qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
150,034 | [
"https://dba.stackexchange.com/questions/150034",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/33196/"
] | what I am trying to do is performing a query that has multiple results of the same query by just editing only a where clause.
The goal is to query a result of the same dataset in different date ranges, but instead of performing multiple separated queries, having one single query that queries the tables X times (depend... | Your pseudo-SQL is surprising close to the <strong>standard</strong> SQL clause <code>FILTER</code>, which has only been implemented by Postgres but unfortunately not by MySQL:
<pre><code>SELECT database_one.users.firstname,
database_one.users.lastname,
COUNT(*) AS "Total",
-- Standard SQL: FILTER... | Here's a sketch (note that I changed the GROUP BY and removed the ORDER BY since it was not clear to me what the query was suppose to mean)
<pre><code>SELECT database_one.users.firstname,
database_one.users.lastname,
COUNT(*) AS "Total",
COUNT(CASE WHEN database_two.announcements.archived_at > ... | https://dba.stackexchange.com |
32,799 | [
"https://mathoverflow.net/questions/32799",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7804/"
] | Let <em>X</em> be a normed space and denote by <em>X<sup>*</sup></em> the space of all bounded linear functionals on <em>X</em>. Take a linear subspace <em>G ≤ X<sup>*</sup></em> which separates the elements of <em>X</em>, i.e., for each <em>x ∈ X</em>, there is an <em>f ∈ G</em> with <em>f(x) ≠ 0</em>.... | If I understand the question correctly, then maybe you are after special cases, as well as a general comment. So, as one of your examples suggests, one special case is to let G be a Banach space, considered as sitting inside its own bidual, and let $X=G^*$. Thus G induces the usual weak*-topology on X.
So an example... | I am not sure if this counter example works, but I am pretty sure. It is related to the counterexample mentioned in the question.
Consider in $\ell^1(\mathbb{Z})$ the usual ``base'' formed by the vectors $e_i$ given by the sequence having a $1$ in the position $i$.
We consider $G$ to be the subspace of $(\ell^1)^\as... | https://mathoverflow.net |
534,745 | [
"https://physics.stackexchange.com/questions/534745",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/225773/"
] | Suppose I have a closed piston-cylinder system which contains an ideal gas,and it is being compressed adiabatically by the piston which has a vertical orientation,and in doing so,the piston is actually undergoing SHM. Now if I use a similar piston in a horizontal orientation (keeping in mind the dimensions of the cylin... | The equilibrium position of the piston would change due to the weight of piston. However it would not interfere with time period or frequency as it is acting throughout the process. In the second position equilibrium position would be different. For more accuracy you could also take into account the change in external ... | It is straightforward to show that if <span class="math-container">$$pV^\gamma =\text{constant}$$</span>
then
<span class="math-container">$$\frac{dp}{dV}=-\gamma \frac pV$$</span>
Therefore for small changes, <span class="math-container">$\Delta V$</span>, in volume, giving rise to small changes, <span class="math-con... | https://physics.stackexchange.com |
2,791 | [
"https://mathoverflow.net/questions/2791",
"https://mathoverflow.net",
"https://mathoverflow.net/users/683/"
] | I have heard people say that a major goal of number theory is to understand the absolute Galois group of the rational numbers $G = \mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$. What do people mean when they say this? The Kronecker-Weber theorem gives a good idea of what the abelianization of $G$ looks like. But in one of... | What would it mean to understand this Galois group? You could mean several things.
You could mean trying to give the group in terms of some smallish generators and relations. This would be nice, and help to answer questions like the inverse Galois problem that Greg Muller mentioned, and having a certain family of "gen... | $\newcommand{\bb}{\mathbb}$
This is a response to Charles' remark to JSE's answer, why doesn't $\bar{\bb Q}$ come with a <i>standard</i> algebraic closure inside the complex numbers $\bb C$?
First, if one considers an abstract extension $K/\bb Q$, then $K$ has $d = [K:\bb Q]$
embeddings into the complex numbers, whic... | https://mathoverflow.net |
176,922 | [
"https://softwareengineering.stackexchange.com/questions/176922",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/73435/"
] | We have a large project that has nearly 20 modules on it. We want to use WCF for the business layer.
We have thought of three ways to implement WCF our project:
<ol>
<li>Use only one datacontract and one operation contract. Send
ClassName, MethodName to operation and create class by reflection
then invoke the method ... | Assuming that the 20 modules are not completely unrelated, the second way is the normal approach.
Ideally, you would like calling your services via WCF to feel very similar to calling methods in a DLL. That's the whole point of the WCF (and going back to earlier days, webservice) client proxies.
The first idea - usin... | <ol>
<li>Don't, It will be a mess.</li>
<li>If you need all modules everytime do it.</li>
<li>On my side I have several services serving different usecase domain.
I want them to be injected in my app through an abstract interface so our app can use local implementation, wcf distant implementation or anyother transport.... | https://softwareengineering.stackexchange.com |
314,462 | [
"https://math.stackexchange.com/questions/314462",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/62874/"
] | Suppose the order of $g$ is odd. What can you say about the order of $g^2$?
I think that the order of $g^2$ is going to be even. Is this true or false?
| Suppose that $g$ has order $k$, where $k$ is odd. Then $g^k$ is the identity, and therefore $g^{k+1}=g$. Thus $(g^2)^{(k+1)/2}=g$.
That means that the subgroup generated by $g^2$ is <em>the same</em> as the subgroup generated by $g$. We conclude that $g^2$ also has order $k$.
| Not necessarily. Consider G is ($\mathbb{Z}_5, +$) and $g=1$.
| https://math.stackexchange.com |
2,225,637 | [
"https://math.stackexchange.com/questions/2225637",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/430020/"
] | <blockquote>
Example 8. Consider
$$\Bbb Z_2\times\Bbb Z_2 = \{(0,0),(0,1),(1,0),(1,1)\}$$
Although $\Bbb Z_2\times\Bbb Z_2$ and $\Bbb Z_4$ both contain four elements, it is easy to see that they are not isomorphic since for every element $(a,b)$ in $\Bbb Z_2\times\Bbb Z_2$, $$(a,b) + (a,b) = (0,0),$$ but
$\Bbb ... | You should think of isomorphic groups as being really the "same". For instance:
<blockquote>
<strong>Fact</strong>: If $G$ and $H$ are isomorphic groups, and $g\in G$ corresponds to $h\in H$ under this isomorphism, then $g$ and $h$ have the same order.
</blockquote>
This is what is being used in the proof you're as... | Well, $(a,b)+(a,b)=(2a,2b)=(0,0)$ since $2a=0$ for all $a\in \mathbb{Z}_2$. It shows that there are no elements of order greater than $2$ in $\mathbb{Z}_2\times \mathbb{Z}_2$. By definition, $\mathbb{Z}_4$ does have an element of order $4$.
You can show that isomorphisms of groups preserve orders of elements. (Any pro... | https://math.stackexchange.com |
82,858 | [
"https://mathoverflow.net/questions/82858",
"https://mathoverflow.net",
"https://mathoverflow.net/users/19781/"
] | Consider the matrix $H=H^T$, $H>0$, $H \in R^{n \times n}$, and the vector $v \in R^n$. In a numerical algorithm, I need to compute the product $b = Hv$. Right now I am following the naive approach:
$b_i = \sum_{j=1}^{n} h_{ij} v_j, i=1,...,n$.
Is there a faster way to compute this product? $H$ is non-sparse and co... | If I understand the question right, by "constant" it is meant that $H$ is a fixed, but arbitrary positive definite matrix.
In general, I don't think that you can compute the matrix-vector product $Hv$ faster than $O(n^2)$. But if $H$ has structure (Toeplitz, Circulant, Strictly diagonally dominant, etc.), or if you ar... | In fact, $O(n^2)$ arithmetic operations is not avoidable, in general.
A general result by Winograd (see "Algebraic complexity theory" by Buergisser, Clausen, and Shokrollahi, Sect. 13.2) shows that the for a generic $m\times n$ matrix (all the entries are algebraically independent) and a generic vector one will need $O... | https://mathoverflow.net |
300,438 | [
"https://physics.stackexchange.com/questions/300438",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | The gravitational constant $G$ has units of $N m^2 kg^{-1} = m^3 kg^{-1} s^{-2}$.
Since seconds appear as units, time dilation would seem to affect the value of $G$ for different observers. That is, the "second" of one observer may differ from that of another observer, and that would seem to affect $G$. Similarly, the... | Take a string and hold it tight between your hands. And just hold it there. Tight.
No net force on any piece of the string, of course. But a net force at the ends? <strong>Also no</strong>! Otherwise they would move (accelerate).
Here is the line of thought:
<ul>
<li>One hand pulls in one end. Since that end doesn... | You are correct that the net force at any point on the spring must be zero when the spring is in equilibrium - if it were not zero, something would have to be moving. This is always the case any time you're considering different forces acting on an object - if the net force works out to be non-zero, then the object mus... | https://physics.stackexchange.com |
124,930 | [
"https://mathoverflow.net/questions/124930",
"https://mathoverflow.net",
"https://mathoverflow.net/users/21095/"
] | <strong>Edit:</strong> Zhen Lin incisively observes in a comment below that the category of compact Hausdorff spaces is monadic over the category of sets, hence is cocomplete. That answers the first part of question 1 as it was stated previously. I have changed that question accordingly.
<strong>Final edit:</strong> C... | As Zhen Lin points out in the comments to your question, the category of compact Hausdorff spaces has all small colimits. However the inclusion functor from CHTop to Top does not preserve these colimits in general. It seems from your other questions that you are interested in a category, either CHTop or something simil... | The examples given are part of the case for homotopy colimits. For example the pushout of the two maps $$S^1 \leftarrow S^1 \to S^!$$
given by $z\mapsto z^2, z \mapsto z^3$ is not Hausdorff. But the double mapping cylinder $M$ is a nice CW-complex. Amusingly, this is rel;ated to the case for groupoids, where the pusho... | https://mathoverflow.net |
578,876 | [
"https://physics.stackexchange.com/questions/578876",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/273611/"
] | I have a question about this equation: <span class="math-container">$$\frac{1}{2}\otimes\frac{1}{2}=1\oplus0.$$</span>
I'm a bit confused by the right-hand side. Should '1' and '0' be interpreted as the total spin? If so, if there're two particles both have spin <span class="math-container">$-\frac{1}{2}$</span>, why t... | So the related question is not so much help to you because you have a much more fundamental misunderstanding. Once we clear that up, any further questions should be answered by the above.
There is no such <span class="math-container">$-1$</span> or <span class="math-container">$-1/2$</span> system.
