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 A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the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

    Is this a correct 4-vector identity?

    In our particle physics lecture this term comes up often, it doesn't look right to me but the lecturer uses it so it must be: ##{\partial }^{2}A^{\mu} = - {\partial }_{\mu}{\partial }^{\mu}A^{\mu}+ {\partial }_{\mu}{\partial }^{2}A^{\mu}## I understand if you have: ##F^{\mu v} = {\partial...
  2. T

    4Sine(4X) = -8Sin(2x) Double angle identity

    I kind of understand what to do with this when there are no numbers in front of the expressions, I also kind of understand that you can rewrite 4Sine(4x) as 4Sine(2x+2x) hat do I do with the 4 and 8? In an algebra problem you could divide the 4 into the -8, then simplify that expression, am I...
  3. N

    Complex Analysis: Identity Theorem

    Homework Statement Let f be a function with a power series representation on a disk, say D(0,1). In each case, use the given information to identify the function. Is it unique? (a) f(1/n)=4 for n=1,2,\dots (b) f(i/n)=-\frac{1}{n^2} for n=1,2,\dots A side question: Is corollary 1 from my...
  4. E

    Proving a Trigonometric Identity

    Homework Statement Prove that: \cos^6{(x)} + \sin^6{(x)} = \frac{5}{8} + \frac{3}{8} \cos{(4x)} Homework Equations I am not sure. I used factoring a sum of cubes. The Attempt at a Solution I tried \cos^6{(x)} + \sin^6{(x)} = \cos^4{(x)} - \cos^2{(x)} \sin^2{(x)} + \sin^4{(x)} . But I...
  5. Shackleford

    Apply a corollary to show an identity

    Homework Statement Apply corollary to show that 2 sinz*sinw = cos(z-w) - cos(z+w) for any z,w ∈ ℂ Homework Equations 2 sinz*sinw = cos(z-w) - cos(z+w) for any z,w ∈ ℂ Corollary: Let f and g be analytic functions defined on a domain D ⊂ ℂ. Let E ⊂ D be a subset that has at least one limit...
  6. M

    Identity for Matrix*Vector differentiation w.r.t a vector

    I have J - matrix x and y - vector d [ J(x) y(x)] / dx I can multiply the matrix and vector together and then differentiate but I think for my application it would be better to find an identity like {d [ J(x) y(x)] / dx } = J(x) d y(x) / dx + d J (x) / dx y(x) I am not sure if this identity...
  7. W

    Further Trigonometry Identity (Proving question)

    1) Question: Show that (sin3A-sinA)/(cosA+cos3A)=tanA 2) Relevant equations: tan A=sinA/cos A 1+tan^2A=sec^A cot A=1/tanA cot A=cos A/sinA sin^2A+cos^2A=1 secA=1/cos A cosecA=1/sinA 1+cosec^2A= cot^2A sin2A=2sinAcosA cos2A=1-2sin^2A=cos^2A-sin^2A=2cos^A-1 tan2A=(2tanA)/1-tan^2A 3)Attempt...
  8. A

    Proving Trig Identity: csin(A-B/2)=(a-b)cos(C/2)

    Homework Statement Given a triangle ABC prove that c sin \frac{A-B}{2} = (a-b)cos \frac{C}{2} Homework EquationsThe Attempt at a Solution It looks rather similar to a formula mentioned in my book's lead-in to this exercise: \frac{a-b}{a+b}=tan\frac{A-B}{2}tan\frac{C}{2} Which can be...
  9. E

    MHB Proving a trigonometric identity II

    Hi, I need help proving the following trig identity, (2sinx)\overline{secxtan(2x)}=2cos^2x-csc^2x+cot^2x I have tried starting from the left hand side, the right hand side, and doing both together, but nothing seems to work. One of the ways I tried: LHS...
  10. E

