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 A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the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

    How do you prove this Trig identity?

    Homework Statement (tan/(1-cot))+(cot/(1-tan))=1+(sec)(csc) The Attempt at a Solution This problem showed up in my class as a warm-up, and when my teacher tried to solve it for us he got stuck. I've asked a few classmates in higher level math, and they all seem to get stuck. I...
  2. T

    Solving Complex Identity: Help with z in Polar and Exponential Form

    Hi there. I need help simplifying the following: |\sqrt{z^2 -1} +z| + |\sqrt{z^2 -1} -z| What I did was I rewrote z in polar coordinates, but I ran into some difficulties taking the square root of r^2(cos2θ-sin2θ)-1. I also tried rewritting z in exponential form, but also had problems. Help?
  3. C

    Proof of exchangeability in matrix multiplications with Identity matrix I

    Homework Statement Let A be a square matrix such that I-A is nonsingular. Prove that A * (I-a)^-1 = (I-A)^-1 * A Homework Equations Now I think that A^-1 * A = A*A^-1 = I and I*A = A*I are relevant for this. The Attempt at a Solution I tried to express (I-a)^-1 in...
  4. S

    Number of elements in a ring with identity.

    Homework Statement 1_R=identity in the ring R. /=...not equal Having some issues with this any help will be great: Let R be a ring with identity, such that x^2 = 1_R for all 0_R /= x ,where x belongs to R. How many elements are in R? Homework Equations The Attempt at a Solution...
  5. C

    Solving Unsolved Trig Identity: sum[0 to x](sin(x))=180 * sin(x/2)^2 + sin(x)/2

    Hey guys, I stumbled on an interesting and unexpected identity when looking for a simpler summation technique for inverse kinementics. Basically, I was trying to find a simpler way of summing IK vectors for some particular armature (like a tentacle or multi-branch armature on a robot). This...
  6. S

    Every nite domain contains an identity element.

    Homework Statement I'm trying to write a proof ot demonstrate that every finite domain contains an identity element.Homework Equations The Attempt at a Solution If I can think of the operation from the ring as a mapping...like x->yx..where y are just values from the domain and then to consider...
  7. A

    MHB Proving Finite Domain Identity Element: Tips & Tricks

    How can I prove that every finite domain has an identity element? How should I think about the problem and what should I take into consideration?
  8. S

    MHB Prove Ring with Identity on Set S with One Element x

    On a set S with exactly one element x, define x + x = x, x*x = x. Prove that S is a ring. The way I think about this problem is be showing that it verifies certain axioms...like associativity,commutativity,identity,inverse for addition and commutativity for multiplication and a (b + c) = ab +...
  9. A

    Why Can Energy and Volume Changes Be Considered Separately in Thermodynamics?

    dU = TdS - P dV Is in my book derived by viewing a proces of changing volume and energy in two separate steps. First you add energy with volume fixed, then change the volume. I'm just not sure that I understand why, you are allowed to do this. I know the changes are infinitesimal but why is...
  10. A

    MHB Number of elements in a ring with identity.

    1_R=identity in the ring R. /=...not equal Having some issues with this any help will be great: Let R be a ring with identity, such that x_2 = 1_R for all 0_R /= x ,where x belongs to R. How many elements are in R? Thanks
  11. M

    Using the Baker-Campbell-Hausdorff Identity

    Homework Statement Given that U = e^{-i*θ*\hat{n}*\vec{J}/hbar} Show that U^{†}\vec{J}U = \hat{n}(\hat{n}*\vec{J}) - \hat{n}\times(\hat{n}\times\vec{J})cos(θ) + \hat{n}\times\vec{J}sin(θ) Homework Equations The Baker-Campbell-Hausdorff Identity The Attempt at a Solution...
  12. M

    Proof of Identity: Differentiating $\alpha^ax$ and $\alpha^by$

    Homework Statement \alpha\frac{d}{d\alpha}[f(\alpha^ax,\alpha^by)]|_{\alpha=1}=ax\frac{\partial f}{\partial x}+by\frac{\partial f}{\partial y} Homework Equations The Attempt at a Solution Homework Statement I'm confused. I don't know what to do here. How to differentiate left...
  13. S

    So the webpage title would be: How do you show that sin i*theta = i*sinh(theta)?