For this we have to ... | This equation is an equation for representations of the Lie algebra of rotations. It is a fact proven in every quantum mechanics book that the irreducible representations of the angular momentum algebra <span class="math-container">$[J_i,J_j]=\epsilon_{ijk}J_k$</span> are spin <span class="math-container">$j$</span> sy... | https://physics.stackexchange.com |
519,879 | [
"https://physics.stackexchange.com/questions/519879",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/249683/"
] | The textbook says the eigenvalue of the Pauli y matrix is 1 and -1, the corresponding eigenvectors are,
<span class="math-container">$$\sqrt{\frac{1}{2}}
\begin{bmatrix}
1\\
i
\end{bmatrix}
, \sqrt{\frac{1}{2}}
\begin{bmatrix}
1\\
-i
\end{bmatrix}
$$</span>
But it seems I cannot get the original Pauli y matrix by ad... | If <span class="math-container">$\psi_1 = \frac{1}{\sqrt{2}} \begin{bmatrix} 1 \\ i \end{bmatrix}$</span> and <span class="math-container">$\psi_2 = \frac{1}{\sqrt{2}} \begin{bmatrix} 1 \\ -i \end{bmatrix}$</span> you get
<span class="math-container">$$ \psi_1 \psi_1^\dagger = \frac{1}{2} \begin{bmatrix} 1 & -i \\ ... | They seem orthogonal: <span class="math-container">$\psi_2^\dagger \psi_1=0$</span>.
| https://physics.stackexchange.com |
3,126,163 | [
"https://math.stackexchange.com/questions/3126163",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/561797/"
] | Excerpt from Topology by Munkres
(1)Definition:
A collection <span class="math-container">$\mathbf A$</span> of subsets of a space X is said to cover X, or to be a covering of X, if the union of the elements of <span class="math-container">$\mathbf A$</span> is equal to X. It is called an open covering of X if its el... | He starts the proof of theorem 27.1 by taking an arbitrary open cover of the interval <span class="math-container">$[a,b]$</span>. To show that the interval is compact it suffices, by definition, to find a finite subcover. Note that <span class="math-container">$A$</span> denotes the original collection of open sets co... | It's an artifact of the way we prove statements of the form <span class="math-container">$\forall x: \exists y: \phi(x,y)$</span>: we take some arbitrary element <span class="math-container">$x$</span> (temporarily fixing it, as it were) and reason on it to "construct" or prove the existence of , some <span class="math... | https://math.stackexchange.com |
130,462 | [
"https://security.stackexchange.com/questions/130462",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/110848/"
] | I am doing some hands-on training with Kali linux and one of the exercise I came across was to make an exe file containing malicious payload(say to obtain reverse shell), send it to a victim and hope for the victim to download the exe file. If he/she downloads it, it is fairly easy after that.
Now this isn't tricky ... | There are a number of ways that people attempt to mitigate these attacks.
<strong>External</strong>
<ul>
<li>Prevent spam filter from allowing MIME types frequently associated with malware (it's highly unlikely there is a business relevant reason to send .exe or .bat files for instance)</li>
<li>Use Anti-Virus as .e... | You'd be surprised how successful something like this can be - especially for a typical user who may not have any security controls in place. Also, I would argue that if you are able to convince a user to execute code you have provided, a malicious exploit is probably not even necessary - (i.e. "Microsoft Tech Support... | https://security.stackexchange.com |
185,768 | [
"https://mathoverflow.net/questions/185768",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8435/"
] | Fix $n$ and let $B, C$ be two $n \times n$ 0-1 matrices of full rank such that $\sum_{i,j} b_{i,j}^2 = \sum_{i,j} c_{i,j}^2$, in other words they have the same number of $0$ entries and the same number of $1$ entries. I want to find $\alpha_n = \max ||B||/||C||$ subject to this constraint as a function of $n$.
| Take $B$ to have $1$s on the main diagaonal and the first superdiagonal, then $\|B\|\leq 2$. If we take $C$ to have $1$s on the diagonal and filling the last column, then $\|C\|\geq \sqrt{n}$. (These both have full rank and $2n-1$ $1$'s.) This shows that $\alpha_n\geq \frac{\sqrt{n}}{2}$, though from the examples in Ro... | The answer is $\sqrt{n}$. You can argue as follows:
<ol>
<li>We know that $$\| X\| \le \| X \|_2 \le \sqrt{n} \cdot \| X\|,$$ for any $X\in M_n$. The condition on $B$ and $C$ implies that $$\| B\|_2 = \| C\|_2.$$ Hence $$a_n = \max \frac{\| B \|}{\| C\|} \le \max \frac{\| B\|_2}{\| C\|} = \max \frac{\| C\|_2}{\| C\... | https://mathoverflow.net |
190,186 | [
"https://security.stackexchange.com/questions/190186",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/182759/"
] | I am an information security intern for a MSP.
The company is set up to work remotely a few days a week. As I was gathering information for the assessment, I found out that one of the employees does not have a packet filtering firewall. She is running a Cisco Umbrella DNS agent and an SSL VPN when working remotely. S... | I assume she expects that Umbrella will protect her from any unauthorised outbound connections because Umbrella whitelists common domains and blocks suspicious domains. A firewall also protects the machine from outbound connections.
The problem with Umbrella is that it only works on <em>domains</em> and not IPs. If ma... | As we don't have the full picture of what the infrastructure looks like this is non-trivial to answer.
To clarify the situation I would suggest checking how the VPN tunnel terminates on the enterprise infrastructure. Very likely it is either terminating directly on a new-gen firewall (that does packet but also statef... | https://security.stackexchange.com |
284,903 | [
"https://softwareengineering.stackexchange.com/questions/284903",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/134886/"
] | Currently, I used to create a new branch each time I have to add a new feature to my application.
When my feature is finished and functional, I merge it with the master branch.
But later, when I need to update this feature (like an improvement) is it better to create a new branch or do I need to rebase the previous w... | Create a new branch, because:
<ul>
<li>A brand new branch is less likely to have merge conflicts when you're done and want to merge it into master. Few things are more error-prone than fixing merge conflicts.</li>
<li>The feature may have gone through several changes and updates since its original implementation, maki... | Use a new branch.
For naming, you could consider using an internal format that <em>this_work</em> is an extension or change to <em>that_work</em>
For example you could name the second branch
<pre><code>modeling-member--attributes
</code></pre>
with the -- signalling that the name name on the left is the original br... | https://softwareengineering.stackexchange.com |
3,890,050 | [
"https://math.stackexchange.com/questions/3890050",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/775699/"
] | The following statement was left as exercise in my Field Theory class.
<blockquote>
Consider a field K and f <span class="math-container">$\in K[x] $</span> an irreducible polynomial. Prove that f is separable in some splitting field of f over K if every root of K is simple root which is equivalent to saying that deriv... | Your iteration is special case of the stationary iteration <span class="math-container">$$x_{n+1} = Gx_n + f$$</span> which can occasionally be used to solve the linear system <span class="math-container">$$x = Gx +f.$$</span> The initial guess <span class="math-container">$x_0$</span> must be selected by the user, but... | It works the same in <span class="math-container">$\Bbb R^n$</span> as in <span class="math-container">$\Bbb R$</span>. Find the limit, which will be a vector. Add a different epsilon to each component of the vector, apply the iteration, and see how much closer to the limit the new value is. You will have three orde... | https://math.stackexchange.com |
149,430 | [
"https://electronics.stackexchange.com/questions/149430",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/57793/"
] | In networks
capacity_of_link = bandwidth*propagation_delay
My doubt is how can a same wire carry multiple signals? Is is because the wire is very long (still the wire can be either high or low). I can understand if parallel wires are the reason for increase in bandwidth and thus capacity increase.
| <em>the wire can be either high or low</em>
This assumption is wrong and is the source of your doubt. At high speed it's perfectly possible for one end to be high and the other low. A transition ("edge") from high/low takes time to propagate along a wire. It doesn't propagate at the speed of light either, but at a rat... | Ethernet standards use signal modulation to increase bandwidth without much frequency increase.
For instance 1000Base-T use PAM-5 modulation, it allows to transmit 2 bits at a time:
<ul>
<li>00 : -1V</li>
<li>01 : -0.5V</li>
<li>Control : 0V</li>
<li>10 : +0.5V</li>
<li>11 : +1V</li>
</ul>
And for 10GBase-T a PAM-16... | https://electronics.stackexchange.com |
3,120,308 | [
"https://math.stackexchange.com/questions/3120308",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/379585/"
] | Is the following deduction correct?
<span class="math-container">$$ (a+b)\bmod20=y $$</span>
<span class="math-container">$$\implies (a+b)\bmod20 = y \bmod20$$</span>
<span class="math-container">$$\implies (a+b) \equiv y\pmod{20}$$</span>
| When viewing <span class="math-container">$\bmod{n}$</span> as a <em>relation</em>, we are using the definition that <span class="math-container">$a \equiv b \pmod{n}\,$</span> means <span class="math-container">$n \mid b-a$</span>. In this context, I don't think you would normally see that first statement at all, and ... | It is correct because we can conclude <span class="math-container">$\ 0\le x<20\ $</span> from the first line, so <span class="math-container">$x$</span> must coincide with <span class="math-container">$x\mod 20$</span>. The second implication is obvious.
| https://math.stackexchange.com |
233,556 | [
"https://electronics.stackexchange.com/questions/233556",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/109627/"
] | <img src="https://i.imgur.com/0CuDzXj.png" alt="capacitor question">
I study 1st year electronic engineering, and my university has a policy against posting past paper solutions. I can derive the equation in part a.) however I don't understand how to complete the 2nd part. If anyone could explain what to do that would... | <ol>
<li>just substitute Vc in the above equation. name it "eq1"</li>
<li>at t=0, Vc=0
now you get V2-K1=K2(R2C2L+1) (L is lambda) :"eq2"</li>
<li>return to "eq1" and substitute V2-K1 to obtain an expression with only L and K2. you can factorize and solve with 2 possible solutions: L=-1/R2C2 or K2=0</li>
<li>for the fi... | Substitution is easy and straight forward but here is the second method : this requires you to rearrange the equation as shown and then apply integration on both sides to get the voltage across the capacitor with respect to time.
$$\frac {dv_c}{v_2-v_c}=R_2C_2 dt$$
this is the rearranged equation.
You may be able to... | https://electronics.stackexchange.com |
2,355,762 | [
"https://math.stackexchange.com/questions/2355762",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/455889/"
] | I want to construct a 2-tape TM, that converts a binary number into unary and takes $O(n)$ time.