    MHB Proving a trigonometric identity

    Hi, I need help proving the following trig identity: \frac{\cot^2(x)-\cot(x)+1}{1-2\tan(x)+\tan^2(x)}=\frac{1+\cot^2(x)}{1+\tan^2(x)} Me and my friend have spent several hours determined to figure this out, starting from the left hand side, the right hand side, and doing both together, but...
  11. M

    MHB Proving a trigonometric identity

    How prove $\cos\frac{8\pi}{35}+\cos\frac{12\pi}{35}+\cos\frac{18\pi}{35}=\frac{1}{2}\cdot\left(\cos\frac{\pi}{5}+\sqrt7\cdot\sin\frac{\pi}{5}\right)$?
  12. SalfordPhysics

    Derive Internal Energy from Thermodynamic Identity

    Homework Statement For a single molecule, derive the internal energy U = 3/2kBT In terms of the partition function Z, F = -kBTlnZ Where Z = V(aT)3/2 Homework Equations Thermodynamic identity: δF = -SδT - pδV p = kBT/V S = kB[ln(Z) + 3/2]The Attempt at a Solution U = F + TS δU = δF +...
  13. C

    Problem in apparent contradiction in Euler's Identity?

    I've worked with Euler's Identity for physics applications quite a few times, but ran into a "proof" of a contradiction in it, which I can't seem to find a flaw in (the only time I've ever had to do any proofs was in high school). I've derived Euler's equation in two different ways in past...
  14. C

    Proving Identity: \frac{1-tan^2(\theta)}{1-cot^2(\theta)}=1-sec^2(\theta)

    Prove the following identity: \frac{1-tan^2(\theta)}{1-cot^2(\theta)}=1-sec^2(\theta) By tan/sec identity, \frac {2-sec^2(\theta)}{2-csc^2(\theta)} separated the variables \frac {2}{2-csc^2}- \frac {sec^2}{2-csc^2} There's absolutely nothing useful I can do with either of those terms, so...
  15. Ganesh Ujwal

    How do I prove this seemingly simple trigonometric identity

    Mod note: Fixed the LaTeX. ##a=sinθ+sinϕ## ##b=tanθ+tanϕ## ##c=secθ+secϕ##Show that, ##8bc=a[4b^2 + (b^2-c^2)^2]## I tried to solve this for hours and have gotten no-where. Here's what I've got so far : ##a= 2\sin(\frac{\theta+\phi}{2})\cos(\frac{\theta-\phi}{2}) ## ## b =...
  16. P

    How Can Identity Operators in Quantum Mechanics Be Demonstrated?

    Homework Statement For the space Lw2(a,b), we can write the basis in a discrete fashion as {en|n∈ℤ} or in a continuous fashion as |x> (as we would in quantum mechanics for the position representation), such that we may write the identity operator as either I=∑n|en><en| or I=∫abdxw(x)|x><x|...
  17. alyafey22

    MHB Harmonic Numbers Identity Proof?

    Prove the following \sum_{k=1}^n \frac{H_k}{k} = \frac{H_n^2+H^{(2)}_n}{2} where we define H^{(k)}_n = \sum_{j=1}^n \frac{1}{j^k} \,\,\, ; \,\,\, H^2_n = \left( \sum_{j=1}^n \frac{1}{j}\right)^2
  18. D

    MHB Secondary Identity Confirmation

    Hey fellahs, got another whopper that's killing me. 1 - \cos2\theta + \cos8\theta - \cos10\theta=? My objective here is to complete the identity, and my worksheet lists the correct solution as: 4\sin\theta\cos4\theta\sin5\theta And once again I've had trouble beating this one. This is what...
  19. B

    Why Does \(\sin^2(nx) + \cos^2(nx) = 1\) Hold True?

