Identity Definition and 1000 Threads

Identity theft occurs when someone uses another person's personal identifying information, like their name, identifying number, or credit card number, without their permission, to commit fraud or other crimes. The term identity theft was coined in 1964. Since that time, the definition of identity theft has been statutorily defined throughout both the U.K. and the United States as the theft of personally identifiable information. Identity theft deliberately uses someone else's identity as a method to gain financial advantages or obtain credit and other benefits, and perhaps to cause other person's disadvantages or loss. The person whose identity has been stolen may suffer adverse consequences, especially if they are falsely held responsible for the perpetrator's actions. Personally identifiable information generally includes a person's name, date of birth, social security number, driver's license number, bank account or credit card numbers, PINs, electronic signatures, fingerprints, passwords, or any other information that can be used to access a person's financial resources.Determining the link between data breaches and identity theft is challenging, primarily because identity theft victims often do not know how their personal information was obtained. According to a report done for the FTC, identity theft is not always detectable by the individual victims. Identity fraud is often but not necessarily the consequence of identity theft. Someone can steal or misappropriate personal information without then committing identity theft using the information about every person, such as when a major data breach occurs. A US Government Accountability Office study determined that "most breaches have not resulted in detected incidents of identity theft". The report also warned that "the full extent is unknown". A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the probability of becoming a victim to identity theft as a result of a data breach is ... around only 2%". For example, in one of the largest data breaches which affected over four million records, it resulted in only about 1,800 instances of identity theft, according to the company whose systems were breached.An October 2010 article entitled "Cyber Crime Made Easy" explained the level to which hackers are using malicious software. As Gunter Ollmann,
Chief Technology Officer of security at Microsoft, said, "Interested in credit card theft? There's an app for that." This statement summed up the ease with which these hackers are accessing all kinds of information online. The new program for infecting users' computers was called Zeus; and the program is so hacker-friendly that even an inexperienced hacker can operate it. Although the hacking program is easy to use, that fact does not diminish the devastating effects that Zeus (or other software like Zeus) can do to a computer and the user. For example, programs like Zeus can steal credit card information, important documents, and even documents necessary for homeland security. If a hacker were to gain this information, it would mean identity theft or even a possible terrorist attack. The ITAC says that about 15 million Americans had their identity stolen in 2012.

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  1. N

    The Summation Identity (Combinatorics)

    Homework Statement Use the Summation Identity to count the cubes of all integers sizes formed by an n by n by n assembly of cubes. Homework Equations Summation Identity: Sum [from i = 0 to n] (i choose k) = (n+1 choose k+1). Sum [from i = 0 to n] (i^3) = (n^2)(n+1)^2 / 4 = (sum[from...
  2. L

    How Does the Laplacian Affect the Helmholtz Equation in Spherical Coordinates?

    Homework Statement required to prove: (\nabla^2+k^2)\frac{e^{ikr}}{r}=-4\pi\delta (r) Homework Equations im assuming we are working in spherical coordinates (not sure - could be cylindrical/2D polar) laplacian for spherical (considering its only a function of r) is...
  3. C

    Verify "Sin2(x)Cos2(x) - Cos2(x) = 0" Identity

    Homework Statement Verify that \frac{Csc(x)}{Cot(x)+Tan(x)}=Cos(x) is an identity. Homework Equations All of the trigonometric identities. Sin^{2}+Cos^{2}=1; tan^{2}+1=Sec^{2}; 1+Cot^{2}=Csc^{2}; etc. The Attempt at a Solution I've literally written about five pages worth trying...
  4. B

    Need Help with Trig Identity Problem - Any Assistance Appreciated!