    I need to show that sin i*theta= i* sinh(theta). where sinh(theta) = .5[e^theta - e^(-theta)] and cos(theta) = .5[e^theta + e^(-theta)] and e^(i*theta) = cos(theta) + isin(theta) if I start with the formula sinh(theta) = .5[e^theta - e^(-theta)] and plug in e^(i*theta) = cos(theta) +...
  14. K

    Proving using calculus without trig identity

    Please I really need help with this homework question Prove without trig identity that f`(x)=0 for F(x)=Asin^2(Bx+C)+Acos^2(Bx+C)
  15. T

    Find a 2 by 2 matrix such that when cubed, is equal to the identity matrix

    Homework Statement Find a 2 by 2 matrix such that when cubed, is equal to the identity matrix. This matrix cannot be equal to the identity matrix unless it is cubed. So for example: B3 = [1 0;0 1] but B≠[1 0;0 1] The Attempt at a Solution The professor told us that we have to use a...
  16. M

    Are These Group Statements True or False?

    Homework Statement Which of following statements are TRUE or FALSE. Why? In any group G with identity element e a) for any x in G, if x2 = e then x = e. b) for any x in G, if x2 = x then x = e. c) for any x in G there exists y in G such that x = y2. d) for any x, y in G there exists z...
  17. K

    Vector Valued Function Using (or misusing) Trig Identity

    Homework Statement The context of the problem is that it's a vector valued function (VVF) problem where I'm supposed to sketch a curve generated by a VVF. To make the sketching easier I'm supposed to convert a VVF to a real valued function so that I can take advantage of the shape of a curve...
  18. K

    Riemann zeta function - one identity

    Let p_n be number of Non-Isomorphic Abelian Groups by order n. For R(s)>1 with \zeta(s)=\sum_{n=1}^{\infty}\frac{1}{n^s} we define Riemann zeta function. Fundamental theorem of arithmetic is biconditional with fact that \zeta(s)=\prod_{p} (1-p^{-s})^{-1} for R(s)>1. Proove that for R(s)>1 is...
  19. P

    QCD Ward Identity in Axial Gauge

    How do (offshell) QCD ward identities look like in the axial gauge? How to derive them? The standard treatment of ward identities uses BRST symmetry in the covariant gauge. I don't know where I can read about the axial gauge version of the ward identities.
  20. T

    Multivariate Taylor expansion or else a double integral identity

    Homework Statement This is part of a larger problem, but in order to take what I believe is the first step, I need to take the Taylor series expansion of f(x,y) = \cos\sqrt{x+y} about (x,y) = (0,0) On the other hand, the purpose of doing this expansion is to find an asymptotic expression for...
  21. R

    What Is Lockwood's Identity and How Does It Relate to Pascal's Triangle?

    i am working on my expository research about integer sequences and their relationship with the pascal's triangle using the Lockwood's identity. but unfortunately i can't provide a complete proof for the said identity. please help me. I've been working on it for months but still i can't do the...
  22. T

    Solving the Log Identity Problem: Understanding the Daume Equation

    Homework Statement http://img39.imageshack.us/img39/4729/daumequation13275759907.png Homework Equations N/A The Attempt at a Solution Hmm... This is a tough one. I thought these two functions have been mathematically proven to be exactly the same? Does it have something to do...
  23. L

    How to show integral identity involving gaussian over x

    So I have come across this integral identity in Krall's Principles of Plasma Physics (right after equ. 6.4.4 in the 1st edition) and I have not been able to show the identity is true. The reason that I would like to understand the integral is that I am trying to solve a similar problem to the...
  24. S

    Hyperbolic cosine identity help

    Homework Statement Show that cosh^2(x) = (cosh(2x) - 1)/2 Homework Equations cosh(x) = (e^x + e^-x)/2 The Attempt at a Solution I have attempted this multiple times and get the same results every time. Squaring cosh(x) I get 1/4(e^2x + e^-2x +2), which is i believe 1/4(cosh(2x) +2)...
  25. T

    Does the vector triple-product identity hold for operators?

    Does the definition of the vector triple-product hold for operators? I know that for regular vectors, the vector triple product can be found as \mathbf{a}\times(\mathbf{b}\times\mathbf{c})=( \mathbf{a} \cdot\mathbf{c})\mathbf{b}-(\mathbf{a}\cdot\mathbf{b})\mathbf{c}. Does this identity hold...
  26. T

    How can the change-base identity be used to prove this equation?