    Why ##\sin^2 2x + \cos^2 2x = 1##? Will ##\sin^2 3x + \cos^2 3x## or ##\sin^2 4x + \cos^2 4x## and so on, be = 1? How to proof this?
  20. H

    Exploring One-Sided vs. Two-Sided Identity Elements in Groups

    Hi I'm taking a math course at university that covers introductory group theory. The textbook's definition of the identity element of a group defines it as two sided; that is, they say that a group ##G## must have an element ##e## such that for all ##a \in G##, ##e \cdot a = a = a \cdot e## ...
  21. D

    Vector identity proof using index notation

    Homework Statement I am trying to prove $$\vec{\nabla}(\vec{a}.\vec{b}) = (\vec{a}.\vec{\nabla})\vec{b} + (\vec{b}.\vec{\nabla})\vec{a} + \vec{b}\times\vec{\nabla}\times\vec{a} + \vec{a}\times\vec{\nabla}\times\vec{b}.$$ I can go from RHS to LHS by writng...
  22. H

    Simplify the matrix product to the identity

    Homework Statement IF G, H and G+H are invertible matrices and have the same dimensions Prove that G(G^-1 + H^-1)H(G+H)^-1 = I 3. Attempt G(G^-1 +H^-1)(G+H)H^-1 = G(G^-1G +G^-1H + H^-1G + H^-1H)H^-1 = (GG^-1GH^-1 +GG^-1HH^-1 +GH^-1GH^-1 +GH^-1HH^-1) = GH^-1+I +GH^-1GH^-1 +GH^-1 =2GH^-1+...
  23. R

    MHB Proving the Floor of nx using Fractional Parts and Induction

    Prove that \lfloor nx \rfloor = \sum_{k=0}^{n-1}\lfloor x+k/n \rfloor. Note \lfloor x\rfloor means the greatest integer less than or equal to x. I proved the cases where n=2 and n=3 by writing x=\lfloor x\rfloor + \{x\}, where \{x\} is the fractional part of x, and then using cases where 0\leq...
  24. D

    Bezout identity corollary generalization

    Homework Statement Hi, I have been trying to prove one of the corollaries of the Bezout's Identity in the general form.Unfortunately,I can't figure it out by myself.I hope someone could solve the problem. If A1,...,Ar are all factors of m and (Ai,Aj) = 1 for all i =/= j,then A1A2...Ar is a...
  25. K

    Ward Identity in Schwartz's QFT Book: Massless Photon Assumption or Not?

    I was reading Schwartz's qft book. I saw the proof of ward identity taking pair annihilation as an example. he claimed he didn't assume that photon is massless in this derivation. but i have confusion with this statement. gauge invariance is a fact related to massless particles. now he has...
  26. K

    Multiplication of an Identity Matrix by a Column

    Homework Statement [/B] This is a seemingly simple problem. All I have to do is multiply two matrices: [ 1 0 ] [ 0 1 ] (A) and [ 2 ] [ 3 ] (B) The Attempt at a Solution [/B] Because the matrix A has the same number of columns as matrix B has rows, and because matrix A is an identity matrix...
  27. G

    Proving an identity and some interesting maths stuff

    So, I would like to prove that \gamma^{\mu_{1}...\mu_{r}}=(-)^{r(r-1)/2}\gamma^{\mu_{r}...\mu_{1}} where the matrix gamma is a totally antisymmetric matrix defined as \gamma^{\mu_{1}...\mu_{r}}=\gamma^{[\mu_{1}}\gamma^{\mu_{2}}...\gamma^{\mu_{r}]} What I have done is to prove that...
  28. G

    Plane EM wave Euler's identity

    For EM wave, magnetic and electrical components are in phase, meaning when E = 0, then B = 0. Thus, I understand if it is written: f(x,t) = A(cos(kx - wt) + icos(kx - wt)) Then why plane wave is always described: f(x,t) = Aei(kx-wt) = A(cos(kx-wt) + isin(kx - wt)) Implying that Real and...
  29. paulmdrdo1