Let $n \in \mathbb N$ be the number I want to convert. My idea was that I just subract 1 from bin(n) until bin(n) = 0 and each time it subracted one, I add one '1' to my unary number on the 2nd tape. But I don't know if th... | Take a look at what the integral provides in a slightly more general case:
\begin{align}
\int_{- \infty}^{\infty} e^{- a x^2} \, dx &= 2 \, \int_{0}^{\infty} e^{- a x^2} \, dx \\
&= \frac{1}{\sqrt{a}} \, \int_{0}^{\infty} e^{- t} \, t^{- \frac{1}{2}} \, dt \hspace{5mm} \text{where} \, t = a \, x^2\\
&= \... | The pdf of normal distribution with mean $0$ and variance $\frac{1}{\sqrt{2}}$ is $f(x) = \frac{1}{\sqrt{2\pi}\frac{1}{\sqrt{2}}}e^{-x^2}$.
Since, $\int_{-\infty}^{\infty}f(x)dx = 1 \implies \frac{1}{\sqrt{\pi}}\int_{-\infty}^{\infty}e^{-x^2}dx = 1$
| https://math.stackexchange.com |
11,331 | [
"https://quantumcomputing.stackexchange.com/questions/11331",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/11510/"
] | I'm studying Quantum Information Theory by Mark M. Wilde, and I got stuck in solving the exercise 3.8.2 in page 100. The exercise is to show that a pure bipartite state is entangled if and only if it has more than one Schmidt coefficient. The hint below the problem says that
<span class="math-container">\begin{equati... | You're asking how to prove
<span class="math-container">\begin{equation*}
\max_{|φ\rangle_A,|ψ\rangle_B} |\langleφ|_A ⊗ \langleψ|_B |ϕ\rangle_{AB}|^2 < 1
\end{equation*}</span>
as opposed to actually answering the question?
To prove this, consider the Schmidt decomposition of <span class="math-container">$|ϕ\rangle... | I'd ignore that hint and instead try to prove the contrapositives: show that a pure state is a product state iff it has one (nonzero) Schmidt coefficient.
| https://quantumcomputing.stackexchange.com |
91,140 | [
"https://security.stackexchange.com/questions/91140",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/29394/"
] | I am evaluating an internal 2 factor authentication implementation in an organization. The system designer wants to remove regular user names and passwords from all user workstations such that each user will have his badge as a login token and will have to enter a 6 digit key to login into his workstation. <strong>Is t... | You basically answered your own question by stating anyone in the world can read this information. This makes me believe it is not necessary.
However, from a security point of view it is always recommended to use best practices, meaning: use transport layer protection.
<strong>Web based Clients</strong>
Since the w... | <blockquote>
I have a MySQL and Apache web server (both are installed on the same machine). Users will interact with it by a VB.NET application and the web. The server is accessible by the Internet.<br>
...<br>
The information is not super critical, it's just stats/benchmarks (especially since anyone in the world... | https://security.stackexchange.com |
4,027 | [
"https://electronics.stackexchange.com/questions/4027",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/989/"
] | I've reviewed the two methods, and multiplexing really only appears to have one advantage, that it would be easier to track down a failed LED than in a Charlieplex array.
Can someone more knowledgeable explain any other trade-offs?
| Yes, multiplexing and charlieplexing both have their advantages, and are each best suited for different tasks.
The main advantage of charlieplexing is that it can be done on a medium-size microcontroller, driving more LEDs with fewer I/O pins, and potentially no external hardware besides the LEDs.
Now, the advantag... | The most significant disadvantage of "Charlieplexing" lights is that it limits the number of LEDs that can be driven with 'n'-way multiplexing to n(n-1). I don't see the tri-state driver requirement as being much of an issue with the technique as a whole. Certainly having to use two conventional drivers instead of a ... | https://electronics.stackexchange.com |
96,797 | [
"https://dba.stackexchange.com/questions/96797",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/62178/"
] | <strong>Background:</strong>
I'm building a SQL command to be executed on the server which involves a lot of accessing store procedure and declaring variables which are used as input to other stored procedures. This is all generated on the client side using C# and send as a big package. I have to do it this way since ... | You cannot redeclare variables, nor can you test to see if they have been declared (at least not that I have ever been able to find). BUT, you shouldn't need to do this anyway. If you know the variable names ahead of time, just declare them all at the beginning of the process. Then, use them throughout the script.
For... | From reading your question I think you are building the SQL code in your application and then sending it to the server as one long script with multiple statements.
If this is the case you can separate your statements with GO to create batches. The following is valid SQL:
<pre><code>DECLARE @a INT;
SET @a = 1;
SELECT... | https://dba.stackexchange.com |
351,103 | [
"https://electronics.stackexchange.com/questions/351103",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/135076/"
] | Is code like the following legal or would this give undefined behavior in case reset is set? Would the compiler turn the initial assignment into a conditional or first increment the counter, then reset to 0? If this is executed sequentially, how are these sequential relationships represented in hardware?
<pre><code>a... | On UART receive event:
<pre><code> FIFO[Wr_pointer]= UART_Char;
WR_Pointer++;
WR_Pointer & = 3FF;// FIFO[1024] roll over 1022..1023...0...1...2
if WR_Pointer==RD_Pointer then
Overrun= true;
else
{
SizeFIFO = (WR_Pointer - RD_Pointer);
SizeFIFO & = 3FF;
}
</cod... | <blockquote>
The problem I'm facing is how to deal with simultaneously writing and reading to and from the FIFO buffer.
</blockquote>
Sequential Not parallel.
<blockquote>
Now I'm trying to find the best solution to prevent overwriting on reading pointer while interrupt routine never stops to put data
</blockquo... | https://electronics.stackexchange.com |
280,056 | [
"https://softwareengineering.stackexchange.com/questions/280056",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/124643/"
] | I say odd like a mathematical function, a mathematical function is odd if
<pre><code>f(-x) = -f(x)
</code></pre>
I understand that comparing two strings may seem to have little to do with this, because the arguments cannot be negative, but I mean that the functions value should be the negative of it's value with swap... | You could do this with <em>any</em> string distance function.
For example, consider the following distance function:
<pre><code>distance(a, b)
{
return calc(a, b);
}
</code></pre>
If you make the order of the arguments significant, then you can invert the sign of the result as needed:
<pre><code>distance(a,... | Yes, there is a lot of them! This is just the theory of <em>even</em> and <em>odd</em> part of functions adapted to this context.
Take any function <em>h</em> defined on pair of strings and set <em>ĥ(a,b) = h(b,a)</em>. Then the <strong>odd</strong> and <strong>even</strong> part of <em>h</em> are respectively <em>h-... | https://softwareengineering.stackexchange.com |
567,387 | [
"https://physics.stackexchange.com/questions/567387",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/231957/"
] | I'm studying special relativity.
A general Lorentz transformation is defined by <span class="math-container">$\Lambda^T\eta\Lambda=\eta$</span>.
Now,
<span class="math-container">\begin{align}
\eta'^{\mu\nu} &= \Lambda^\mu_{\;\;\alpha}\Lambda^\nu_{\;\;\beta}\eta^{\alpha\beta}\\
&= (\Lambda\eta\Lambda^T)^{\mu\nu... | As you pointed out, the matrix form for the transformation equation of <span class="math-container">$\eta$</span> is:
<span class="math-container">$$\eta' = \Lambda \eta \Lambda^T$$</span>
It's possible to show that <span class="math-container">$\eta' = \eta$</span>, given that <span class="math-container">$\eta = \Lam... | The Lorentz transformations are in particular coordinate transformations and the metric tensor is well, a tensor therefore it transforms as a tensor (left hand side of the following equation) and we demand it leaves the metric unchanged (right hand side of the equation):
<span class="math-container">$$\eta_{\alpha\beta... | https://physics.stackexchange.com |
426,126 | [
"https://mathoverflow.net/questions/426126",
"https://mathoverflow.net",
"https://mathoverflow.net/users/485348/"
] | Suppose <span class="math-container">$X$</span> is an infinite set and <span class="math-container">$\mathcal{A}$</span> is a family of subsets of <span class="math-container">$X$</span>.
(1) We say that <span class="math-container">$\mathcal{A}$</span> is <strong><span class="math-container">$k$</span>-cover-free</str... | Yes. Let <span class="math-container">$S$</span> be a set of cardinality <span class="math-container">$|S|\ge k+2$</span>. Let <span class="math-container">$X=\binom Sk$</span>, the set of all <span class="math-container">$k$</span>-element subsets of <span class="math-container">$S$</span>. For each <span class="math-... | For each natural number <span class="math-container">$n\in\omega$</span>, let <span class="math-container">$U_n\subseteq\mathbb{R}^k$</span> be a randomly selected (according to some reasonable distribution) affine hyperplane. Suppose now that <span class="math-container">$a_0,\dots,a_k$</span> are distinct natural num... | https://mathoverflow.net |
211,023 | [
"https://softwareengineering.stackexchange.com/questions/211023",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/60812/"
] | So I was wondering today, where would you put utility classes in an ASP.NET MVC app? By utility classes I mean classes that can be static and are just used to perform a function. Like a class to send an email that takes email address , subject, and body as arguments.<br>
I would assume maybe creating a separate folder ... | You don't. And your own example is a perfect one to show why not.
You want to send emails, right? So you create somewhere a static class <code>CommunicationUtilities</code> with a static <code>SendEmail()</code> in it. You use this method from some class which does a bunch of stuff, , for example resets the password o... | The question is a valid one, even if the example given is not. The answer given by Maina is perfect, in a very specific context, which is not to me, the proper context for said <em>"utility"</em> classes.
Personally, I create a folder <code>Helpers</code> in which I put simple functions to be called from about anywher... | https://softwareengineering.stackexchange.com |
3,156 | [
"https://security.stackexchange.com/questions/3156",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/1864/"
] | I'm referring to "remembered" password that the domain keeps so a user cannot reuse that password until it has expired in what was set at Password Policy on DC (W2003/W2008).
Where is password history stored?
| The historical password hashes are stored in the SAM along with your current one, so are certainly equally breakable.
I used to run password strength audits for large financials, and part of the output would be analysis of the number of individuals who reused passwords with just a change to the final digit (guess how ... | I can't find it now, but I've seen a proposal from academic researchers to Microsoft on how they could fix this. They have a crypto scheme to preserve current functionality (including password history policies, I think), but avoid the normal attacks on old passwords.
| https://security.stackexchange.com |
308,458 | [
"https://electronics.stackexchange.com/questions/308458",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/68402/"
] | My understanding is that ESD safety things (mats, wrist straps, specially marked soldering irons) are designed to bring everything that can touch a component to the same electrical potential energy – ground.
But it seems unreasonable to expect that there's no voltage between my desk and the factory where my components... | Components are damaged by two or more of their pins being at a large enough potential difference. If the component has a conductive case, or pad, then that counts as a 'pin' too.