    Homework Statement http://img843.imageshack.us/img843/3826/help3c.png Homework Equations Not applicable. The Attempt at a Solution http://img810.imageshack.us/img810/5577/help2n.png Can anyone prove this by evaluating the left side and right side independent of each other...
  27. I

    Unclear formulation of Ward identity

    Hello, I am really familiar with the Ward-Takashi identity formulated in the form k_{\mu}M^{\mu\nu}=0 applying the fact that the longitudinal polarization of the 4 vector A is nonphysical (redundant) and should not contribute to the physical amplitudes. But, by opening a test subject on QED, I...
  28. J

    Trig identity with natural logs and absolute value?

    Trig identity with natural logs and absolute value?? Homework Statement -ln|csc(x) + cot(x)|= ln|cscx(x)-cot(x)| Homework Equations The Attempt at a Solution I got that csc(x)=1/sin(x) and cot(x)=cos(x)/sin(x), giving me a common denominator, added together I have...
  29. P

    Understanding the Quadruple Angle Identity for Cosine

    Homework Statement Simplify: cos(4θ) Homework Equations cos(2θ)=2cos^2(θ)-1 sin(2θ)=2sinθcosθ The Attempt at a Solution First, I broke it into cos(2θ+2θ). Then I expanded it and got cos(2θ)cos(2θ)-sin(2θ)sin(2θ). I then expanded that and got...
  30. S

    Complex number question involving de Moivre identity

    Homework Statement cos(4x)(6+2a)+12a+8b=-20 find values for a, b. Then check the values and state which values of x would not have been sufficient checks. Homework Equations Complex number equations The Attempt at a Solution I've simplified it down to this from a harder problem...
  31. T

    Floor Function (Greatest Integer Function) Identity

    Homework Statement Prove that, for all x, y \in \mathbb{R}, [2x] + [2y] \geq [x] + [y] + [x + y]. Homework Equations I am using [\cdot] to represent the floor function, and \{\cdot\} to represent the fractional part of a real number (\{x\} = x - [x] for real numbers x). We may...
  32. K

    Is a Lack of Math Skill a Barrier to a Career in Astrophysics?

    Hello all, I am new to these forums, and I look forward to plumbing the depths of this interesting site. Anywho, I come to you with a bit of a potentially difficult question. I have always been immensely interested in Astronomy and Physics, and I decided long ago to pursue a career in either...
  33. M

    Prove Identity: Partial Derivatives of Vector & Scalar Functions

    Homework Statement \frac{\partial \vec{r}}{\partial q_i}gradf(r)=\frac{\partial f(r)}{\partial q_i} Homework Equations gradf(r)=\frac{df}{dr}gradr=\frac{df}{dr}\frac{ \vec{r}}{r}=\frac{df}{dr}\vec{r}_0 The Attempt at a Solution \frac{\partial \vec{r}}{\partial...
  34. T

    Proving LS=RS in Trigonometry?

    Homework Statement http://img829.imageshack.us/img829/3413/daumequation13237287425.png Prove that LS=RS. Homework Equations There are no relevant equations. The Attempt at a Solution http://img829.imageshack.us/img829/3413/daumequation13237287425.png
  35. T

    Solving sin2x-tan2x=-2(sinx)^2(tan2x) | Proving Identity Step by Step

    Homework Statement sin2x-tan2x=-2(sinx)^2(tan2x) 2. The attempt at a solution I have like two pages of attempts, but I don't know if it would be useful to copy it into the forum. :|
  36. C

    Finding the fundamental matrix where psi(0) = the identity matrix

    Homework Statement If I have a solution to a system of first order linear equations: <x,y> = c_1 e^{-3t} <1,-1> + c_2 e^{-t} <1,1> , how do I find the fundamental matrix psi(t) so that psi(0) = I ? Homework Equations The Attempt at a Solution psi(t) = <<e^{3t}, e^{-t}>...
  37. maverick280857

    Dirac Principle Value Identity applied to Propagators

    Hi, How is \frac{1}{\displaystyle{\not}{P}-m+i\epsilon}-\frac{1}{\displaystyle{\not}{P}-m-i\epsilon} = \frac{2\pi}{i}(\displaystyle{\not}{P}+m)\delta(P^2-m^2) ? This is equation (4-91) of Itzykson and Zuber (page 189). I know that \frac{1}{x\mp i\epsilon} =...
  38. B

