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 A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the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

    Evaluate this trigonometric identity

    (Sinx-2cosx)/ (cotx - sinx) Substitute tan instead of cot (Tanx(sinx-2cosx)/(1-sinx) What do I do from here I don't think what I did there is correct That's why I didn't expand the tan to sin/cos
  2. E

    B A differential equation, or an identity?

    This is quite literally a showerthought; a differential equation is a statement that holds for all ##x## within a specified domain, e.g. ##f''(x) + 5f'(x) + 6f(x) = 0##. So why is it called a differential equation, and not a differential identity? Perhaps because it only holds for a specific set...
  3. victor01

    I Clebsch–Gordan coefficients: An Identity

    Hi, everyone. I'm trying to get the next identity It is in the format <j1, j2; m1, m2 |j, m>. I hope you can help me
  4. anemone

    MHB Unsolved Challenge: Trigonometric Identity

    Prove $\tan 3x=\tan \left(\dfrac{\pi}{3}-x\right) \tan x \tan \left(\dfrac{\pi}{3}+x\right)$ geometrically.
  5. PainterGuy

    B How Can I Reverse a Trigonometric Identity to Find Original Constants?

    Hi, K₁cos(θt+φ)=K₁cos(θt)cos(φ)-K₁sin(θt)sin(φ)=K₁K₂cos(θt)-K₁K₃sin(θt) Let's assume φ=30° , K₁=5 5cos(θt+30°) = 5cos(θt)cos(30°)-5sin(θt)sin(30°) = (5)0.866cos(θt)-(5)0.5sin(θt) = 4.33cos(θt)-2.5sin(θt) If only the final result, 4.33cos(θt)-2.5sin(θt), is given, how do I find the original...
  6. weningth

    A Why does this amplitude not vanish by the Ward identity?

    Consider the process e^-\rightarrow e^-\gamma depicted in the following Feynman diagram. The spin-averaged amplitude with linearly polarised photons is \overline{|M|^2}=8\pi\alpha\left(-g^{\mu\nu}+\epsilon^\mu_+\epsilon^\nu_-+\epsilon^\mu_-\epsilon^\nu_+\right)\left(p_\mu p^\prime_\nu+p_\nu...
  7. K

    I Vector calculus identity format question

    I know there is an identity involving the Laplacian that is like ##\nabla^2 \vec A = \nabla^2 A## where ##\vec A## is a vector and ##A## is its magnitude, but can't remember the correct form. Does anyone knows it?
  8. O

    A Help with the Proof of an Operator Identity

    I'm trying to come up with a proof of the operator identity typically used in the Mori projector operator formalism for Generalized Langevin Equations, e^{tL} = e^{t(1-P)L}+\int_{0}^{t}dse^{(t-s)L}PLe^{s(1-P)L}, where L is the Liouville operator and P is a projection operator that projects...
  9. P

    I Proof of Commutator Operator Identity

    Hi All, I try to prove the following commutator operator Identity used in Harmonic Oscillator of Quantum Mechanics. In the process, I do not know how to proceed forward. I need help to complete my proof. Many Thanks.
  10. M

    I Stokes Theorem: Vector Integral Identity Proof

    Hi, My question pertains to the question in the image attached. My current method: Part (a) of the question was to state what Stokes' theorem was, so I am assuming that this part is using Stokes' Theorem in some way, but I fail to see all the steps. I noted that \nabla \times \vec F = \nabla...
  11. Arman777

    Deriving an identity using Einstein's summation notation

    I have an identity $$\vec{\nabla} \times (\frac{\vec{m} \times \hat{r}}{r^2})$$ which should give us $$3(\vec{m} \cdot \hat{r}) \hat{r} - \vec{m}$$ But I have to derive it using the Einstein summation notation. How can I approach this problem to simplify things ? Should I do something like...
  12. J

    Levi-Civita Identity Proof Help (εijk εijl = 2δkl)

    I assumed that this would be a straightforward proof, as I could just make the substitution l=j and m=l, but upon doing this, I end up with: δjj δkl - δjl δkj = δkl - δlk Clearly I did not take the right approach in this proof and have no clue as to how to proceed.
  13. G

    I Generalisation of Polarization identity

    Hello, If I have a quadratic form ##q## on a ##\mathbb{R}## vectorial space ##E##, its associated bilinear symmetric form ##b## can be deduce by the following formula : ##b(., .) = \frac{q(. + .) - q(.) - q(.)}{2}##. So that, an homogeneous polynomial of degree 2 can be associated to a blinear...
  14. MathematicalPhysicist