    Hey all, hope you could help me, would be very gratefull if you could. Homework Statement Show that sin(x) + cos(x) = √2sin(x + π/4) Homework Equations sin(x+z) = sin(x)cos(z)+sin(z)cos(x) The Attempt at a Solution Ive been doing some of these trig identity problems without an...
  5. J

    Simple Rings: Commutativity and Identity

    Hello everyone, i was checking out a paper on simple rings http://www.imsc.res.in/~knr/RT09/sssrings.pdf and they said that all commutative simple rings are fields. i just don't see why they should have identity. thank you.
  6. F

    Vector identity show that question

    Homework Statement u and v are vectors Homework Equations show that : mod(u x v)^2 +(u.v)^2 = mod(u)^2 x mod(v)^2 The Attempt at a Solution I thought about let u =(a,b,c) let v = (x,y,z) and then doing the calculations. However I have done this but then squaring everything out...
  7. M

    Understanding Ward Identity and Its Connection to Gauge Invariance

    This is a question about Ward-Takahashi Identity.I go through the materials presented about Ward Identity in Peskin's book. there are two sections where mentioned this identity. First, in section 5.5, when the author discussed photon polarization sums. Second, in section7.4, where the author...
  8. kreil

    Proving Identity for Generalized Sum S(x)

    Homework Statement In order to solve the problem I am working on, I have to prove the following generalized problem, S(x)=\sum_{n=0}^{\infty} n x^n =\frac{x}{(x-1)^2} for |x|< 1 I evaluated this sum using Wolfram Alpha. Clearly it looks related to the geometric series solution, but I am...
  9. A

    What Is Dirac's Identity in Minkowski Spacetime?

    Do somebody knows anything about the Dirca's identity? \begin{equation} \label{Dirac} \frac{\partial^2}{\partial x_{\mu}\partial x^{\mu}} \delta(xb_{\mu}xb^{\mu}) = -4\pi \delta(xb_0)\delta(xb_1)\delta(xb_2)\delta(xb_3) \end{equation} here xb, is the 4-vector $x-b$ in Minkowsky spacetime...
  10. R

    Solving Integral Identity: Gradstein & Ryzhik

    Hey folks! I'm trying to figure out an identity from a paper on dimensional regularization. Here's the identity: -\frac{1}{2}\frac{d}{ds}|_{s=0}\int_0^\infty \frac{d^4k}{(2\pi)^4}(k^2+m^2)^{-s} after performing the k-integral this becomes...
  11. P

    Simple identity for antisymmetric tensor

    Is it true that for all antisymmetric tensors F^{\mu\nu} the following identity is true: \nabla_\mu \nabla_\nu F^{\mu\nu}=0 (I've checked it but I'm not absolutely sure).
  12. A

    Hardest Identity Evar involving sum and differences

    Homework Statement sin (x) + sin (3x) + sin (5x) + sin (7x) = 4cos(x)cos(2x)sin(4x) Homework Equations sin(a+b)=sin(a)cos(b)+sin(b)cos(a) sin(a-b)=sin(a)cos(b)-sin(b)cos(a) The Attempt at a Solution Me and four of my classmates have tried to do this proof and it kicked our ***...
  13. M

    Understanding the Vector Identity and Its Matrix Representation

    vector identity?? Homework Statement The text that I'm reading has a line that reads \left(\mathbf{b}\mathbf{k}\cdot-\mathbf{b}\cdot\mathbf{k}\right)\mathbf{v}=\omega\mathbf{B} and I'm not sure what it means by \mathbf{b}\mathbf{k}; it's clearly not the dot product nor the cross product. A...
  14. moe darklight

    I've never felt dumber: me understand Fibonacci identity.

    This is crazy. I have no idea what the textbook is saying at the end. So far, so good. Then this flies at me out of nowhere: We do?? Where the hell did that come from? I've never stared at something for so long without having the slightest clue what is going on. I held up the whole class...
  15. Amith2006

    Does Measurement in the X Direction Affect Y Coordinate in Quantum Systems?

    Does x & y directions commute? Seem trivial! Just wondering whether any measurement made in the x direction affect it's y coordinate.
  16. D

    Verifying Identity: tan^2(x/2)=(sec x-1)/(sec x+1)

    Homework Statement tan^2(x/2)=(sec x-1)/(sec x+1) Homework Equations The Attempt at a Solution
  17. J

    Why Use Different Trig Identities for Standing Waves and Superposition?