    MHB Solving Identifying $\theta$ in Trigonometric Equation

    Kindly help me with this problem. I'm stuck! $\frac{\csc\theta+1}{\cot\theta}=\frac{\cot\theta}{\csc\theta-1}$ this is how far I can get to $\sec\theta+\tan\theta=\frac{1}{\sec\theta-\tan\theta}$
  30. DiracPool

    Solving Trig Identity Problem: Asin^2(wt) + Bcos^2(wt) = A = B

    I can't quite work out this derivation I ran into which is essentially...Asin^2(wt) + Bcos^2(wt) = A = B. Is this correct? I know that sin^2(wt) + cos^2(wt) = 1, but I can't reason out how the factoring works here? Any help?
  31. U

    MHB How to Prove This Identity in the Classical Normal Linear Regression Model?

    The context of the following identity is in the Classical Normal Linear Regression Model, ie, $\boldsymbol{y} = \boldsymbol{X}\boldsymbol{\beta}+ \boldsymbol{u}$ where $\boldsymbol{u}$ is a $n \times 1$ matrix and $u_i \sim iid.N(0, \sigma^2)$ for $i = 1, 2, \cdots, n$ Show that...
  32. PcumP_Ravenclaw

    Doubts from transposition, fixing and Identity

    Dear All, Please see the attachment for the text i will be referring to. what does "I = τ1 · · · τm, where each τj is a transposition acting on {1, . . . , n}. Clearly, m != 1, thus m ≥ 2. Suppose, for the moment, that τm does not fix n". what does fixing n mean in a...
  33. M

    Personal identity within marketing and advertising

    Hello everyone, I'm currently writing my dissertation based around the question of whether photo editing within the spheres of fashion and beauty media and advertising rids the subjects of their identity - I have looked at numerous books about personal identity, such as Paul Ricoeur's Oneself...
  34. M

    Let S be the subset of group G that contains identity element 1?

    Homework Statement Let S be the subset of group G that contains identity element 1 such that left co sets aS with a in G, partition G .Probe that S is a subgroup of G. Homework Equations {hS : h belongs to G } is a partition of G. The Attempt at a Solution For h in S if I show that hS is S...
  35. K

    MHB Interesting identity arising from fractional factorial design of resolution III

    I am learning about statistical design of experiments, and in the process of mathematically rigorizing the concepts behind fractional factorial designs of resolution III, I derived an interesting equation: $$k = \sum_{i=1}^{3}{\lceil{\log_2{k}}\rceil \choose i},$$ for which the solutions $k$...
  36. deedsy

    Deriving sin(a-b) trig identity using Cross Product of Unit Vectors

    Homework Statement A and B are two unit vectors in the x-y plane. A = <cos(a), sin(a)> B = <cos(b), sin(b)> I need to derive the trig identity: sin(a-b) = sin(a) cos(b) - sin(b) cos (a) I'm told to do it using the properties of the cross product A x B Homework Equations A x B =...
  37. Ascendant78

    Use the Euler identity to prove sin^2x+cos^2x=1

    Homework Statement Just like my title says, we are to prove the trig identity sin^2x+cos^2x=1 using the Euler identity. Homework Equations Euler - e^(ix) = cosx + isinx trig identity - sin^2x + cos^2x = 1 The Attempt at a Solution I tried solving the Euler for sinx and cosx...
  38. D

    Conceptual questions on proving identity element of a group is unique

    Hi, I'm hoping to clear up a few uncertainties in my mind about proving that the identity element and inverses of elements in a group are unique. Suppose we have a group \left(G, \ast\right). From the group axioms, we know that at least one element b exists in G, such that a \ast b = b \ast...
  39. Telemachus

    Identity, vector product and gradient

    Hi there. I was following a deduction on continuum mechanics for the invariant nature of the first two laws of thermodynamics. The thing is that this deduction works with an identity, and there is something I'm missing to get it. I have the vector product: ##\vec \omega \times grad \theta##...
  40. MathematicalPhysicist