    I Derivation of an identity for ##\partial^2_t \int T^{00}(x^i x_i)^2d^3

    I'll write down my calculations, and I would like if someone can point me to my mistakes. $$\partial_t \int T^{00}(x^i x_i)^2 d^3 x = -\int T^{0k}_{,k}(x^i x_i)^2 d^3 x = \Dcancelto[0]{-\int (T^{0k}(x_ix^i)^2)_{,k}d^3 x} +\int (T^{0k}(x_i x^i)^2_{,k})d^3 x$$ After that: $$\partial_t \int...
  15. dRic2

    Vector calculus identity and electric/magnetic polarization

    I spent a good amount of time thinking about it and in the end I gave up and asked to a friend of mine. He said it's a 1-line-proof: just "integrate by parts" and that's it. I'm not sure you can do that, so instead I tried using the identity: to express the first term on the right-hand side...
  16. V

    Finding the limit using a trig identity

    Find the limit as x approaches 0 of x2/(sin2x(9x)) I thought I could break it up into: limit as x approaches 0 ((x)(x))/((sinx)(sinx)(9x)). So that I could get: limx→0x/sinx ⋅ limx→0x/sinx ⋅ limx→01/9x. I would then get 1 ⋅ 1 ⋅ 1/0. Meaning it would not exist. However the solution is 1/81...
  17. M

    Why do we care about the identity property of an operation?

    I am reading a lot of stuff on advanced algebra and running into these questions. Thank you
  18. peguerosdc

    Understanding Green's second identity and the reciprocity theorem

    This is Jackson's 3rd edition 1.12 problem. So, for both ## \phi ## and ## \phi' ##, I started from Green's second identity: ## \int_V ( \phi \nabla^2 \phi' - \phi' \nabla^2 \phi )dV = \int_S ( \phi \frac {\partial \phi'} {\partial n} - \phi' \frac {\partial \phi} {\partial n} ) dS ## And...
  19. H

    B Understanding the Quadratic Form Identity in Two-Variable Equations

    Summary: could you explain why this equality is a quadratic form identity? i read this equality (4.26) here w depends on two variables. it is written that if B is bounded (L2) then it is a quadratic form identity on S. what does it mean? is it related to the two variables? next the author...
  20. 0

    An identity to prove using calculus 1

    I have a feeling that I forgot to copy something from the black board, maybe some f' because as it is I'm not seeing a solution.
  21. Hiero

    Proving the Curl Identity for a Simple Curl Equation

    Attempt: $$\nabla \times ( a\nabla b) = \epsilon_{ijk}\frac{\partial}{\partial x_j}(a\frac{\partial b}{\partial x_k})\hat e_i$$ $$ = \epsilon_{ijk}\big(\frac{\partial a}{\partial x_j}\frac{\partial b}{\partial x_k}+a\frac{\partial b}{\partial x_j\partial x_k}\big)\hat e_i$$ $$= \nabla a \times...
  22. H

    I Request for a clarification about the Ward identity

    Hi I've been reading Peskin & Schroeder lately and I have some confusions over the ward identity. So I think I understand how the identity works at a practical level but not exactly where it comes from. To illustrate my questions (which are difficult to state generally), I will make use the...
  23. Wrichik Basu

    I Some questions in QFT (EM vertex, Ward identity, etc.)

    I am reading the A First Book of Quantum Field Theory. I have reached the chapter of renormalization, where the authors describe how the infinities of the self-energy diagrams can be corrected. They have also discussed later how the infrared and ultraviolet divergences are corrected. Just before...
  24. Haorong Wu

    Prove that the product of two n qubits Hadamard gates is identity

    From the properties of tensor product, ##H^{\otimes n} \cdot H^{\otimes n} =\left ( H_1 \cdot H_1 \right ) \otimes \left ( H_2 \cdot H_2 \right ) \otimes \cdots \otimes \left ( H_n \cdot H_n \right ) =I \otimes I \otimes \cdots \otimes I =I## where ##H_i## acts on the ##i^{th}## qubit. But I...
  25. M

    A What Is the Significance of the Matrix Identity Involving \( S^{-1}_{ij} \)?

