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 A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the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. P

    Is δ(x+y)=δ(x-y) for Dirac Delta Function?

    Homework Statement Good day. May I know, for Dirac Delta Function, Is δ(x+y)=δ(x-y)? The Attempt at a Solution Since δ(x)=δ(-x), I would say δ(x+y)=δ(x-y). Am I correct?
  2. hxthanh

    MHB Summation: trigonometric identity

    Prove that: $\displaystyle\sum_{k=0}^n \frac{\cos(k x)}{\cos^kx} = \frac{1+(-1)^n}{2\cos^nx} + \dfrac{2\sin\big(\lfloor\frac{n+1}{2}\rfloor x\big) \cos\big(\lfloor\frac{n+2}{2}\rfloor x\big)} {\sin x\cos^n x} \qquad\qquad (\frac{2x}{\pi}\not\in \mathbb Z)$ *note: $\lfloor x\rfloor$ is floor...
  3. T

    Interpretation for identity with binomial coefficients

    I am looking for a counting interpretation to make the following identity evident: \sum_{k=0}^{n-j}(-1)^k\binom{j-1+k}{j-1}\binom{n}{j+k} = 1 The form of it looks like inclusion-exclusion. The sum is 1, more or less independent of j. So that makes me think it would be something like "how...
  4. TheFerruccio

    Prove the following tensor identity

    I am back again, with more tensor questions. I am getting better at this, but it is still a tough challenge of pattern recognition. Problem Statement Prove the following identity is true, using indicial notation: \nabla\times(\nabla \vec{v})^T = \nabla(\nabla\times\vec{v}) Attempt at...
  5. Y

    Proving uniqueness of inverse by identity (Groups)

    1. Which of the following is a group? To find the identity element, which in these problems is an ordered pair (e1, e2) of real numbers, solve the equation (a,b)*(e1, e2)=(a,b) for e1 and e2. 2. (a,b)*(c,d)=(ac-bd,ad+bc), on the set ℝxℝ with the origin deleted. 3. The question...
  6. C

    Proving the Gamma Matrix Identity in QFT: Is There a Mistake in My Attempt?

    Homework Statement Prove that \gamma^{a}\gamma^{b}\gamma^{c}\gamma^{d}\gamma^{e}\gamma_{a} = 2\left(\gamma^{e}\gamma^{b}\gamma^{c}\gamma^{d}+\gamma^{d}\gamma^{c} \gamma^{b}\gamma^{e}\right) Each of the \gamma^{i}s are as used in the Dirac equation. Homework Equations...
  7. C

    Covariant derivative of a commutator (deriving Bianchi identity)

    Hi. I'm trying to understand a derivation of the Bianchi idenity which starts from the torsion tensor in a torsion free space; $$ 0 = T(X,Y) = \nabla_X Y - \nabla_Y X - [X,Y]$$ according to the author, covariant differentiation of this identity with respect to a vector Z yields $$$ 0 =...
  8. X

    Quantum Mechanics: Show that this identity is true

    Homework Statement Show that.. e^{L}a e^{-L}=a+[L,a]+\frac{1}{2!}[L,[L,a]]+\frac{1}{3!}[L[L[L,a]]]+... Where L and a are operators. The Attempt at a Solution Right now I am writing the exponentials as their Taylor expansions, and then expanding the RHS of the above equation to see...
  9. C

    Misunderstanding part of pascals identity algebraic proof

    I understand the combinatorial proof and the common sense behind why it works but lately I am trying to play around with proofs since I am still new to them. So I understand part of this...
  10. M

    Tryimg to understand this logarithmic identity

    (I know the title contains a typo, but I can't edit it!) I'm trying to understand and/or prove this identity: blogbx = x I've inserted numbers, and it does work, but I just don't seem to understand why. I mean, some identities are obvious, like: logb bx = x since bx = bx but I can't make...
  11. M

    Is it possible to completely change your identity and start a new life?

    I've been watching a TV series recently called Person of Interest, it's really cool you should check it out. I'm curious though about people who somehow manage to completely wipe their identity and literally become a nobody and then acquire a new identity. I think legally the most thorough...
  12. A

    Trying to prove a trig identity

    Homework Statement prove that (sinA +sin3A + sin5A)/(cosA + cos3A + cos5A) = tan3A Homework Equations sinP + sinQ = 2sin((P+Q)/2)cos((P-Q)/2) cosP + cosQ = 2cos((P+Q)/2)cos((P-Q)/2) The Attempt at a Solution (sin3A + sinA) + sin5A = 2sin2AcosA + 2sin((5/2)A)cos((5/2)A) (cos3A +...
  13. G