It's possible to break them by trying to charge them up to a new potential through one sensitive pin, while the voltage of the other pins is... | Hopefully your parts are packaged in an ESD-dissipative tray or bag. Then when you set them down on your ESD mat in your lab, any charge that's built up on them can drain away through the packaging and the mat. They won't discharge quickly enough to damage the components because both the bag and the mat have substantia... | https://electronics.stackexchange.com |
477,659 | [
"https://physics.stackexchange.com/questions/477659",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/231016/"
] | I was doing a physics problem, and it seemed simple at first, but now it doesn't at all, and I need help. Here it is.
Three identical spheres are thrown from the same height above the ground. Sphere X is thrown vertically up, sphere Y is thrown horizontally, and sphere Z is thrown vertically down. All three spheres ar... | For X or Z:
Final speed would be:<span class="math-container">$\sqrt{v^2+2gH}$</span>(Using equation of motion for a uniformly accelerated motion).
For Y , you saw, the net speed would be the resultant of horizontal and vertical components: <span class="math-container">$\sqrt{v^2+(\sqrt{2gH})^2}$</span>.(horizontal com... | Your logic seems to be the following:
<blockquote>
Suppose that the velocity that a ball would reach if it were just dropped is <span class="math-container">$v_1$</span>. Suppose that it's instead thrown with velocity <span class="math-container">$v_2$</span>. The velocity of the horizontally thrown ball will be <sp... | https://physics.stackexchange.com |
187,418 | [
"https://electronics.stackexchange.com/questions/187418",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/84078/"
] | I have an LED strip that uses around 2A from 12V DC (25W). I will probably use less than the full strip, so if I cut the strip, will it draw more current (the voltage will stay at 12V) or less? I want to figure out if the LED's will get brighter or hotter if I use less of the strip.
| Another way you could look at this situation is that removing a few LEDs will not influence the voltage over the other LEDs(all in parallel), so the current through the remaining LEDs will stay the same while the removed LEDs do not draw current anymore of course, so the required current is less.
| If the strip is meant to be cut then all the LEDs are connected in parallel, and each of them should have its limiting resistor.
If this is true you can power the shorter strip with a 12V source, but the strip will draw <em>less</em> current.
Let me explain this with an example. Let's say the strip consists of 10 LED... | https://electronics.stackexchange.com |
478,767 | [
"https://physics.stackexchange.com/questions/478767",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/205771/"
] | I know that Maxwell's equations of electromagnetism are Lorentz invariant in a vacuum. But what about in a generalized medium, e.g. a metal, a rubber, a dielectric, a magnet? I have read it comes down to whether the electric and magnetic polarizations, <span class="math-container">$M$</span> and <span class="math-conta... | Maxwell is not Lorentz invariant in matter because the material selects a preferred reference frame — the one in which the lump of matter is at rest.
Of course you can make it all look Lorentz covariant by including the local four velocity <span class="math-container">$u^\mu$</span> of the piece of matter in the e... | <blockquote>
Are Maxwell's equations in a medium Lorentz invariant?
</blockquote>
No, they're not. An electromagnetic wave can have a speed <span class="math-container">$v<c$</span> in a medium. That means you can choose a frame in which the wave's velocity is zero. A zero-velocity wave is a solution in that fram... | https://physics.stackexchange.com |
2,757,326 | [
"https://math.stackexchange.com/questions/2757326",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/88896/"
] | Suppose <span class="math-container">$(c_j)$</span> is a sequence of complex numbers indexed by <span class="math-container">$j \in \mathbb{Z}$</span>, which is of bounded variation in that
<span class="math-container">$$
\sum_{j \in \mathbb{Z}} \lvert c_j - c_{j - 1} \rvert < \infty.
$$</span>
Then, does it follow ... | How about
$$c_j = \begin{cases} 0 & \text{for } j \leqslant 0 \\ 1 & \text{for } j > 0 \end{cases}$$
| No. Consider $d_n = 2^{-n}$, $c_0 = 0$, $c_n = d_1 + \dots + d_n$ and $c_{-n} = -c_n$ for all $n \in \Bbb{N}$.
$$\sum_{j \in \mathbb{Z}} \lvert c_j - c_{j - 1} \rvert = \sum_{j \in \mathbb{N}} d_j + \sum_{j \in \mathbb{N}} d_{j-1} < \infty,$$
but each term in $$\lvert c_1 - c_0 \rvert + \lvert c_{-1} - c_1 \rvert... | https://math.stackexchange.com |
685,234 | [
"https://physics.stackexchange.com/questions/685234",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/279645/"
] | Assuming there are two pieces of machines that are used to simulate kicking soccer balls. The machines are identical to each other except for the lengths of "leg" that is used to kick soccer balls, i.e. one machine (calling it Machine A) has a longer "leg" than than the other (calling it Machine B).... | <blockquote>
Since Machine A has longer "leg" than Machine B, so the linear
velocity of Machine A's leg will be higher than Machine B
</blockquote>
That is not correct.
The linear velocity of the "boot" end of each leg and the linear velocity of each soccer ball will be the same when the ball and bo... | In the case of a short duration impulse during the kick from a “boot” with mass on the end of a “mass-less” arm, the machine will deliver the same energy to the boot (before the kick) for any length of arm.
| https://physics.stackexchange.com |
52,646 | [
"https://physics.stackexchange.com/questions/52646",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7502/"
] | Let's say I cut off the end of a gun barrel at a 45° angle: What would the effect be on the trajectory of a bullet fired through that barrel?
Would the bullet be less stable (I guess)? Would it make the gun fire with an angle, and would that be toward the "small" end?
| Suppose you make the cut so that the slant is downward – i.e., the top part of the barrel is shortest, the bottom is longest. The bullet is driven down the barrel by the pressure of propellant gases on its base. As the base of the bullet leaves the barrel the propellant gases begin to act asymmetrically on the ... | I think the main effect would be that the muzzle velocity will be lower.
This is because the expanding gases of the gun power will have a shorter distance along which they push the bullet. Once the back of the bullet emerges out the short side of the barrel, the gases will escape and depressurize, loosing the ability ... | https://physics.stackexchange.com |
626,307 | [
"https://physics.stackexchange.com/questions/626307",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/278044/"
] | Can it be explained via blackbody radiation? Or is it purely to do with the material itself? For example, why does the line at 589.0 nm has twice the intensity of the line at 589.6 nm for sodium?
| I will take a stab at this.
Sodium vapor lamps work by forcing electrical flow through an ionized cloud of sodium vapor. This heats the vapor and kicks sodium electrons temporarily into higher energy orbitals. After a very short (but unpredictable) time, the electrons fall back into their original orbitals and emit a p... | Here's the difference between the Na lamp's output and the output of a laser.
The laser generates output (photons) via stimulated emission, a process which produces photons which are in phase with the stimulating (input) photons. However, the Na lamp generates photons, albeit from the same electron quantum gap (betw... | https://physics.stackexchange.com |
226,678 | [
"https://electronics.stackexchange.com/questions/226678",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/43263/"
] | How is hysteresis used for DSP?
| To keep the heater example of Ecnerwal, the code below turns on and off a heater. It keeps room temperature at 25ºC, with a hysteresis of 2 degrees. The objective of such a code is to reduce the number of calls to startupHeater() and shutdownHeater(), which would harm the heater if executed too often:
<pre><code>#defi... | Let's consider your thermostat in your house.
Lacking hysteresis, it flips the furnace on for a few seconds, flips it off for a few seconds, flips it on for a few seconds, burns out the motor from starting it too frequently, and leaves you freezing in the middle of the night (it's always the middle of the night, or wh... | https://electronics.stackexchange.com |
199,412 | [
"https://physics.stackexchange.com/questions/199412",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/88794/"
] | There is no formula for solar energy, mechanical energy etc,
so Why there is no formulas for some energies?
| There are formulas and equations involving energy in all branches of physics, it is almost impossible not to have some equation involving energy in any area of physics you study.
For example there is an equation for the luminosity of a star, which is the power emitted, which in turn is the energy per unit time put ou... | At first glance, this question sounds ill-posed. What do you mean by "solar energy"? If you mean the energy given off in the form of light, than you can calculate this. The luminosity of the sun is the energy given off per unit time. The sun (to a good approximation) gives off it's energy in the form of blackbody radia... | https://physics.stackexchange.com |
611,287 | [
"https://physics.stackexchange.com/questions/611287",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/140404/"
] | The frequency <span class="math-container">$\nu$</span> it is defined as:
<span class="math-container">$$\nu=\frac1T \tag 1$$</span>
where with <span class="math-container">$1$</span> indicate one cycle and <span class="math-container">$T$</span> the period, i.e. when a material point completes a complete circle. If I ... | I don't know what this question is supposed to be useful for. But the answer is pretty simple. We have the functional relationship
<span class="math-container">$$n:\Bbb R\times\Bbb R\to \Bbb R$$</span>
<span class="math-container">$$n:(\nu,\Delta t)\to \nu\cdot\Delta t$$</span>
Since you require
<span class="math-conta... | I don't see how <span class="math-container">$\nu$</span> and <span class="math-container">$\nu^*$</span> can be different from each other. You are defining <span class="math-container">$\nu*$</span> as <span class="math-container">$n/\Delta t$</span>, but clearly the time for one cycle, the periodic time, <span class... | https://physics.stackexchange.com |
596,253 | [
"https://math.stackexchange.com/questions/596253",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/110324/"
] | $$\lim_{h\to0}(\frac{x}{h(x+h+1)} + \frac{1}{x+h+1} - \frac{x}{h(x+1)})$$
I know the answer is $$\frac{1}{(1+x)^2}$$
But I can't get there
| Another definition of an orthogonal matrix (from MathWorld) is that $A^T = A^{-1}$ (A is square) meaning $A^T A = I$
Recall that the transpose of a square matrix has the same eigenvalues as the original matrix (Meaning $A \vec v = \lambda \vec v = A^T \vec v$)
Taking our eigenvalue equation $A\vec v = \lambda \vec v$... | Recall that if $U$ is an orthogonal matrix, we then have $\Vert Ux \Vert_2 = \Vert x \Vert_2$ for all $x \in \mathbb{R}^{N}$.
Let $\lambda$ be an eigenvalue of $U$ and let $v$ be an eigenvector corresponding to $\lambda$. We then have
$$U v = \lambda v \implies \Vert Uv \Vert_2 = \vert \lambda \vert \Vert v \Vert_2$$... | https://math.stackexchange.com |
447,451 | [
"https://physics.stackexchange.com/questions/447451",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/115337/"
] | I really think that I might be overthinking it but I was thinking about a door. When you try and open it with a force, it will produce a translational AND a rotational effect on the door. Any good door you have probably doesn't translate so that means the hinges must be applying a force to oppose this translational mot... | Torque depends on the force and the distance between the hinge and the point where the force is applied.