    Proving an identity related to Sterling Numbers of the 2nd Kind

    Homework Statement I am to prove, by induction, that S(n,2)=\sum_{m=1}^{n-1}\cdot S(m,1) + \sum_{m=2}^{n-1}\cdot S(m,2) where the S function is the Sterling function (S(n,k) is the number of k-partitions of an n-set) Homework Equations S(n,1) = 1 S(n,2) = 2^{n-1}-1 The Attempt...
  39. L

    Proving Shouten identity in QFT

    Hi, I'm trying to prove the Shouten identity for twistors: \langle pq\rangle\langle rs\rangle+\langle pr\rangle\langle sq\rangle+\langle ps\rangle\langle qr\rangle=0 It's easy to show that the LHS here is cyclically symmetric under q\to r\to s \to q, and also completely antisymmetric...
  40. U

    Is there a trigonometric identity for this ?

    Hi, I am trying to figure out what the result is when adding two sinusoids of the same frequency but with different phase and amplitudes. Specifically I want to know if the result is always another sinusoid of the same frequency. For the case of the the same amplitude I have: cos(wt) +...
  41. A

    Additive identity over linear transformation

    Given vector spaces V, W over a field, and linear transformation T:V\rightarrow W, prove T(0_{v})=0_{w} where 0_v and 0_w are additive identities of V and W. I'm trying to use the definition of additive identity. So, \forall\vec{v}\in V,\vec{v}+0=\vec{v+0=0} . Where do I go from here?
  42. K

    Solving "sin 2x = sin 2y" with Double Angle Identity

    Homework Statement I'm stuck on a question that results in this equality sin 2x = sin 2y how do I solve that for x or y? the only identity is the double angle one I can use I think but I don't know how that would help. Homework Equations The Attempt at a Solution
  43. L

    Number of permutations to obtain identity

    Homework Statement Let s*(f) be the minimum number of transpositions of adjacent elements needed to transform the permutation f to the identity permutation. Prove that the maximum value of s*(f) over permutations of [n] is {n \choose 2}. Explain how to determine s*(f) by examining f...
  44. N

    Does Ward Identity in QCD has origin of U(1) or SU(3) symmetry?

    Please teach me this: Can we deduce Ward Identity in QCD from U(1) symmetry of QED?Because QCD is a theory of quarks and quarks have electric charge.So we need not deduce the Ward Identity from SU(3) symmetry,but we can be able to demontrate the Ward Identity( considering gluons)with U(1)...
  45. L

    How does the identity Ln(detA)=Tr(lnJ) hold true?

    Hi, I've come across the identity det(expA)=exp(Tr(A)) many times now, but recently came across log(detA)=Tr(log(A)), can anyone explain to me why this is true? or if it can be derived from the more familiar first identity? I'm not sure if there are any particular constraints the matrix must...
  46. nomadreid

    Why does Euler's identity work only in Radians?

    e^iA = cosA + i*sinA is true iff A is expressed in Radians. Why that particular unit? (I'm not sure this rubric is the right one for this question, but since it didn't seem to fit any of the other rubrics, I put it here.)
  47. J

    Vector differential identity proof

    Hi, I am a engineering student and I am currently upgrading my maths level on my own to follow physics courses. While reading a book, I came across a vector differential identity that I don't manage to prove using index notation. The identity is the following: \nabla(\vec{A}\cdot\vec{B}) =...
  48. L

    Does every Hilbert space have an identity?

    I am sure that my questions are stupid. If we have a Hilbert space H, what do we mean by the closed subspace of H. Also, Does every Hilbert space have an identity? :P. Could anyone please clean to me these things . Thanks!
  49. C

    Vector identity involving grad and a function

    Homework Statement The question is to use index notation to show that the following is true, where a is a three-vector and f is some function. Homework Equations The Attempt at a Solution Hmmmm . . . I haven't really got anything to put here! I am starting to get to grips...
  50. T

    Trig Identity Integral Homework: Solving a Tricky Equation Using Substitutions

    Homework Statement I missed one class on trigonometric identities in integrals, and I feel that one is needed here: \int^3_0\frac{1+arctan(\frac{x}{3})}{9+x^2}dxHomework Equations The Attempt at a Solution Again, I'm unsure what to do. I think that it is a trig identity, but I could be wrong...
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