    Homework Statement For two waves in superposition, we have, let say \[y_{1} = Asin(kx-wt), y_{2} = Asin(kx-wt+\Phi )\] We use the trig identity sin A + sin B to simplify the combination Whereas for standing waves, we use the trig identity sin(a +/- b) to combine the result. As I...
  18. Char. Limit

    Identity true in the reals, not in complex?

    Are there any identities that are true for all real numbers, but not for all complex numbers? The only one I can think of is... \sqrt{ab}=\sqrt{a}\sqrt{b} Which is only true if a and b are POSITIVE, not real. But is there any identity that works for all real numbers, but fails for complex...
  19. kreil

    Prove Commutator Identity: e^xA B e-xA = B + [A,B]x + ...

    Homework Statement Prove the following identity: e^{x \hat A} \hat B e^{-x \hat A} = \hat B + [\hat A, \hat B]x + \frac{[\hat A, [\hat A, \hat B]]x^2}{2!}+\frac{[\hat A,[\hat A, [\hat A, \hat B]]]x^3}{3!}+... where A and B are operators and x is some parameter. Homework Equations...
  20. B

    Vector identity proof using index notation

    Homework Statement Using index notation to prove \vec{\nabla}\times\left(\vec{A}\times\vec{B}\right) = \left(\vec{B}\bullet\vec{\nabla}\right)\vec{A} - \left(\vec{A}\bullet\vec{\nabla}\right)\vec{B} + \vec{A}\left(\vec{\nabla}\bullet\vec{B}\right) -...
  21. maverick280857

    Proving Schwinger's Identity: A Challenge for Mathematicians

    Hi, I'm working my way through Schwinger's paper (http://www.physics.princeton.edu/~mcdonald/examples/QED/schwinger_pr_82_664_51.pdf" ) and I came across the following identity -(\gamma\pi)^2 = \pi_{\mu}^2 - \frac{1}{2}e\sigma_{\mu\nu}F^{\mu\nu} where \pi_{\mu} = p_{\mu} - eA_{\mu}...
  22. C

    Applied Algebra (Prove the identity)?

    let m,n be positive integer. Prove the identity: sum (i from 0 to k): { C(m, i) * C(n, k - i) } = C(m + n, k) Hint: Consider the polynomial equation: sum (k from 0 to m+n) {C(m + n, k) *z^k } = (1 + z)^(m+n) = ((1+z)^m) * ((1+z)^n) I tried long time, still have no idea.
  23. Fredrik

    Is Simplifying Group Axioms to Just Left Identity and Inverses Valid?

    Consider a binary operation on a set G. A an element e of G is said to be a left identity if ex=x for all x. If x is in G, an element y of G is said to be a left inverse of x if yx is a left identity. A right identity and right inverse is defined similarly. Is the following an adequate...
  24. R

    Multiplicative Identity under Matrix Multiplication

    I've been asked by my professor to identify a group of singular matrices. At first, I did not think this was possible, since a singular matrix is non-invertible by definition, yet to prove a groups existence, every such singular matrix must have an inverse. It has been brought to my...
  25. R

    Solution to Cauchy's Identity Problem #20

    Can anyone provide me solution to this identity http://books.google.com/books?id=PJeHprppOLsC&printsec=frontcover&dq=complex+variables&hl=en&ei=rFl7TMj0E4P-8AbNgOGFBw&sa=X&oi=book_result&ct=book-thumbnail&resnum=2&ved=0CDYQ6wEwAQ#v=onepage&q&f=false" page 10 , problem 20
  26. J

    Proving an identity to have solutions over all the integers

    Hello, I was looking at some math problems and one kind caught my attention. The idea was to prove that let's say 3x+2y=5 has infinitely many solutions over the integers. Can someone show me the procedure how a problem like this might be solved?
  27. Y

    Understanding Green's Identity: Solving Laplace Equation for Harmonic Functions

    Harmonic function satisfies Laplace equation and have continuous 1st and 2nd partial derivatives. Laplace equation is \nabla^2 u=0. Using Green's 1st identity: \int_{\Omega} v \nabla^2 u \;+\; \nabla u \;\cdot \; \nabla v \; dx\;dy \;=\; \int_{\Gamma} v\frac{\partial u}{\partial n} \; ds...
  28. G