When you pull on the door at the handle, you apply a force and there is a nonzero distance between handle and hinges, so you get torque and as a consequence rotation around the hinges.
The hinges apply their force... | When you pull open a door, you are applying a force, and a torque, the cross product of force and distance is produced. However, since the door pivots and swings about the center (hinges), the hinges are unable to produce any torque since they themselves are the centre. However, they do apply a force towards the cent... | https://physics.stackexchange.com |
707,452 | [
"https://physics.stackexchange.com/questions/707452",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/318923/"
] | Because the CMB is everywhere and is isotropic, if an object would have a certain velocity, it could have a pressure differential produced by the CMB which would produce drag till it would stop with respect to the CMB.
However, wouldn't this mean that there is a 'universal' reference frame created by the CMB? Wouldn't ... | The CMB does in fact produce a preferential reference frame. Even without pressure, the preferential frame would be the one that equalizes the red and blue shift in all directions. For example Earth's motion around the Sun and the Sun's motion around the galaxy can be extracted from the red and blue shift in CMB data.... | Indeed the existence of the CMB constitutes a reference of velocity.
The thing is: the CMB is not unique in that regard.
As a thought experiment: what is still possible in a Universe that is observationally the same as our Universe, but without CMB? With otherwise full access to any astronomical observations, what is s... | https://physics.stackexchange.com |
34,205 | [
"https://mathoverflow.net/questions/34205",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2036/"
] | There are short and sweet proofs of various forms of Stirling's approximation. But even the sweetest among them don't instill the same conviction in the reader as a direct bijective proof.
Computer scientists can often get away with a very weak form of Stirling's approximation:
$$(n/2)^{n/2} \leq n! \leq n^n$$
From ... | Think of all maps from the first $n/2$ elements of {$1,...,n$} to the last $n/2$. Say, let $a_1< \ldots < a_k \to z$. Make a cycle $a_1 \to a_2 \to \ldots \to a_k \to z \to a_1$. Do this for all $z$. The details are straightforward. This proves the lower bound.
| n! counts one-to-one functions from {1,2,...,n} to itself while $n^n$ counts all such functions. For a bijective proof of the lower bound one would likely want n=2m, Then the lower number is the $m^m$ functions g from {1,...,m} to itself . I thought I had an easy bijection to a class of partial one-to-one functions ... | https://mathoverflow.net |
226,661 | [
"https://physics.stackexchange.com/questions/226661",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/93317/"
] | The boiling point of water is always defined as the temperature at which the vapour pressure of water is equal to the atmospheric pressure. How does the definition relate to why there is intense nucleation exactly at the boiling point? I know that the water in the container will start evaporating the moment the vapour ... | <h1>Basic Idea:</h1>
For gaseous bubbles to exist, you need that the <strong>pressure inside</strong> the bubbles is <strong>greater than</strong> (or equal) the <strong>pressure acting on</strong> the bubble. Otherwise pressure gradient force would make the bubbles to collapse.
<hr />
The pressure inside the bubbles i... | Obviously, water molecules on the surface can evaporate (escape and never come back) at any temperature. Concerning what happens in the bulk of the water, Lukas has already provided the correct answer. Let me elaborate on what he means by <strong>bubble collapsing</strong>.
Consider water at $25^\circ\mathrm{C}$ and ... | https://physics.stackexchange.com |
29,792 | [
"https://softwareengineering.stackexchange.com/questions/29792",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/11344/"
] | Do you think it makes sense to enforce that every member of a team must use the same IDE?
For instance all engineers that are already on the team use IDE X. Two new engineers come and want to use IDE Y instead because that's what they have been using for several years now.
Do you have any experience with "mixed IDE" ... | Provided the 'official' build system (as used by the Continuous Build servers) is the same for all, I don't see any reason why each member of the team could not choose the tools he wants...
| If your team relies on certain plugins available only to certain IDEs, then it only makes sense to unify everyone under the same development platform. I also find it easier to help someone with a development issue if they have the same IDE as me, whereas if I'm to read someones screen with an unfamiliar interface it'll... | https://softwareengineering.stackexchange.com |
73 | [
"https://mechanics.stackexchange.com/questions/73",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/64/"
] | I have heard it is proper practice to replace or resurface your brake rotors every time your do a brake pad replacement. Does this need to be done every single time or is it overkill? Maybe it is just something easy to do, might as well replace while you are in there type of thing?
| The decision to replace is largely based on the thickness. The repair manual should tell you the minimum thickness, below which you should replace the rotors when doing the repair. Use a pair of calipers and measure the rotor thickness, if you're below this number you need to replace the rotors.
You may also wish to... | There are three cases that cause brake rotors to need to be resurfaced/turned and/or replaced.
<ol>
<li>Gouging of the rotor by the brake pad holding mechanism (the pad were rubbed completely away and the metal holding the pad start digging into the rotor)</li>
<li>Warping of the rotor from extreme use (rotor gets too... | https://mechanics.stackexchange.com |
65,690 | [
"https://stats.stackexchange.com/questions/65690",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/28514/"
] | I fit a logistic on three numeric continuous variables, followed by a categorical factor [Y, N].
<pre><code>logit2A <- glm(DisclosedDriver ~ VehDrvr_Dif+POL_SEQ_NUM+PRMTOTAL+SAFE_DRVR_PLEDGE_FLG, data = DF, family = "binomial")
</code></pre>
Fit looks wonderful.
<pre><code>Coefficients:
Estim... | Using my magic crystal ball to see the output of <code>str(DF)</code>...
Aha! <code>SAFE_DRVR_PLEDGE_FLG</code> has another level, <code>""</code>, and that in that same row, one of the other variables is missing. So it's not using that row to do the fit, but when it tries to construct the data matrix to get the pre... | Without seeing your data, it's difficult to know what's happening. This illustration might be helpful:
<pre><code># Construct dataset to illustrate question
d <- data.frame(w=rnorm(100),
x=rnorm(100),
y=sample(LETTERS[1:2], 100, replace=TRUE),
z=sample(LETTERS[3:4], 100, replace=TRUE)
)
fm <... | https://stats.stackexchange.com |
244,785 | [
"https://physics.stackexchange.com/questions/244785",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/101600/"
] | Classical physics models events occuring in the spacetime $\mathcal E\times \mathcal T$ where $\mathcal E$ is a dimension 3 euclidean point space and
$\mathcal T$ is an interval of $(\mathbb R, <)$ (an ordered set).
An observer is a fictitious human being or sensor that can infinitely precisely describs events.
A... | You have a wrong idea of classical spacetime $V^4$. It is <strong>not</strong> the Cartesian product $\mathbb E^3 \times \mathbb R$.
It is instead a <strong>fiber bundle</strong> $$T: V^4 \to \mathbb R$$
such that each fiber $\Sigma_t = T^{-1}(t)$, the <strong>absolute space at fixed time</strong> $t$, is isomorphic... | <blockquote>
It seems to me that only point O is needed, we actually don't care about the basis.
</blockquote>
We actually do care about the basis, very much so. In Newtonian mechanics, the displacement vector between one point and another in $\mathbb R^3$ is indeed frame independent. This displacement vector might ... | https://physics.stackexchange.com |
3,983,810 | [
"https://math.stackexchange.com/questions/3983810",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/865056/"
] | Let <span class="math-container">$ S: U \rightarrow V $</span> and <span class="math-container">$ T: V \rightarrow W $</span> be linear transformations over field <span class="math-container">$ F $</span>.
Prove that <span class="math-container">$ T ◦ S $</span> is surjective iff <span class="math-container">$ $</spa... | I think it might be the easiest to verify the equality by direct computation via elements instead of dimension (the latter approach is actually a bit problematic if the vector spaces are no longer finite-dimensional)<br />
For <span class="math-container">$\Rightarrow$</span>: Let <span class="math-container">$v\in V$<... | For the "<span class="math-container">$\Leftarrow$</span>" part: Let <span class="math-container">$T$</span> be surjective and let's assume <span class="math-container">$V = \operatorname{Ker}(T) + \operatorname{Im}(S)$</span>. Let <span class="math-container">$w \in W$</span>. We need to find <span class="ma... | https://math.stackexchange.com |
67,159 | [
"https://dsp.stackexchange.com/questions/67159",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/36797/"
] | I notice that almost all papers use the number of subcarriers of 64, 128,256.. so on, which is a number of <span class="math-container">$2^k$</span> and <span class="math-container">$k$</span> is an integer.
Why is the number of subcarriers always like that? Can we use any number or it must be only using one of those... | Implementing an IFFT and FFT engine which is a power of <span class="math-container">$2$</span> is easier in hardware and hence if an OFDM system is talked about, it is talked about in <span class="math-container">$2^k$</span> length FFT. All practical Communication system based on OFDM use <span class="math-container"... | Not necessary. In DRM (Digital Radio Mondaile) specification, for some channels number of careers are not the power of 2. Power of 2 makes the implementation of FFT and IFFT simpler.
| https://dsp.stackexchange.com |
131,406 | [
"https://physics.stackexchange.com/questions/131406",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21843/"
] | I was told by my professor that the current in a purely LR Circuit with at initial state (JUST after closing the switch) is zero. Can you please help me understand why it that so?
| Intuitively, inductors create back EMFs that "resist" changes in current. Anytime there is an inductor in a circuit, it will resist such changes. Mathematically, inductors force the current in a circuit to be continuous. Let's consider an LR circuit where the inductor and resistor are both in series. Regardless of the ... | The voltage drop across an inductor is proportional to the change in current, or V = L*dI/dt. When the switch is closed, the circuit is completed and a current starts to increase dramatically. This then causes a time increasing flux of magnetic field in the inductor. According to Lenz's Law, an opposite current will be... | https://physics.stackexchange.com |
367,331 | [
"https://physics.stackexchange.com/questions/367331",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/159268/"
] | It's an established fact that:
<ol>
<li>Convex lenses produce inverted images of objects beyond the focus, on the other side of the lens.
</li>
<li>Any object placed at a finite distance from a concave lens appears to be somewhere between the focus and the optical centre when viewed from the other side.
</li>
</ol>
Bot... | Objects through spectacles appear both at a different distance <em>and</em> magnified. It turns out these effects cancel out, and the object subtends the same solid angle in your vision as without the spectacles. Your eye cannot directly perceive distance- your brain estimates it in several ways.