    Understanding if you come up with an equation or an identity

    Hi guys! When I'm doing math problems with multiples variables and I have to build up equations, I often come up with identities rather than the variable equal to a value. Is there anyway to understand how we have to build up the equations without obtaining an identity at the end? Thank you.
  14. Mathelogician

    MHB Question on the concept of " Identity "

    Hi all; Look at the attached part from Van Dalen's Logic and structure. What is he doing exactly? In axiomatizing 'Identity' as he does, what is gained rather than what we had before (i.e., looking at 'Identity' as a binary predicate)?! Even in the axioms, he is again using a symbol in the...
  15. R

    MHB Lagrange's Identity and Cauhchy-Schwarz Inequality for complex numbers

    I guess the best way to start this is by admitting that my conceptual understanding of the Cauchy-Schwarz Inequality and the Lagrange Identity, as the title suggests, is not as deep as it could be. I'm working through Marsden's 3e "Basic Complex Analysis" and it contains a proof of the Cauchy...
  16. lalo_u

    Right handed neutrino identity

    I am reading Mohapatra's book: "Massive Neutrinos in Physics and Astrophysics". At the beginning of chapter 7, it is sought expressions where the right neutrino was considered in the Electroweak Standard Model. Everything was fine until I found the expression...
  17. PhizKid

    Exterior derivative identity in vacuum space-time

    I was reading a paper by Geroch and I was confused by the following: given a scalar field ##\omega## satisfying ##\nabla_{a}\omega = \omega_{a} = \epsilon_{abcd}\xi^{b}\nabla^{c}\xi^{d}## and the scalar ##\lambda = \xi^{a}\xi_{a}##, where ##\xi^{a}## is a killing vector field, can someone prove...
  18. D

    MHB Trying to resolve a trig identity

    I am trying to resolve a trig identity for some notes I am typing up. On paper, I wrote recall $e(\sin(E_1) - \sin(E_0)) = 2\cos(\zeta)\sin(E_m)$. I have no idea what I am recalling this from now at least. Identities I have set up are: \begin{align} E_p &= \frac{1}{2}(E_1 + E_2)\\ E_m &=...
  19. R

    Evaluating Hermite Identity with Integers: Help with Homework Equations

    Homework Statement Let a and b be integers and m an integer >1 Evaluate [b/m] + [(b+a)/m]+ [(b+2a)/m]+ [(b+3a)/m]+ [(b+4a)/m]+ [(b+5a)/m]+...+ [(b+(m-1)a)/m] Homework Equations The Attempt at a Solution i tried to use hermite identity. [x] + [x + 1/n] + [x + 2/n] +...+ [x +...
  20. P

    Use the Jacobi identity to show Lie algebra structure constant id.

    Homework Statement Use the Jacobi identity in the form $$ \left[e_i, \left[e_j,e_k\right]\right] + \left[e_j, \left[e_k,e_i\right]\right] + \left[e_k, \left[e_i,e_j\right]\right] $$ and ## \left[e_i,e_j\right] = c^k_{ij}e_k ## to show that the structure constants ## c^k_{ij} ## satisfy the...
  21. anemone

    MHB How to Prove this Trigonometric Identity?

    Prove \frac{\sin\left(5\tfrac{3}{4}^{\circ} \right)}{\cos\left(17\tfrac{1}{4}^{\circ} \right)}+\frac{\sin\left(17\tfrac{1}{4}^{\circ} \right)}{\cos\left(51\tfrac{3}{4}^{\circ} \right)}+\frac{\sin\left(51\tfrac{3}{4}^{\circ} \right)}{\cos\left(155\tfrac{1}{4}^{\circ}...
  22. C

    Why does dimensional regularization respect the Ward identity?

    It is often stated that this is the case, but I have often wondered if it is a general statement or just something that we observe to be the case when calculating the relevant loop corrections. Can it be proven generally? Is it somehow easy to see?
  23. C

    Does the Ward identity rescue a zero photon mass?

    In Peskin at page 248 he finds that if he calculates the vacuum polarization that $$\Pi(q)^{\mu \nu} \propto g^{\mu \nu}\Lambda^2$$ a result which violates the Ward identity and would cause a non-zero photon mass $$M \propto \Lambda$$. But as Peskin states, the proof of the Ward identity...
  24. T

    How to Solve Trig Identity Questions: Tips and Examples

    Hey guys,I need some help on the following trig identities: 1) sin2x = 2tanx/1+tan^2x 2) sin2x/sinx - cos2x/cosx = secx My attempts: 1) LS: sin2x 2sinxcosx 2sinx/cosx 2tanx/1+tanx Not sure if this is right or not. I kind of understand my third step but it just doesn't seem...
  25. D

    Fourier Series & Parceval's identity

    Homework Statement Calculate the following integral: \int_{0}^{2\pi}(\sum_{k=0}^{\infty} \frac{\cos(kx)}{3^k})^2 dx Homework Equations Parseval's identity: \frac{1}{2 \pi} \int_{-\pi}^{\pi} {|f(x)|^2 dx} = \sum_{n=0}^{\infty} {|a_n|^2+|b_n|^2} Where a_n, and b_n are the trigonometric...
  26. K

    How can vector identity be applied to compute electric and magnetic fields?

