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 A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the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.
Consider this proof:
Is it a valid proof?
When we divide by ##z##, we assume that ##z \neq 0##. So, we cannot put ##z=0## on the next step. IOW, after dividing by ##z## we only know that $$c_1+c_2z+c_3z^2+...=d_1+d_2z+d_3z^2+...$$ in a neighborhood of ##0## excluding ##0##.
Hi all,
I'm trying to verify the following formula (from Fetter and Walecka, just below equation (12.38)) but it doesn't quite make sense to me:
where and
The authors are using the fact that ##\delta(ax) = |a|^{-1}\delta(x)## but to me, it seems like the...
Hi together!
Say we have ## \Lambda_q{(A)} = \{\mathbf{x} \in \mathbb{Z}^m: \mathbf{x} = A^T\mathbf{s} \text{ mod }q \text{ for some } \mathbf{s} \in \mathbb{Z}^n_q\} ##.
How can we proof that this is a subgroup of ##\mathbb{Z}^m## ?
For a sufficient proof we need to check, closure...
Since ##AB = B##, so matrix ##A## is an identity matrix.
Similarly, since ##BA = A## so matrix ##B## is an identity matrix.
Also, we can say that ##A^2 = AA=IA= A## and ##B^2 = BB=IB= B##.
Therefore, ##A^2 + B^2 = A + B## which means (a) is a correct answer.
Also we can say that ##A^2 + B^2 =...
Hey all,
I saw a formula in this paper: (https://arxiv.org/pdf/physics/0011069.pdf), specifically equation (22):
and wanted to know if anyone knew how to derive it. It doesn't seem like a simple application of BCH to me.
Thanks.
There is a proof that shows by induction (and by contradiction) that the identity permutation decomposes into an even number of transpositions. The proof is presented in the first comment here...
Hello.
Does anybody know a proof of this formula?
$$J_{2}(e)\equiv\frac{1}{e}\sum_{i=1}^{\infty}\frac{J_{i}(i\cdot e)}{i}\cdot\frac{J_{i+1}((i+1)\cdot e)}{i+1}$$with$$0<e<1$$
We ran into this formula in a project, and think that it is correct. It can be checked successfully with numeric...
I don't understand why the identity is mentioned in the group's definition and how I am supposed to incorporate it into the table. I honestly have missed some lectures on Linear Algebra, and I can't find any examples or definitions for this in the prof's notes. I'd appreciate some help for sure...
I would appreciate help walking through this. I put solid effort into it, but there's these road blocks and questions that I can't seem to get past. This is homework I've assigned myself because these are nagging questions that are bothering me that I can't figure out. I'm studying purely on my...
I'm trying to use the following trigonometric identity:
$$ a \cos ( \omega t ) + b \sin ( \omega t ) = \sqrt{a^2+b^2} \cos ( \omega t - \phi )$$ Where ##\phi = \tan^{-1} \left( \frac{b}{a} \right)## for the following equation:
$$ x(t) = -\frac{g}{ \omega^2} \cos ( \omega t) + \frac{v_o}{...
Refreshing on trig. today...a good day it is...ok find the text problem here; With maths i realize one has to keep on refreshing at all times... my target is to solve 5 questions from a collection of 10 textbooks i.e 50 questions on a day-day basis...motivation from late Erdos...
I found this identity: ##x\int e^{-x^2} dx - \int \int e^{-x^2} dx dx = e^{-x^2}/2## by solving the integral of ##x*e^{-x^2}## and then finding its integration-by-parts equivalent. Is this identity useful at all?
I have a question about the Thermodynamic Identity.
The Thermodynamic Identity is given by
dU = TdS - PdV + \mu dN .
We assume that the volume V and that the number of particles N is constant.
Thus the Thermodynamic Identity becomes
dU = TdS .
Assume that we add heat to the system (we see that...
My tests are submitted and marked anonymously. I got a 2/5 on the following, but the grader wrote no feedback besides that more detail was required. What details could I have added? How could I perfect my proof?