One way is by compar... | The eye itself has its own lens that is intended to create an image at the retina. IF this lens is faulty for one reason or another, the image does not form at the retina - rather, it forms in front of or "behind" the retina. The additional lenses (glasses) shift the path of light rays by a small amount before they e... | https://physics.stackexchange.com |
24,700 | [
"https://chemistry.stackexchange.com/questions/24700",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/7757/"
] | I was wondering what salts of gold are soluble and which are insoluble. From what I understand, silver is soluble as silver nitrate but insoluble as most other common salts like chlorides and sulphates. How does this work with gold? I was also wondering if there are any rules for solubility of salts, or whether there i... | Old question, but I thought I'd add to it:
In your example, the first undissolved solid is indeed gold. It's not easily dissolved by $\ce{HNO3}$ alone, but requires a mixture of $\ce{HNO3}$ and $\ce{HCl}$ (aqua regia). $\ce{Ag}$ and $\ce{Cu}$ would dissolve by hot $\ce{HNO3}$. The precipitate formed by addition of $\c... | Here is What I know:<br/>
Gold(III) chloride is Highly Hygroscopic [1] and is highly soluble in water,
I don't know which salts are not soluble never researched it,
maybe Gold-Mercury amalgam is not soluble in water but its not a salt.. <br/>
[1] = absorbing or attracting moisture from the air.
| https://chemistry.stackexchange.com |
146,038 | [
"https://softwareengineering.stackexchange.com/questions/146038",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/52748/"
] | I have an API that is EJB based (i.e. there are remote interfaces defined) that most of the clients use. As the client base grows there are issues with updates to the API and forcing clients to have to update to the latest version and interface definition.
I would like to possibly look at having a couple versions of ... | It can be quite common to host multiple versions of an API (I'd only recommend having 2 at Max BTW). Typically you would host each API on a different shard/server/whatever and work with your clients to help them upgrade to the new API in an x time-frame.
An EJB centric API might suit your business needs now (which is ... | You can use the same EAR and just have different JNDI names for the different versions of your EJB. Then the old clients can still connect to the old EJB using the old client libs and new clients can connect to the new client libs. As Martijn pointed you don't want to have too many different versions floating around ... | https://softwareengineering.stackexchange.com |
51,322 | [
"https://stats.stackexchange.com/questions/51322",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/12923/"
] | If two or more variables A, B, C, etc. are jointly mutually independent of one another, does this imply that that they are also conditionally independent given some set of conditioning variables X, Y, Z, etc.?
If you test variables A, B, C,, etc., and the hypothesis of independence is not rejected, are you generally s... | No.
Consider three boolean variables: A, B, X where X and A are i.i.d. Bernoulli with probabilty 0.5, while B = X $\oplus$ A (that is, B is equal to the xor of X and A).
It's easy to show that B is also Bernoulli distributed with probabilty 0.5, and A and B are mutually independent, though obviously they aren't condi... | It depends on your definition of independence. I have seen at least one textbook that used the term "stocastic indepedence" or something like that to refer to the case where 2 variables were independent, and still conditionally independent when conditioned on other variables. Other textbooks seem to imply this added ... | https://stats.stackexchange.com |
660,447 | [
"https://physics.stackexchange.com/questions/660447",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/291589/"
] | I am struggling to differentiate relativistic momentum formula.
Considering special relativity,
<span class="math-container">$$ \vec{F}=\frac{d\vec{P}}{dt}=\frac{d}{dt}\frac{m\vec{v}}{\sqrt{1-v^2/c^2}}$$</span>
which I understand.
The textbook proceeds, "when the net force and velocity are both along the x-axis,&q... | If net force and velocity are both along the <span class="math-container">$x$</span>-axis, <span class="math-container">$F_y,F_z,v_y,v_z$</span> are 0 and there remains
<span class="math-container">$$
F = F_x = \partial_t \frac{m v_x}{\sqrt{1 - v^2/c^2}}~,
$$</span>
where also <span class="math-container">$v = v_x$</sp... | We have <span class="math-container">$v=v_x$</span> so we can write
<span class="math-container">$$F_x =\frac{d}{dt} \left(\frac{mv_x}{\sqrt{(1-v_x^2/c^2}}\right)$$</span>
So you have a quotient to differentiate. Note that <span class="math-container">$\frac{dv_x}{dt}\ (= a_x)$</span>, appears in the derivative of the ... | https://physics.stackexchange.com |
4,294,678 | [
"https://math.stackexchange.com/questions/4294678",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <blockquote>
The positve integer satisfying value of <span class="math-container">$n: n>3$</span> satisfying the equation: <span class="math-container">$\dfrac{1}{\sin(\pi/n)}=\dfrac{1}{\sin(2\pi/n)}+\dfrac{1}{\sin(3\pi/n)}$</span> is
</blockquote>
This question is from a Practice Book for CBSE Term<span class="math... | Your work is fine.
Since this is an multiple choice question, we can also do the following to identify the correct choice:
<span class="math-container">\begin{align}(xD+I)\left[ \frac{\ln x}{x^k}\right]&=x\left[ \frac{x^{k-1}-kx^{k-1}\ln x}{x^{2k}}\right]+\frac{\ln x}{x^k}\\
&=\frac1{x^k}-\frac{k\ln x}{x^k} + \... | <span class="math-container">$$(xD+1)y=xy'+y=x^{-1}$$</span> integrates immediately as <span class="math-container">$$xy=\log x+C.$$</span>
| https://math.stackexchange.com |
942,156 | [
"https://math.stackexchange.com/questions/942156",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/177703/"
] | I need to find the equation of the tangent line at the point $(3,1)$ for
$$x\ln y + 2xy = 6.$$
Can you point out a way to start.
| First you have to find $\frac{dy}{dx}$ if you do it you will get:
$\frac{dy}{dx} = \frac{y ln y + 2y^{2}}{-2xy-x}$
$\frac{dy}{dx} = m_{t}$ which is the slope of the tangent line, now you have to evaluate the point$(3,1)$ in $m_{t}$ then you have that:
$m_{t} = \frac{(1) ln (1) + 2(1)^{2}}{-2(3)(1)-(3)} = \frac{-2}{9... | <strong>Hints:</strong> Either
(1) use implicit differentiation to find $\left.\frac{dy}{dx}\right|_{(x,y)=(3,1)}$, or
(2) note that you can write $x$ as a function of $y$ and find the tangent line as a function of $y$.
| https://math.stackexchange.com |
6,593 | [
"https://electronics.stackexchange.com/questions/6593",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/954/"
] | I need to send 800 bytes of data from a computer to an arduino board every 20ms (approximately). I began with the serial library which works nicely but it is too slow even at its highest rate (115200 baud) for interfacing with a computer.
What other interfaces are available that can send at a faster rate? Can I use ... | How about only sending changed bytes each 20 ms? You'd need an additional 9 bits for addressing, but if you stuffed that bit in the empty bit in your 15-bit color data, you could do it with just one extra byte per LED. Depending on how fast your display is changing colors, that might work well. You could make a thresho... | The limiting factor is likely your computer's serial port, drivers and/or the Arduino library. If I recall correctly, the AVR UART can go up to its clock rate divided by 8 or 16, and an FTDI chip can be at arbitrary baud rates equally high (3 Mbaud for this FT232RL on my desk).
Most shields are going to communicate o... | https://electronics.stackexchange.com |
494,280 | [
"https://math.stackexchange.com/questions/494280",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/94963/"
] | I was wondering how it would be possible for me
to rotate a cube diagonally 360 degrees.
I am able to rotate it over the x-axis, y-axis and z-axis with
the following formulas :
<pre><code>**x-axis**
y = v.y*cos(degree) - v.z*sin(degree);
z = v.y*sin(degree) + v.z*cos(degree);
**y-axis**
x = v.z * sin(degree) + v.x... | Hint: $$\begin{pmatrix} \cos \varphi & \sin \varphi & 0 & \ldots & 0 \\ \sin \varphi & -\cos \varphi & 0 & \ldots & 0 \\ 0 & 0& 0& \ldots & 0\\ \vdots & \vdots& \vdots& \ddots & \vdots\\ 0 & 0& 0& \ldots & 0 \end{pmatrix}^2 = ?$$
| We have $$\begin{pmatrix} \cos \varphi & \sin \varphi & 0 & \ldots & 0 \\ \sin \varphi & -\cos \varphi & 0 & \ldots & 0 \\ 0 & 0& 0& \ldots & 0\\ \vdots & \vdots& \vdots& \ddots & \vdots\\ 0 & 0& 0& \ldots & 0 \end{pmatrix}^2 = \begin... | https://math.stackexchange.com |
240,688 | [
"https://softwareengineering.stackexchange.com/questions/240688",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/81091/"
] | When I set a variable to an object in VBA / VBScript, I always need to prefix the statement with "Set" such as: <code>Set Dict = CreateObject("Scripting.Dictionary")</code>
If I set a variable to a primitive or array value, I have to omit the "Set" such as: <code>Num = 123</code>
This is different from languages such... | VB and VBA had something called "default properties". If your code mentioned the object without any property/ method specified, then you got the default property, not the object!
<blockquote>
Dim vValue as Variant
vValue = textBox1
? TypeName( vValue )
String
</blockquote>
Should this work? Well, yes, becau... | Note: when I say "Visual Basic" here I mean Visual Basic 6 and before - <strong>not</strong> Visual Basic.NET.
Visual Basic is designed to be easy to use. Pointers are hard - and to some extent, so are reference types, like the ones used for objects in most modern languages.
the <code>Set</code> syntax is a way to hi... | https://softwareengineering.stackexchange.com |
293,009 | [
"https://physics.stackexchange.com/questions/293009",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/136055/"
] | So I was reading about EM waves and radiation. My textbook says that frequency of light depends on the temperature of a body. As the frequency rise up, the color shifts from red to blue. For example, copper. This is supposedly true.
I have this weird doubt - if copper changes its color with temperature, how do crayons... | You are missing the difference between emitted and reflected light. They all look different because they reflect different wavelengths, but if you look at them with a thermal camera you will see that they emit the same infrared color. It will be impossible to distinguish their hue.
To stimulate your curiosity, emissio... | The light you see from the crayons is reflected by them. If the color is say yellow, that means that the crayon mostly absorbed and scattered all other wavelengths, and reflected the yellow one
| https://physics.stackexchange.com |
555,855 | [
"https://stats.stackexchange.com/questions/555855",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/343230/"
] | Title. I'd like to understand the intuition behind how regression coefficients are calculated, and why <span class="math-container">$$\frac{cov(x,y)}{var(x)}$$</span> gives a regression coefficient for dependent variable y and independent variable x? This feels like an elementary question but I have looked around the i... | <blockquote>
Why <span class="math-container">$$\frac{cov(x,y)}{var(x)}$$</span> gives a regression coefficient for dependent variable y and independent variable x?