    Proof of complex number identity

    Homework Statement Attached question Homework Equations The Attempt at a Solution The second part of question is relatively easy, it is the first part of the question where I need help with(using arg zw = arg z + arg w to show arg z^n = n arg z). Also, is the question asking...
  29. K

    Need help to prove this Identity

    Help! I spent 3 hours attempting this question. Prove the following identity : (tan x + sec x -1) / (tan x - sec x + 1) = tan x + sec x I've simplified Left Hand Side into cos and sine. Which ended up like this (sine x - cos x + 1) / (sine x + cos x -1) Then I'm stuck. Any help is...
  30. E

    What do you think of people who have fake identity?

    what do u think of people who have face identity? are they liar or sick? can u trust them? it happens on net a lot that people introduce themselves somebody else. some of them try to impress others by telling lies but i know of so many people who just tell lies about their names...
  31. Simfish

    QM: Sum of projection operators = identity operator?

    Homework Statement So we have an observable K = \begin{bmatrix} 0 & -i \\ -i & 0 \end{bmatrix} and its eigenvectors are v1 = (-i, 1)T and v2 = (i, 1)T corresponding to eigenvalues 1 and -1, respectively. Now if we take the outer products, we get these... |1><1| = (-i, 1)T*(i, 1) =...
  32. T

    Trigonometric Identity Verification | Simplifying sin(4x) and Solving for x

    Homework Statement sin(4x) = 8cos3(x)sin(x)-4sin(x)cos(x) Homework Equations All trigonometric identities The Attempt at a Solution I can simplify the right side using the double angle identity to: sin(4x) = 4sin(2x)cos2(x)-2sin(2x) However, now I'm not sure what to do. Did...
  33. S

    The true mystery is Identity NOT Mechanics

    A lot has been discussed/posted about various models/theories to explain consciousness, the systems of laws, fundamental physics, emergence, upward and downward causality etc. However I think too much of these theories focus on GENERAL universals and ultimately on the mechanisms, but not on...
  34. S

    Trig identity in complex multiplication

    Just wondering how this is simplified to the third line: If w, z are complex numbers wz = rs( cos\alpha + isin \alpha ) (cos \varphi + isin \varphi) wz = rs(cos\alpha cos \varphi - sin \alphasin\varphi) + i(sin \alphacos\varphi + cos \alpha sin \varphi)) wz = rs(cos (\alpha...
  35. A

    How Can the Hermite Polynomial Identity Be Proven?

    Does anyone know how to prove the following identity: \Sigma_{k=0}^{n}\left(\stackrel{n}{k}\right) H_{k}(x)H_{n-k}(y)=2^{n/2}H_{n}(2^{-1/2}(x+y)) where H_{i}(z)represents the Hermite polynomial?
  36. L

    Is this valid when using arctanh ln identity?

    Hi, I start with arctanh\left(\frac{A}{\sqrt{A^2-1}}\right)=\frac{1}{2}ln\left( \frac{1+\frac{A}{\sqrt{A^2-1}}}{1-\frac{A}{\sqrt{A^2-1}}}\right) The function \frac{A}{\sqrt{A^2-1}} is real, and since A>1, it too is always greater than 1. Is it true that it should really be the modulus...
  37. C

    Integral Identity: Showing LHS = RHS

    1. By considering, seperately, each component of the vector A, show that \iint A(u.n) ds = \iiint {(u.\nabla)A + A(\nabla.u)} dV (A,u and n are vectors) Homework Equations 3. Attempt at solution L.H.S. Let A = a\vec{i} + b\vec{j} + c\vec{k} \iint (a\vec{i} +...
  38. C

    Understanding Vector Integrals: A Closer Look at Integral Identity 1

    1. By considering each component of the vector A show that \iint A(u.n)ds = \iiint{(u.nambla)A+A(nambla.u)}dV (A,u and n are vectors) Homework Equations 3. Let A = ai + bj + ck. L.H.S: \iint ai (u.n)ds + \iint bj (u.n)ds +\iint ck (u.n)ds R.H.S. = \iiint(u.nambla)ai dV+...
  39. E