    Homework Statement I want to compute the electric field knowing the magnetic field using a vector identity Homework Equations E=i \frac{c}{k} (∇\timesB) B(r,t)=(μ0ωk/4π) (\hat{r}×\vec{p})[1-\frac{1}{ikr}](eikr/r) \vec{p}=dipole moment,constant vector we have ti use the identity...
  27. C

    Ward identity from Ward-Takahashi identity?

    The Ward-Takahashi identity for the simplest QED vertex function states that $$q_\mu \Gamma^\mu (p + q, p) = S^{-1}(p+q) - S^(p)^{-1}.$$ Often the 'Ward-identity' is stated as, if one have a physical process involving an external photon with the amplitude $$M = \epsilon_\mu M^\mu$$...
  28. C

    MHB How Do You Prove a Logarithmic Identity Involving Powers of x?

    Hello MHB. How can i proof this equation? log(x).log(x^2).log(x^3)... log(x^90)=4095
  29. DiracPool

    How to Derive Euler's Identity?

    Hello. Please tell me how do I derive: cos(θ)=1/2 (e^{iθ}+e^{-iθ}) from: e^{iθ}=cos(θ) + isin(θ) as well as: sin(θ)=1/2i (e^{iθ}-e^{-iθ}) I can't figure it out...for example, where does the 1/2 come from? Thank you:smile:
  30. L

    Help Understanding Trig Identity

    Hello there, I have a problem I'm hoping someone can help me with. I'm writing a bit of code for computing the value of pi that converges faster than a previous piece that relies on the leibniz series. Anyway, I'm struggling with showing how this identity arises. tan(2t) = 2 * tan(t) / 1 -...
  31. B

    Uniqueness of identity elements for rectangular matrices

    Let A be the set of n \times n matrices. Then the identity element of this set under matrix multiplication is the identity matrix and it is unique. The proof follows from the monoidal properties of multiplication of square matrices. But if the matrix is not square, the left and right...
  32. MarkFL

    MHB Chloe's question at Yahoo Answers involving the angle sum identity for cosine

    Here is the question: Here is a link to the question: Help with precalculus! Sum or difference formula? - Yahoo! Answers I have posted a link there to this question so the OP can find my response.
  33. T

    Using trig identity to simplify?

    I have this equation 1/(r^2+l^2)^(3/2) and I need to integrate it quickly. My first thought is using this integral formula 1/(1+x^2)^(3/2)=x/sqrt(1+x^2) but how exactly do I get my equation into that form?
  34. E

    Confirming a Summation Identity

    Hi all, I found this "identity" online on Wikipedia, and realized that it would actually come in pretty useful for me, if only I could prove that it is true. Can you guys help me on that?: $$\sum_{k=1}^nk^m=\frac{1}{m+1}\sum_{k=0}^{m}\binom{m+1}{k}B_k\;n^{m-k+1}$$ where ##B_k## denotes the kth...
  35. A

    Proving This Trigonometric Identity

    1. Prove:\frac{cscx +cotx}{cscx-cotx} = \frac{1+2cosx+cos^2x}{sin^2x} Homework Equations tanx = \frac{sinx}{cosx} cotx = \frac{cosx}{sinx} cscx secx cotx sin^2x + cos^2x = 1 The Attempt at a Solution Left side: =\frac{cscx +cotx}{cscx-cotx} =\frac{1/sinx + cosx / sinx}{1/sinx - cosx/sinx}...
  36. E

    Trigonometric identity from Euler's intro to analysis of infinite

    So I'm trying to get through euler's introduction to the analysis of the infinite so I could eventually read his books on calculus but I'm stuck somewhere and can't seem to figure out how he equates this identity so by expanding I get sin(2y) * cos(z) + cos(2y) * sin(z). I get that the...
  37. G

    Quantum objects and the law of identity over time

    Over the years, I am slowly becoming more radicalized about what QM is trying to tell us about our world. I am coming to a point where I am close to giving up entirely by just saying that it tells us nothing at all (don't get too bothered by this statement... just let me explain...). We are...
  38. Y

    Can the Chain Rule be Applied to Show the Identity in Vector Calculus Homework?