</blockquote>
A linear regression coefficient tells us: If predictor variable <span class="math-container">$x$</span> increases by 1, what is the <em>expec... | In simple linear regression we are dealing with the model
<span class="math-container">\begin{eqnarray*}
y_i = \beta_0 + \beta_1 x_i + \varepsilon_i, \quad \mbox{for} \quad i=1,\cdots,n.
\end{eqnarray*}</span>
Let <span class="math-container">$\boldsymbol{y} = \left(y_1, \cdots, y_n\right)^{\prime}$</span>, <span class... | https://stats.stackexchange.com |
220,430 | [
"https://softwareengineering.stackexchange.com/questions/220430",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/109212/"
] | <pre><code>public final class ImmutableClass {
private StringBuffer name;
public ImmutableClass(StringBuffer name) {
this.name=name;
}
public StringBuffer getName() {
return name;
}
}
</code></pre>
Points that I have considered:
<ol>
<li>Make the class <code>final</code> so that ... | Consider:
<pre><code>ImmutableClass a = new ImmutableClass(new StringBuffer("hello"));
a.getName().append(" world");
System.out.println(a.getName()); // prints "hello world"
</code></pre>
The above allows the caller to mutate the value of <code>name</code>. Or:
<pre><code>StringBuffer b = new StringBuffer("hello");
... | Whether the class is immutable or not depends upon whether you are intending it to encapsulate the <em>identity</em> of the StringBuffer or the <em>contents</em> thereof. The design of the class suggests that it encapsulates the identity of the <code>StringBuffer</code>; because it will never identify any <code>String... | https://softwareengineering.stackexchange.com |
67,420 | [
"https://stats.stackexchange.com/questions/67420",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/29163/"
] | I'm trying to do a multiple linear regression model to correlate a dependent $Y$ variable (normally distributed) against a set of 642 variables. These 642 variables codify for the presence or absence of a particular chemical group in a molecule, therefore they can assume only <code>1</code> or <code>0</code> as value. ... | <strong>Provided each chemical group appears in at least two experiments you can be successful.</strong>
A good way to explore the issues is with a simulation. What matters is how much any random variation in the values of $Y$ compares to the sizes of the effects: when that variation is relatively small, you can pret... | It will not create problems, although inclusion of all 642 variables in your regression will. You have only 1300 observations for each variable and if you include all variables you will be asking the data to answer 642 questions (asking whether this variable is significant or not) which is too many in my opinion. Somet... | https://stats.stackexchange.com |
146,065 | [
"https://security.stackexchange.com/questions/146065",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/134145/"
] | What are the possible attack vectors if I am running user-submitted docker image, e.g. pull via <code>docker pull FOO; ... docker run FOO</code> where FOO is a user-submitted string containing the name of a Docker Hub repository?
This is <em>not</em> a question about simply running untrusted code <em>inside</em> docke... | There's various ways that a rogue container might be able to damage the host or other containers on the network, depending on the configuration of the docker daemon.
<ul>
<li>By default all containers share the same network. As such a rogue container can attempt to attacker other containers. This could include attac... | It depends the specific version of docker and the containers you are running. <strong>And</strong> how you are using your containers.
While the dream is that a container is isolated from the host, there have been times when a bug or vulnerability has been discovered that has allowed a container to gain root access to ... | https://security.stackexchange.com |
1,604,172 | [
"https://math.stackexchange.com/questions/1604172",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/183974/"
] | A college plays 8 football games during a season. In how many ways can the team end the season with 4 wins, 3 losses and a tie?
I started this question by trying to count the total number of possible permutations of wins, losses and draws for the 8 games: $3^8$.
I then thought I would divide the total by the number o... | By Taylor expansion we know that
$$\begin{align}
y(-h) &=y(0)\color{red}{-}hy'(0)+\frac{h^2}{2!}y''(0)\color{red}{-}\frac{h^3}{3!}y'''(0)+\frac{h^4}{4!}y''''(0)+O(h^4) \\
y(h) &=y(0)+hy'(0)+\frac{h^2}{2!}y''(0)+\frac{h^3}{3!}y'''(0)+\frac{h^4}{4!}y''''(0)+O(h^4)
\end{align} \tag{1}$$
and hence
$$y(-h)+y(h)= ... | If $v(x)=y(-x)$ then $v''(0)=y''(0)$, so
if $y''(0) \approx \dfrac{ay(2h)+by(h)+cy(0)+dy(-h)+ey(-2h)}{h^2}$
then $v''(0) \approx \dfrac{av(2h)+bv(h)+cv(0)+dv(-h)+ev(-2h)}{h^2} \\ \qquad\,= \dfrac{ey(2h)+dy(h)+cy(0)+by(-h)+ay(-2h)}{h^2}$
but if these approximations are not equal then a better approximation for eac... | https://math.stackexchange.com |
26,749 | [
"https://chemistry.stackexchange.com/questions/26749",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/8208/"
] | I know that this is a rather ambiguous question; but my question is, whenever we take water and freeze it in the freezer, it still tends to stay clear. Since snow is just frozen water, why is it white? Is it due to contents of the air - i.e. dust - that make snow this color?
Or is my freezer just weird?
| The difference between snow and ordinary ice cubes is mainly about the size of the particles. Snow is made from small, irregular crystals with many edges at a very small scale. Light is refracted or scattered by the edges (or the interface between air and the edges). Snow is white because the scattering effect of those... | As matt_black said, it's about the size.
If you take a tall, thick glass tube, it'll be transparent, right? It'll transmit the light falling on it. But make it thinner and thinner(think human hair) then it'll appear white, as it'll refract the light passing through it.
As the light from the sun(which is a combination o... | https://chemistry.stackexchange.com |
722,151 | [
"https://physics.stackexchange.com/questions/722151",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/342825/"
] | <span class="math-container">$\renewcommand{\ket}[1]{\left \lvert #1 \right \rangle}$</span>
In the attached photo, my professor has evaluated the action of the exponential of the x and y Pauli matrices on z-basis eigenstates, and there is also a phase attached to the operator of pi/4. Can somebody explain how did the ... | It doesn't mean literally infinite. Just so many free charges that no current you can create will be limited by a lack. Your ability to positively charge the conductor by pulling electrons off will not be limited by a lack.
| <span class="math-container">$$\vec{J} = \sigma \vec{E} $$</span> If there is a depletion of charge in any location, the conductivity decreases.
A perfect conductor is defined as
<span class="math-container">$$\sigma = \infty$$</span>
This in reality, can not exist. There are finite charges and thus any movement of el... | https://physics.stackexchange.com |
652,820 | [
"https://math.stackexchange.com/questions/652820",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/92329/"
] | Let $f(x) = g(1/x)$ for $x>0$. Prove: $\lim_{x \to \infty} f(x) = L \iff \lim_{x \to 0} g(x) = L$ for some $L \in \mathbb{R}$.
I assume I am supposed to use l'Hopital's rule in some way (considering that is what section we are in). I've tried looking at the definition of a limit and the sequential criterion for li... | You know
$$\forall\epsilon>0:\exists y>0:\forall x>y: |f(x)-L|<\epsilon,$$
i.e.
$$\forall\epsilon>0:\exists y>0:\forall x>y: |g(1/x)-L|<\epsilon,$$
i.e.
$$\forall\epsilon>0:\exists y>0:\forall 0<x<1/y: |g(x)-L|<\epsilon,$$
and vice versa.
| Here is the right direction:
Given $\lim_{x \rightarrow \infty} f(x) = L$ we know $\exists N : x> N \Rightarrow |f(x) -L| < \epsilon$.
Set $x' = \frac 1 x$ and $\delta = \frac 1 N$. Then $x>N \Leftarrow\Rightarrow x' < \frac 1 N = \delta$.
Thus $x' < \delta \Rightarrow x> N \Rightarrow |f(x) -L| = ... | https://math.stackexchange.com |
424,734 | [
"https://mathoverflow.net/questions/424734",
"https://mathoverflow.net",
"https://mathoverflow.net/users/484187/"
] | Let <span class="math-container">$ \Omega = \mathbb{T}^d (1 \leq d \leq 3)$</span> be the <span class="math-container">$d$</span> dimensional torus and <span class="math-container">$ u \in H^2(\Omega) $</span> be a complex valued function. For some <span class="math-container">$ 0 < \alpha < 1 $</span>, let <span... | In Christ-Weinstein, JFA 100 (1991) 87-109 you can find the fractional chain rule (Proposition 3.1)
<span class="math-container">$$
\|F(u)\|_{\dot H^s_r}\le C
\|F'(u)\|_{L^p}\|u\|_{\dot H^s_q}
$$</span>
where <span class="math-container">$s\in(0,1)$</span>, <span class="math-container">$p,q,r\in(1,\infty)$</span>, <spa... | In general this depends on the value of <span class="math-container">$\alpha$</span>, <span class="math-container">$d$</span> and <span class="math-container">$s$</span>. For instance, when <span class="math-container">$d=1$</span>, we have
<span class="math-container">$$ \||u|^\alpha u\|_{\dot{H}^s}\lesssim\|u\|_{\inf... | https://mathoverflow.net |
240,870 | [
"https://softwareengineering.stackexchange.com/questions/240870",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/132255/"
] | I have been away from computers for about 3 years and starting to get back into programming. Lots has changed in resources and help sites available on the web especially the evolving StackExchange community. I come from the IRC #javascript, #html, #php days with php.net and a bit of google search finds here and there.
... | It depends on whether or not you're writing a lot of bare Javascript code to perform functions that are already well-served (or perhaps better served) by the libraries.
In the specific case of jQuery, it is specifically designed to provide a library of useful functions <em>in a cross-browser independent way.</em> So ... | I think you should ask yourself if there is a reason you <strong>shouldn't</strong> stay up to date on current technologies in your field. I think that is part of being a good software developer, and it allows you to make more informed decisions.
Choosing not to use a framework because it doesn't work for your situat... | https://softwareengineering.stackexchange.com |
160,514 | [
"https://physics.stackexchange.com/questions/160514",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/59215/"
] | I use Wald's notation: $I^+$ is the chronological future and $J^+$ is the causal future.
My confusion arises from the following passage in Wald (1984):
<blockquote>
Now, let $S$ be a closed, achronal set (possibly with edge). We define the <em>future domain of dependence</em> of $S$, denoted $D^+(S)$, by
$$D^+(S)... | As the causal future of $p$ is the set of points joined to $p$ by timelike or null curves, and the constant path $\gamma(t) = p$ joining $p$ to $p$ itself has vanishing tangent vector and hence is a null curve (though a rather silly one), $p \in J^+(p)$, and so, $S \subset J^+(S)$.
| The causal relation <span class="math-container">$J$</span> is defined so as to be reflexive.