    Schouten identity resembles Jacobi identity

    Am I the only one who sees the resemblance between these two identities? Schouten: <p q> <r s> +<p r> <s q>+ <p s > <q r> =0 Jacobi: [A,[B,C]]+[C,[A,B]]+[B,[C,A]]=0 In Schouten the p occours in each term in the three terms, so we can regard it as dumby variable, and somehow get a...
  41. A

    Proof of trig identity (difficult)

    Homework Statement Prove that [tan(a) + 1][cot(a+pi/4) + 1] = 2 Homework Equations [tan(a) + 1][cot(a+pi/4) + 1] = 2 The Attempt at a Solution This was very hard, I tried my best at expanding. [tan(a) + 1][cot(a+pi/4) + 1] = tan(a)cot(a+pi/4) + tan(a) + cot(a+pi/4) + 1...
  42. J

    Cyclic Group - Isomorphism of Non Identity Mapping

    Homework Statement Prove that if G is a cyclic group with more than two elements, then there always exists an isomorphism: ψ: G--> G that is not the identity mapping. Homework Equations The Attempt at a Solution So if G is a cyclic group of prime order with n>2, then by Euler's...
  43. Albert1

    MHB Solving the Identity Challenge: $3=\sqrt{1+2...9}$

    prove: $3=\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+5\sqrt{1+6\sqrt{1+7\sqrt{1+8\sqrt{1+9--}}}}}}}}$
  44. L

    Schouten's identity in Ian Aitchison's supersymmetry book

    In 'Supersymmetry in Particle Physics, An Elementary Introduction', the author Ian Aitchison used for several times the following identity: λa(ζ · ρ) + ζa(ρ · λ) + ρa(λ · ζ) = 0. I know that this identity is called Schouten's Identity, which is correct when all the variables are common...
  45. H

    Associated Legendre Polynomial Identity

    Does anyone know how to prove this identity? I don't quote understand why the associated Legendre function is allowed to have arguments where |x|>1. h_n(kr)P_n^m(\cos\theta)=\frac{(-i)^{n+1}}{\pi}\int_{-\infty}^\infty e^{ikzt}K_m(k\rho\gamma(t))P_n^m(t)\,dt where \gamma(t)=\begin{cases}...
  46. W

    Ward Identity in Srednicki QFT book

    Hello guys, I am working on Ch22 "Continuous symmetries and conserved currents" of Srednicki QFT book. I am trying to understand how to prove the Ward-Takahashi identity using path integral method, done in page 136 of Srednicki. I understood everything up to Equation 22.22, which is 0 =...
  47. A

    MHB Proving r*r=q in S, a Ring with Identity

    Let S={p,q,r} and S=(S,+,*) a ring with identity. Let p be the identity for + and q the identity for *. Use the equation r*(r+q)=r*r+r*q to deduce that r*r=q. Attempt of a solution r*r=r*(r+q)- r*q =r*r+r*q - r*q But I'm not finding a clever way to deduce what is required. Any type of help...
  48. C

    Trigonometric identity double definite integral

    Double integral of (52-x^2-y^2)^.5 2<_ x <_ 4 2<_ y <_ 6 I get up to this simplicity that results in a zero! 1-cos^2(@) - sin^2(@) = 0 This identity seems to be useless. HELP PLEASE.
  49. P

    Green's First Identity involving Electric Potential

    I am attempting to work through a paper that involves some slightly unfamiliar vector calculus, as well as many omitted steps. It begins with the potential energy due to an electric field, familiarly expressed as: U_{el} = \frac{\epsilon_r\epsilon_0}{2} \iiint_VE^2dV =...
  50. M

    MHB Understanding Orthogonality in Inner Product Spaces

    Hey! :o We know that: $$(x,x)=0 \Rightarrow x=0$$ When we have $\displaystyle{(x,y)=0}$, do we conclude that $\displaystyle{x=0 \text{ AND } y=0}$. Or is this wrong? (Wondering)
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