    Homework Statement \widetilde{F}(r)=F1(r)i+F2(r)j+F3(r)k \hat{r}=r/r r(x,y,z)=xi+yj+zk, r=abs(r)=sqrt(x2+y2+z2) (Hint: The chain rule will be helpful for this question.) Show that: \nabla\cdotF = \hat{r}\cdotdF/dr. Homework Equations The Attempt at a Solution My attempt...
  39. C

    Sum to Product Trigonometric identity does not work

    "Sum to Product" Trigonometric identity does not work Hi, The identity sin(u) + sin(v) = 2 * sin (\frac{u+v}{2}) * cos(\frac{u-v}{2}) http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Product-to-sum_and_sum-to-product_identities Does not always work. I put the equation : (sin(u)...
  40. quasar987

    Jacobi identity in local coordinates?

    Jacobi identity in local coordinates?!? Apparently (i.e. according to an article written by physicists), the Jacobi identity for the Poisson bracket associated to a Poisson bivector \pi = \sum\pi^{ij}\partial_i\wedge\partial_j is equivalent to...
  41. WannabeNewton

    Energy-momentum tensor identity - linearized gravity

    Homework Statement Consider a stationary solution with stress-energy ##T_{ab}## in the context of linearized gravity. Choose a global inertial coordinate system for the flat metric ##\eta_{ab}## so that the "time direction" ##(\frac{\partial }{\partial t})^{a}## of this coordinate system agrees...
  42. S

    Solving Identity Matrices Homework Problems

    Homework Statement Homework Equations ImA = AIn = A. (A−1)−1 = A (AB)−1 = B−1A−1 The Attempt at a Solution Determinates: Det(A) = 3 – 0 = 3 Det (2A+BT) = 4 – 8 = -2 Matrices B^T = 2 -2 0 -5 (2A + B^T)^-1 = -8 -4 -8 -2 So I've kinda figured...
  43. MarkFL

    MHB Katlynsbirds' question at Yahoo Answers regarding inverse trigonometric identity

    Here is the question: Here is a link to the question: Prove the identity, pre calc!? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  44. anemone

    MHB Simplifying the Summation Identity Using Complex Numbers

    Hi, I have been trying to solve this difficult problem for some time and I thought of at least two ways to prove it but to no avail...the second method that I thought of was to employ binomial expansion on the denominator and that did lead me to the result where it only has x terms in my final...
  45. S

    3x3 Identity and rotation matrices and how they work

    I'm trying to rotate a point about the origin (0,0,0) and starting with an identity matrix, this works fine for the x- and y-rotation axes, but fails with the z-axis, where the point just sits in place. \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} M_{ID} \times M_Z...
  46. K

    Rund-Trautman Identity Electromagnetic Field

    I have been having trouble with a bunch of examples to do with the Rund Trauman Identity. I have the identity in this form/notation: \frac {\partial L}{\partial q^ \mu}\zeta ^\mu+p_\mu \dot \zeta^\mu+\frac{\partial L}{\partial t}\tau-H \dot \tau=\frac{dF}{dt} Now for the...
  47. P

    Prove identity sec^-1(x) = cos^-1(1/x)

    Homework Statement Find and prove the identity sec^-1(x) in terms of cos^-1(arg) (Note that 1/cos^-1(x) is not equal to sec^-1(x). Homework Equations None. The Attempt at a Solution sec(sec^-1(x)) = x 1/cos(sec^-1(x)) = x 1/cos(cos^-1(x)) = 1/x 1/cos(cos^-1(1/x)) = 1/1/x...
  48. trollcast

    Proving Trig Identity: $\csc(2\theta)-\cot(2\theta)\equiv\tan(\theta)$

    Homework Statement Prove the identity: $$\csc(2\theta)-\cot(2\theta)\equiv\tan(\theta)$$ Homework Equations The Attempt at a Solution Starting with the LHS: $$\csc(2\theta)-\cot(2\theta)$$ $$\frac{1}{\sin(2\theta)}-\frac{\cos(2\theta)}{\sin(2\theta)}$$...
  49. T

    Prove angular momentum operator identity

    Homework Statement Using the operator identity: \hat{L}^2=\hat{L}_-\hat{L}_+ +\hat{L}_z^2 + \hbar\hat{L}_z show explicitly: \hat{L}^2 = -\hbar^2 \left[ \frac{1}{\sin^2\theta} \frac{\partial^2}{\partial\phi^2} + \frac{1}{\sin\theta} \frac{\partial}{\partial\theta}...
  50. S

    Trigonometric Identity Proof: v cosδ = V(1-cosβ) + u cos(α-β)

    Homework Statement Given the following two triangles: Show that v \cos{\delta} = V(1-\cos{\beta})+u\cos(\alpha - \beta) The Attempt at a Solution Using the cosine law I've got: v^{2}=x^{2}+V^{2}-2xV\cos{(\theta + \beta)} and u^{2}=x^{2}+V^{2}-2xV\cos{(\theta)} I figured maybe using the...
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