    Hi all, I've come across an interesting matrix identity in my work. I'll define the NxN matrix as S_{ij} = 2^{-(2N - i - j + 1)} \frac{(2N - i - j)!}{(N-i)!(N-j)!}. I find numerically that \sum_{i,j=1}^N S^{-1}_{ij} = 2N, (the sum is over the elements of the matrix inverse). In fact, I...
  26. F

    B Equation vs Identity: Why We Differ Both Sides

    Why are we allowed to differentiate both sides of something like ##y=x^2## but not something like ##x=x^2## I believe the answer might be that the first equation is an identity that is true for all values while the second equation is an equation and is only true for some values. Although...
  27. G

    MHB Prove identity (sinx+cosx)/(secx+cscx)= sinxcosx

    prove this identity (sinx+cosx)/(secx+cscx)= sinxcosx if you could list out the steps it would be appreciated
  28. ali PMPAINT

    Understanding the Arctan Identity: Solving for Inverse Trigonometric Functions

    So, I saw the answer but I couldn't understand it. But I think it can be solved by tan(a)+tab(b)+tan(c)=tan(a)*tan(b)*tan(c) (where a+b+c=Pi) , but I don't know how to transfer it to its inverse. The answer:
  29. W

    MHB Logarithm Identity: Prove Loga(1/x)=log1/x(a)

    If a>1, a cannot = 1, x>0, show that Loga(1/x) = log1/x(a). (COULD NOT SOLVE)
  30. lfdahl

    MHB Prove the binomial identity ∑(-1)^j(n choose j)=0

    Prove the binomial identity: $$\sum_{j=0}^{n}(-1)^j{n \choose j}=0$$ - in two different ways
  31. D

    I Maxwell Tensor Identity Explained: Deriving Formula 8.23 in Schawrtz's Book

    Hello, In Schawrtz, Page 116, formula 8.23, he seems to suggest that the square of the Maxwell tensor can be expanded out as follows: $$-\frac{1}{4}F_{\mu \nu}^{2}=\frac{1}{2}A_{\mu}\square A_{\mu}-\frac{1}{2}A_{\mu}\partial_{\mu}\partial_{\nu}A_{\nu}$$ where: $$F_{\mu\nu}=\partial_{\mu}...
  32. tanaygupta2000

    Proof of Parseval's Identity for a Fourier Sine/Cosine transform

    Can anyone help me with the Proof of Parseval Identity for Fourier Sine/Cosine transform : 2/π [integration 0 to ∞] Fs(s)•Gs(s) ds = [integration 0 to ∞] f(x)•g(x) dx I've successfully proved the Parseval Identity for Complex Fourier Transform, but I'm unable to figure out from where does the...
  33. karush

    MHB Prove trig identity (cot x -1)/(cot x +1)=(1-sin 2x)/(cos 2x)

    $\begin{align*} \frac{\cot {x}-1}{\cot{x}+1}&=\frac{1-\sin 2x}{\cos 2x}\\ \frac{\cos {x}-\sin x}{\cos{x}+\sin x} \frac{\cos x-\sin x}{\cos x-\sin x}&= \\ \frac{\cos^2x-2\sin x\cos x+\cos^2 x}{\cos^2 x-\sin^2 x} \end{align*}$ so far..
  34. J

    MHB "Approximation to the Identity" and "Convolution" Proof

    Problem: Let $\phi(x), x \in \Bbb{R}$ be a bounded measurable function such that $\phi(x) = 0$ for $|x| \geq 1$ and $\int \phi = 1$. For $\epsilon > 0$, let $\phi_{\epsilon}(x) = \frac{1}{\epsilon}\phi \frac{x}{\epsilon}$. ($\phi_{\epsilon}$ is called an approximation to the identity.) If $f \in...
  35. W

    I Proving Commutator Identity for Baker-Campbell-Hausdorff Formula

    I'm having a little trouble proving the following identity that is used in the derivation of the Baker-Campbell-Hausdorff Formula: $$[e^{tT},S] = -t[S,T]e^{tT}$$ It is assumed that [S,T] commutes with S and T, these being linear operators. I tried opening both sides and comparing terms to no...
  36. Quarky nerd

    I Exploring Euler's Identity: eiΘ = cosΘ + i sinΘ

    fig 1 Given: eiΘ= cosΘ + i sinΘ (radians) eπi=-1 Deduced e2πi=(-1)2 e2πi=1 e(2/3)πi=11/3 e(2/3)iπ=1 e(2/3)iπ=cos(2i/3)+i sin(2i/3) e(2/3)iπ=-1/2+i(3/2) -1/2+i(31/2/2)=1 where n is greater than or equal to 1 or n=a/b where a is greater than or equal to 1 and b is odd 1n=1 ∴...
  37. J