    Symmetric difference of set identity

    Is there a shorter way to verify this identity, as you can see I haven't even finished it. I know you can use Ven diagrams and truth tables but I wanted to avoid them inorder to use a more general formal approach. picture is attached
  40. W

    Identity map and Inverse Image

    Hello everyone, I would like to ask what's the purpose of identity map? Recently I came across something that apparently use this to find the inverse image of a function F(x) in the form of F(x) = ( f(x) , x ) . Thanks. Wayne
  41. P

    Identity proof using Stoke's Theorem

    Homework Statement Show using Stoke's Theorem that S is an open surface with boundary C (a space curve). f(\vec r) is a scalar field. Homework Equations Stoke's theorem \iint_S (\nabla\times \vec F) \cdot d\vec S = \int_C F \cdot d\vec r The Attempt at a Solution Thus far...
  42. L

    Deriving Lagrange's Trig Identity: Real Part of Complex # in Exp Form

    Homework Statement I did the question with help, but did not understand why did we multiply e^-i(x/2) How do I know what to multiply for getting the real part of a complex number in exponential form? Homework Equations The Attempt at a Solution
  43. K

    Trigonometric identity for inverse tan

    Hello, Could you please clarify if this is correct: If tan^(-1)(x) = Pi/2 - tan^(-1)(1/x) Then if we have (ax) as the angle where a is a constant, do we get: tan^(-1)(ax) = Pi/2 - tan^(-1)(a/x) or does the constant go on the bottom with the x? i.e. or: tan^(-1)(ax) = Pi/2 -...
  44. M

    Inverse trig functions and pythagorean identity

    Hi. I'm having trouble trying to understand the relationship between inverse trig functions, especially arcsin x, and pythagorean identity. I know that because cosx=sqrt(1-(sinx)^2), derivative of arcsin x is 1/(cos(arcsin x)) = 1/(sqrt(1-(sinx)^2)arcsinx)) = 1/(sqrt(1-x^2). But how does...
  45. Ivan Seeking

    The identity thief in your office

    http://www.identitytheft.com/article/are_photocopiers_a_risk
  46. E

    Complex variables conformal mapping trig identity

    Homework Statement map the function \begin{equation}w = \Big(\frac{z-1}{z+1}\Big)^{2} \end{equation} on some domain which contains z=e^{i\theta}. \theta between 0 and \pi Hint: Map the semicircular arc bounding the top of the disc by putting $z=e^{i\theta}$ in the above formula. The...
  47. J

    Vector Analysis Identity simplification/manipulation

    Homework Statement Let \mathbf{G}(x,y,z) be an irrotational vector field and g(x,y,z) a C^1 function. Use vector identities to simplify: \nabla\cdot(g\nabla \times (g\mathbf{G})) Homework Equations The '14 basic vector identities' The Attempt at a Solution I tried using the...
  48. M

    Proving Vector Identity Using Standard Identities of Vector Analysis

    Homework Statement Let F(x,y,z) be an irrotational vector field and f(x,y,z) a C^1 scalar functions. Using the standard identities of vector analysis (provided in section 2 below), simplify (\nabla f \times F) \cdot \nabla f Homework Equations Note: The identities below require...
  49. M

    Proof of Vector Identity Using Standard Identities | C^2 Scalar Functions

    Homework Statement Let f(x,y,z), g(x,y,z), h(x,y,z) be any C^2 scalar functions. Using the standard identities of vector analysis (provided in section 2 below), prove that \nabla \cdot ( f \nabla g \times \nabla h ) = \nabla f \cdot ( \nabla g \times \nabla h) Homework...
  50. M

    C^1 or C^2? Investigating Vector Identity

    One of the basic vector identities is \nabla \cdot (\nabla f \times \nabla g) = 0 Is this true if f and g are C^{1} ? (Or they must be C^{2} functions? Thanks!
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