Beneath is my proof graded 2/5.
My tests are submitted and marked anonymously. I got a 2/5 on the following, but the grader wrote no feedback besides that more detail was required. What details could I have added? How could I perfect my proof?
Beneath is my proof graded 2/5.
My intuition about the Lie algebra is that it tries to capture how infinitestimal group generators fails to commute. This means ##[a, a] = 0## makes sense naturally. However the Jacobi identity ##[a,[b,c]]+[b,[c,a]]+[c,[a,b]] = 0## makes less sense. After some search, I found this article...
So, this problem I sort of get conceptually but I don't know how I can possibly rewrite (idX)∗ : π1(X) → π1(X). Does this involve group theory? It's supposed to be simple but I honestly I don't see how. Again, any help is greatly appreciated. Thanks.
Dear All,
I am trying to prove the following identity:
\[\binom{n}{k}=\binom{n-2}{k}+2\binom{n-2}{k-1}+\binom{n-2}{k-2}\]
My attempt was based on transforming the binomial coefficients into fractions with factorials, and then elimintating similar expressions. Somehow it didn't work out.
I...
I am reading this book:
https://web.stanford.edu/class/math285/ts-gmt.pdf
on page 2 in remark 1.5(1), it's written that:
##\cap_{j=1}^\infty A_j = X\setminus (X\setminus \cup_{j=1}^\infty A_j)##
this seems totally wrong, shouldn't it be ##X\setminus \cup_{j=1}^\infty (X\setminus A_j)## ?
I...
First of all, sorry for the title I don't know the name of this formula and that's part of the problem, I can't find anything on google.
I have to show the identity above. Here's what I did. I don't know if this is correct so far.
##\vec{u} + \vec{r}(\vec{\nabla} \cdot \vec{u}) + i(\vec{L}...
This alternating series indentity with ascending and descending reciprocal factorials has me stumped.
\frac{1}{k! \, n!} + \frac{-1}{(k+1)! \, (n-1)!} + \frac{1}{(k+2)! \, (n-2)!} \cdots \frac{(-1)^n}{(k+n)! \, (0)!} = \frac{1}{(k-1)! \, n! \, (k+n)}
Or more compactly,
\sum_{r=0}^{n} (...
Cool article by By Molly Harris (BBC), 23rd April 2019
https://www.bbc.com/travel/article/20190422-the-swiss-language-that-few-know
I've wondered about places like Alsace and Lorraine that have moved back and forth among two nations/states/regions, or for that matter, the borders of nations...
Came across this trig identity working another problem and I've never seen it before in my life. I don't need to prove it myself, necessarily, but I would really like to see a proof of it (my scouring of the internet has yielded no results). If someone more trigonometrically talented than myself...
What I mean is the way that a product of cosines in which the angles increment the same amount is equal, with some extra terms, of the sum of the cosines.
It is discussed here...
I have accidentally derived a very wrong result from the contracted Bianchi identity and I can't see where the error is. I'm sure it's something obvious, but I need someone to point it out to me as I've gone blind. Thanks!
Start with the contracted Bianchi identity,
$$
\nabla_a \left(...
All we should need for this problem are the basic rules for the Grassmann algebra
\begin{equation*}
\{ \theta_i, \theta_j\} = 0, \quad \theta^2_i=0
\end{equation*}
\begin{equation*}
\int d\theta_i = 0, \quad \int d\theta_i \ \theta_i = 1
\end{equation*}
Starting from left to right...
I tried to understand proof of this identity from electromagnetics. but I was puzzled at the last expression.
why is that line integral of dV = 0 ?
In fact, I'm wondering if this expression makes sense.
The book I'm following (Gallian) basically says:
r can't be 1 since then it won't map all elements to themselves.
If r=2, then it's already even, nothing else to do.
If r>2,
Then consider the last two factors: ##\beta_{r-1} \beta_r##.