    A derivative identity (Zangwill)

    Homework Statement Without using vector identities, show that ##\nabla \cdot [\vec{A}(r) \times \vec{r}] = 0##. Homework Equations The definitions and elementary properties of the dot and cross products in terms of Levi-Civita symbols. The "standard" calculus III identities for the divergence...
  38. S

    I Bezout Identity: Is r∈S U {0} Necessary to Prove?

    what is the need to show that r belongs to S U {0} in proof (https://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity#Proof) r is zero afterall, whether it lies in S U {0} or not doesn't affect.
  39. A

    MHB Does Every Standard Deductive Apparatus Include Common Identity Axioms?

    I'm going through Peter Smith's book on Godel's Theorems. He mentions a simple formal theory ("Baby Arithmetic") whose logic needs to prove every instance of 'tau = tau'. Does every 'standard deductive apparatus' include the common identity axioms (e.g. 'x = x')?. The axioms of "Baby...
  40. PeroK

    A Rund_Trautman Identity for fields

    I think I have found a majot error in Neuenschwander's book on Noether's Theorem, but I'd like some confirmation from someone familiar with the book or with the Rund_Trautman identity for fields. As far as I can see the extension of the R-T identity for fields seems to be Neuenschwander's work...
  41. F

    Use Abel's identity to find the Wronskian

    Homework Statement Homework Equations The Attempt at a Solution [/B] Is my answer correct ?
  42. J

    MHB Notion of a ring with identity 1=0

    Could someone clarify the notion of a ring with identity element $1=0$? Apparently it's just the zero ring, but then why do we always talk about a ring with identity $1 \ne 0$? It's like having to talk about prime $p \ne 1$; instead we don't define $1$ as a prime but also because we would lose...
  43. CMJ96

    A Help Understanding a Quantum Circuit Identity

    Hello I have the following quantum circuit identity for converting a controlled U gate (4x4 matrix) into a series of CNOT gates and single qubit gates $$ U= AXA^{\dagger}X$$ where A is a unitary matrix. Here is a picture of the mentioned identity. Can someone help me understand conceptually...
  44. E

    I Linear Algebra and Identity Operator Generalized to 3D

    I'm just getting into 3D quantum mechanics in my class, as in the hydrogen atom, particle in a box etc. But we have already been thoroughly acquainted with 1D systems, spin-1/2, dirac notation, etc. I am trying to understand some of the subtleties of moving to 3D. In particular, for any...
  45. M

    Vectors: How to prove the BAC-CAB identity w/o components?

    Homework Statement Prove that $$\bf{ a \times ( b \times c ) = \phi [ b(a \bullet c) - c(a \bullet b) ]} $$ for some constant phi Homework EquationsThe Attempt at a Solution So I have used the unit vectors i, j, and k and found out that phi = 1. With the main part of the proof, we are not...
  46. M

    Prove the following identity [Einstein notation]

    Homework Statement [/B] Prove the following identity: \vec{\nabla}(\vec{A} \cdot \vec{B}) = (\vec{A} \cdot \vec{\nabla})\vec{B} + (\vec{B} \cdot \vec{\nabla})\vec{A} + \vec{A} \times (\vec{\nabla} \times \vec{B}) + \vec{B} \times (\vec{\nabla} \times \vec{A}) Homework Equations Kronecker's...
  47. C

    I Can [A,B^n] always equal 0 if [A,B] equals 0?

    This is not a homework problem. It was stated in a textbook as trivial but I cannot prove it myself in general. If [A,B]=0 then [A,B^n] = 0 where n is a positive integer. This seems rather intuitive and I can easily see it to be true when I plug in n=2, n=3, n=4, etc. However, I cannot prove it...
  48. V

    B Proof of the identity A\(A\B)=B

    I'm trying to proof an identity from Munkres' Topology A \ ( A \ B ) = B By definition A \ B = {x : x in A and x not in B} A \( A \ B) = A \ (A ∩ Bc) = A ∩ (A ∩ Bc)c = A ∩ (Ac ∪ B) = (A ∩ Ac) ∪ (A ∩ B) = ∅ ∪ (A ∩ B) = A ∩ B What did I miss?
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