm trying to grasp how the indices are listed when writing out multiple vector products or divergences or gradients, etc. I'm working with 'An Introduction to General Relativity' by Hughston and Tod.Homework Equations A\wedge B = \varepsilon_{ijk}A_{j}B_{k} [A,B,C] =...
  27. M

    General formula for refractive index of moist air?

    Not sure if one exists but can anyone point me in the right direction? Looking for a formula which includes the temperature and partial/total pressure dependencies? I'm trying to find the trajectory of a photon through a cloud of varying (but known) temperature, pressure and humidity. If...
  28. S

    Standardized precipitation index formula

    Can some help me what really is the formula of the standardized precipitation index and how will it be computed? I am thinking of using the index to classify the 40 years into dry year, average year , or wet year using total annual rainfall data. I understand that SPI is an index based on the...
  29. E

    Low Cost, High Index of Refraction?

    I have my introductory physics students determine the index of refraction of various solids using fairly conventional methods (lining up pins or determining critical angle). I think this experiment would be more interesting if I could vary it more. I would like to find a substance with the...
  30. C

    Is H a Free Commutative Group of Rank n in Z^n?

    show that H is subgroup of finite index in Z^n exactly when H is free comutative group of rank n
  31. stripes

    Finding Array Element Index in Java?

    Homework Statement If I am given a regular, single dimensional array in Java, how do I search for an element in it, and then how do I get the index of that element? I have been trying: int largest; //some number that has been predetermined in earlier code int index3 =...
  32. R

    Index of refraction and thickness of materials

    Hi, my current research is to determine the thickness and the index of refraction of semiconductor materials.. using reflectivity.. my adviser gave me the results of the sample by GRAPHS the reflectance percentage vs. the wavelength.. i know that i can measure the index of refraction.. if i...
  33. V

    Negative index of refraction with anisotropy, quick question

    Hey all, I'm trying to solve a problem in which I have a uniaxial (uniform in two directions, different in the other) crystal with the optical axis normal to the plane of reflection. I call the permittivity parallel to the optical axis ε_par and the permittivity in the other two directions...
  34. E

    Index Notation: ∂_i 1/r = -x_i/r^3?

    Hello world, Index notation is driving me crazy: why on Earth is ∂_i 1/r = -x_i/r^3 ? I would expect it to be -x_i/r^2... Thanks for commenting
  35. J

    Index of Refraction of Outer/Interplanetary Space

    In electricity and magnetism, we typically assume that the relative permittivity (or dielectric constant) ε of air is equal to the "permittivity of free space" ε0, and likewise we assume that air has a relative permeability μ equal to the "permeability of free space" μ0. This is equivalent to...
  36. B

    Basis vectors and abstract index notation

    First of all, I'd like to say hi to all the peole here on the forum! Now to my question: When reading some general relativity articles, I came upon this strange notation: T^{a}_{b} = C(dt)^{a}(∂_{t})_{b} + D(∂_{t})^{a}(dt)_{b}. Can someone please explain to me what this means? Clearly...
  37. C

    Group refraction index, group velocity

    Can the group refractive index ng be 1>ng>0 ?
  38. A

    Can refractive index of a substance be increased?

    or is it possible to create a material with very high refractive index(order of 100's or more)
  39. E

    Amplitude reflection coefficient for high to low refractive index

    For a wave traveling from a medium with refractive index n1 to n2 with n2 > n1, the amplitude reflection coefficient is given by: r = (n2 - n1)/(n2 + n1) Consider a beam of light passing through a single pane of glass. There is a reflection at the front surface of the pane, with the...
  40. R

    Index of refraction related to wavelength & frequency

    I'm going through the Light & Optics chapter of Kaplan MCAT prep material & am having a hard time conceptually understanding the relationship between index of refraction & wavelength or with frequency. It says in the book that n = c/v, & "when the speed of the light wave varies with...
  41. A

    Index Raising in Linearized General Relavitiy

    I'm reading a few textbooks (Straumann, Schutz, Hartle) on GR and am a little confused working through a small part of each on linearized GR. 1. Relevant equations Using Straumann, the Ricci tensor is given by R_{\mu\nu} = \partial_{\lambda} \Gamma^{\lambda}_{\phantom{k}\nu\mu} -...
  42. B

    Maximal subgroups of solvable groups have prime power index

    I would like to ask if somebody can verify the solution I wrote up to an exercise in my book. It's kind of long, but I have no one else to check it for me :) Homework Statement If H is a maximal proper subgroup of a finite solvable group G, then [G:H] is a prime power.Homework Equations Lemma...
  43. T

    If z is one of the roots of unity with index n, find the sum

    Homework Statement Given the fact that z is one of the n-th roots of unity, find the sum below: 1 + 2z + 3z2 + ... + nzn-1Homework Equations (1-x)(1+x+...+xn-1) = 1 - xn The Attempt at a Solution honestly I don't know how to do this. any help is appreciated
  44. G

    Refraction in a medium with a gradient of refractive index

    Hi Folks, After a general search online, I have not yet found a simple description of refraction in a medium with an inhomogeneous refractive index. For example: if we have a block of glass with a beam of light shining through it, and the block has a gradient in the real part of the...
  45. F

    How to find subgroup of index n in a given group

    Dear Folks: Is there a general method to find all subgroups in a given abstract group?? Many Thanks! This question came into my classmates' mind when he wants to find a 2 sheet covering of the Klein Bottle. This question is equivalent to find a subgroup of index 2 in Z free product...
  46. L

    Refractive Index - A Mixing Question Answered

    Hi all, I am thinking about the refractive index, if I have two components with refractive index n1 and n2, respectively, then I mix them up (chemical reactions might happen after the mixing), and should I expect a mixture with refractive index:n=a*n1 + b*n2, where a+b=1. In other words...
  47. M

    Refraction and Complex refractive index

    Homework Statement At a wavelength of 400nm, the semiconductor ZnSe has a complex refractive index n= 3.0+0.32i A) If 400nm is incidient from air onto ZnSe with θ=tan-1(NR) = 71.6°, What is the refraction angle of the transmitted wave? B) Calculate the magnitude R and phase shift ψ...
  48. F

    How can frequency be used to calculate refractive index?

    How can i calculate the refractive index knowing only the frequency of the light entering the medium from air? n(refractive index) = (speed of light in vacuum) / (speed of light in medium)
  49. MathematicalPhysicist

    Understanding the Product Property of Maslov Index: A Proof Using Homotopy Axiom

    How do I show that Maslov index satisfies the next property (product property). Let \Lambda : \mathbb{R} / \mathbb{Z} \rightarrow \mathcal{L}(n), and \Psi : \mathbb{R}/\mathbb{Z} \rightarrow Sp(2n) be two loops, then if \mu is defined as the Maslov index then \mu(\Psi \Lambda )=...
  50. A

    Index raising and lowering: GR

    Homework Statement Consider a 2-dimensional line element: ds^2=x^2dx+2dxdy-dy^2 Raise and lower the indices of given vectors by finding the raised index metric, etc, blah blahHomework Equations V_a = (1,-1) and W^a = (0,1)The Attempt at a Solution Solution is given and I understand how to...
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