Let the last one be (ab).
Since the order of elements...
My attempt at this:
From the general result
$$\int \frac{d^Dl}{(2\pi)^D} \frac{1}{(l^2+m^2)^n} = \frac{im^{D-2n}}{(4\pi)^{D/2}} \frac{\Gamma(n-D/2)}{\Gamma(n)},$$
we get by setting ##D=4##, ##n=1##, ##m^2=-\sigma^2##
$$-\frac{\lambda^4}{M^4}U_S \int\frac{d^4k}{(2\pi)^4} \frac{1}{k^2-\sigma^2} =...
Attempt : I could not progress far, but the following is what I could do.
$$\begin{align*}
\mathbf{\text{LHS}} & = (\tan A+\tan B+\tan C)(\cot A+\cot B+\cot C) \\
& = 3+\tan A \cot B+\tan B \cot A+\tan A \cot C+\tan C \cot A+\tan B \cot C+\tan C \cot B\\
& = 3+\frac{\tan^2A+\tan^2B}{\tan A \tan...
We have some potential that depends on slowly varying parameters ##\lambda_a##. Using the angle-action variables ##(I, \theta)##, the claim is that we can define a two-form$$W_{ab} = \left\langle \frac{\partial \theta}{\partial \lambda_a} \frac{\partial I}{\partial \lambda_b} - \frac{\partial...
I am probably missing a crucial point here, but what does it means that (12)(34) squares to the identity? How do we prove it?
((12)(34))² = (12)(34)(12)(34) = (12)(12)(34)(34) = (12)(34) ##\neq I ##
Is not this the algorithm?
Let us suppose we have a function such that
$$z = e^{1/ab} - 1$$
Where we have two free parameters, a and b.
Q1) Can we say that as ##b \rightarrow \infty##, ##z = 0##?
Or, since ##a## is a free parameter, there is always some value for ##a## such that ##z \neq 0## for ##b \rightarrow...
Am I(always) legitimized to write ##-(a-b)^n=(b-a)^n##?
I don't know why but it's confusing me... can't really understand when and why I can use that identity
Hi!
The topic is electrodynamic but it's a question about Nabla identity. Given $$ F = (p \cdot \nabla)E $$
How does one compute F? Is this correct?
$$ F = \sum_{i} p_i \partial_{i} E_{i} e_{i} $$
Theorem “Identities of + are unique”: O₁ = O₂
Proof:
O₁
= Left Identity of +
O₁ + x
I'm a little confused where to begin this proof, I don't know if that is the first step either I think it is. Proofs are not a strength of mine so I struggle to see how to show that O₁ = O₂. Any guidance would...
##(\nabla\times\vec B) \times \vec B=\nabla \cdot (\vec B\vec B -\frac 1 2B^2\mathcal I)-(\nabla \cdot \vec B)\vec B##
##\mathcal I## is the unit tensor
So the Legendre transforms are straightforward; define ##S_1=S-\beta E## and ##S_2= S-\beta E + \beta \mu n## then we get:
##dS_1 = -Ed\beta - \beta \mu dn + \beta PdV##
##dS_2 = -Ed\beta + nd(\beta \mu) + \beta PdV##
And so by applying the equality of mixed partials of ##S_1## and ##S_2## we...
I was just wondering what is wrong with the following logic;
From the Gibbs-Duhem relation we get,
##\frac{\partial \mu}{\partial P}\Big\rvert_T = v##
Now consider,
##\frac{\partial v}{\partial \mu}\Big\rvert_T = \frac{\partial }{\partial \mu}\Big (\frac{\partial \mu}{\partial P}\Big\rvert_T...
If we can identify ##|c_n|^2## as the probability of having an energy ##E_n##, then that equation is just the bog standard one for expectation. But the book has not proved this yet, so I assumed it wants a derivation from the start.
I tried $$
\begin{align*}
\Psi(x,t) = \sum_n c_n...
(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
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...