For instance, the causal future is defined as follows
<span class="math-container">$$
J^+(S)=\cup_{p\in S} J^+(p)
$$</span>
where
<span class="math-container">$$
J^+(p)=\{q: q=p \textrm{ or there is a causal curve from } p \... | https://physics.stackexchange.com |
269,841 | [
"https://softwareengineering.stackexchange.com/questions/269841",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/164228/"
] | I am given a task which I need to do research on codebase and report my progress.
The dev environment is not set up. I can only read the code and analyze it, e.g. the workflow of user account creation.
There is a lot of uncertainty as my understanding on the code may not reflect the actual execution of the code.
I u... | Given that the question is about reporting progress I would propose adapting one of the agile development methodologies to your case.
More precisely:
<ol>
<li>Start dividing the bulk of research work in User Stories, each of them for the different parts of the basecode you have to cover. You don't need to know all th... | <h2>Take notes.</h2>
Think about why you have been asked to do this? Are you a new hire, tasked with becoming familiar before you do actual development? Are you a consultant? Is this a project for school?
Think about the reason you have been tasked to do this, and write down (in a Word document or similar) the informat... | https://softwareengineering.stackexchange.com |
555,487 | [
"https://electronics.stackexchange.com/questions/555487",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/280227/"
] | We build large machinery which we require UL, CE and several other marks for shipping globally. Does using components that are not UL certified preclude us from getting these certs or do the components not matter as long as we pass the machine as a whole?
| Ethernet is a way to connect, mostly, two computers, or a computer or many computers to a printer, or scanner, and so on.
Ethernet specifies how its OSI Layer 2 is, and it can be implemented via several different OSI Layer 1: for example, 10BASE-T, 100BASE-T, 1000BASE-T are very similar, but with different speeds.
Ethe... | This is a rather vague and broad question, but I’ll attempt an answer.
Ethernet IEEE 802.3 was originally and primarily intended for remote communication between devices using coax, twisted pair, fiber, and even radio. Ethernet may be used for local networks such as within a building, or regional metropolitan networks ... | https://electronics.stackexchange.com |
60,925 | [
"https://physics.stackexchange.com/questions/60925",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/22830/"
] | If time stops inside a black hole, due to gravitational time dilation, how can it's life end after a very long time? If time doesn't pass inside a black hole, then an event to occur inside a black hole needs infinite time relative to the outside. Thus, it will never age.
Please keep it simple..
| I assume you're asking how a black hole can evaporate due to Hawking radiation. The answer is that the Hawking radiation does not come from the event horizon, but instead comes from a region just outside the event horizon so time has not stopped at its position.
If you were to watch a black hole form then evaporate, y... | The time dilation you speak of is a description of the apparent time an observer outside witnesses someone falling into a black hole. That is, if you are standing outside the black hole (some distance away) and you watch you buddy jump in, it will look at if he slows down as he reaches the horizon, and never quite gets... | https://physics.stackexchange.com |
39,923 | [
"https://mathoverflow.net/questions/39923",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9504/"
] | This should be a trivial question for mathematicians but not for typical physicists.
I know that the spectrum of a linear operator on a Banach space splits into the so-called "point," "continuous" and "residual" parts [I gather that no boundedness assumption is needed but I could be wrong]. I further know that the po... | Eigenvectors for different eigenvalues of a self-adjoint operator are orthogonal. In a separable Hilbert space, any orthogonal set is countable. So a self-adjoint operator on separable Hilbert space has only countably many eigenvalues. (As noted, this does not mean the spectrum is countable.)
| You are confusing two notions. First of all, the point spectrum just means eigenvalues; there is no assumption that these form a discrete set. The shift operator is a simple example where the spectrum is "continuous".
The condition for the eigenvalues to be discrete is precicsely that the operator $A:H \to H$ is <em>c... | https://mathoverflow.net |
1,303,827 | [
"https://math.stackexchange.com/questions/1303827",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/239635/"
] | I have the following set and I want to know whether it's a vector space or not:
<blockquote>
$W = \{(x, y, z) ∈ \Bbb R^3 : (x + y)(2y − z) = 0\}$
</blockquote>
Now, I understand that if I have a set W and it's a vector space then $0\in W$ and it should have vector addition and scalar multiplication for some $w_1, w... | It is not closed under addition. For example, $(0,0,z)$, where $z$ is an arbitrary number, is in $W$.
Now find another vector in $W$, for example $(1,1,2)$. Add these two together. You get $(1,1,z+2)$, again, where $z$ is arbitrary. This is clearly not in $W$, except for $z=0$.
| $\newcommand{\Reals}{\mathbf{R}}$In case some theory helps clarify your strategy: Your set $W$ is the union of two planes through the origin:
$$
W_{1} = \{(x, y, z) \in \Reals^{3} : x + y = 0\},\qquad
W_{2} = \{(x, y, z) \in \Reals^{3} : 2y - z = 0\},
$$
since $(x + y)(2y - z) = 0$ if and only if $x + y = 0$ or $2y - z... | https://math.stackexchange.com |
58,685 | [
"https://mathoverflow.net/questions/58685",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13700/"
] | Suppose $(E,p,B;F)$ is a fiber bundle such that $E$ is homeomorphic to $B\times F$, is it true that the fiber bundle is trivial?
A non connected counter example has been provided, so I'll ask for E,B and F to be connected (hopefully low dimensional) manifolds.
| Consider the pullback $\xi$ of $TS^2$ via the projection of $S^2\times\mathbb R$ onto the first factor. The bundle $\xi$ is a nontrivial $\mathbb R^2$-bundle over $S^2\times\mathbb R$ because its pullback under the inclusion $S^2\to S^2\times\mathbb R$ is $TS^2$, which is nontrivial. On the other hand, its total space ... | No. Let $B=S^1$, $F=\mathbb Z$, $E=S^1\times\mathbb Z$, and let $p$ be a two-fold covering on each component: $p(z,n)=z^2$ where $S^1$ is regarded as the unit circle in $\mathbb C$ (for the purposes of computing $z^2$).
| https://mathoverflow.net |
158,856 | [
"https://dba.stackexchange.com/questions/158856",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/114619/"
] | What is the least amount of privileges (Administrator, db_owner, etc) for a user to perform following in SQL Server ?
<ol>
<li>Backup</li>
<li>Restore</li>
</ol>
| If your Label has fixed pattern, i.e. IP_BLOCK_X.info#NNN, where NNN is an integer.
You can easily do this way
<pre><code>use tempdb
drop table #t;
create table #t (Block varchar(100), Label varchar(100));
go
insert into #t (Block, Label) values ('Block_A','IP_BLOCK_X.info#9'), ('Block_A','IP_BLOCK_X.info#8'), ('Bloc... | You can use charindex and sub string to build a column to order by
So you could do something like this:
<pre><code>SELECT info
FROM (
SELECT info,
CAST(SUBSTRING(info,CHARINDEX('#',info,0)+1,(LEN(info)-CHARINDEX('#',info,0))) AS INT) [OrderBy_Column]
FROM (
SELECT 'IP_BLOCK_X.info#8' AS info
... | https://dba.stackexchange.com |
576,789 | [
"https://physics.stackexchange.com/questions/576789",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/265836/"
] | I am just starting to solve the first couple of didactic problems of quantum mechanics, particles subjected to really simple Hamiltonians. Before checking them out I was thinking that the best approach to solve them would be to find the wave function using the Schrodinger's equation. Instead the first step seems to be ... | I can give you two reasons for studying the eigenvalue problem for the Hamiltonian operator.
<ol>
<li>In Quantum Mechanics states are unit vectors in a Hilbert space and obserables are hermitian operators in this space. The postulates state that given one observable <span class="math-container">${\cal O}$</span> the po... | Aside of the physical interpretation, one always would like to have the eigenvalues and eigenvectors of a given operator. Think e.g. in time evolution: an arbitrary vector state can be written in the eigenbasis of your operator in question, in this case <span class="math-container">$H$</span>. The time evolution simply... | https://physics.stackexchange.com |
1,533 | [
"https://softwareengineering.stackexchange.com/questions/1533",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/212/"
] | If you're developer (Senior or Lead Developer) and you'd rather stay with code/design than pursue a management career, what are the available career paths at your company, or any you've heard of? How far can you go?
Is it possible to continue being a geek until you bite the dust or is that too naive?
Are people like ... | I am going to go out on a limb here and say something that is not likely to be the answer you want to hear, but if you don't like management, your career path is going to be very limited. If what you like to do is code, and if you are really good at it, and you don't want to stop, then your career path is on a single t... | Depends on the sort of company you work for.
Many companies don't value talented, experienced developers as highly as managers, and will never reward them to the same level <- This is not the sort of company people like you should be working for.
Other (usually more tech-focused) companies will value their develop... | https://softwareengineering.stackexchange.com |
135,093 | [
"https://stats.stackexchange.com/questions/135093",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/67514/"
] | I have two proportions and I need to see if they are associated somehow. The null hypothesis is that they are equal. I'm using R.
So I get the pooled proportion:
<pre><code>pp = (prop_1+prop_2)/(dim(dist_1)+dim(dist_2))
</code></pre>
then the standard error:
<pre><code>se = sqrt((pp*(1-pp))/dim(dist_1)+(pp*(1-pp))/... | You haven't described your question very well, but it seems to me you are asking: Is it plausible that the two proportions were sampled from populations where the proportion "success" (whatever your outcome is) is equal.
Assuming you did the calculations correctly (you didn't give any of the key details), your P valu... | +1 to @Harvey Motulsky. Let me add a quick note, just to address your explicit question. You should not use <code>pt()</code> instead of <code>pnorm()</code>. When you are working with normally distributed data, but you have to estimate the group SDs from the same data, you have to account for the fact that the SDs ... | https://stats.stackexchange.com |
455,051 | [
"https://electronics.stackexchange.com/questions/455051",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/211198/"
] | I used to work with PIC and now I need to use STM32 chip. I was using HAL library but it gave me some problems so now I want to use it without HAL_Library. There are some questions I could not get any answer.
<ol>
<li>In the datasheet of any PIC there are registers and each bit of those registers are showed and explai... | <blockquote>
In the datasheet of any PIC there are registers and each bit of those registers are showed and explained. But in the datasheet of STM32 chips I could not find any registers. How can I find all registers in STM32 chips and specific bits of these register.
</blockquote>
The <strong>Datasheet</strong> cont... | You are looking at the datasheet. It is not there. It is in the reference manual. For STM32, datasheet is mostly for package specific things like pinouts and electrical specifications (that's the only time I ever look at it anyways). User reference manual is for device common things like registers and peripherals which... | https://electronics.stackexchange.com |
262,975 | [
"https://electronics.stackexchange.com/questions/262975",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/70149/"
] | So I bought a couple of switching power supplies for a project of mine and I am currently recalculating my actual power usage out of my wall socket to figure out how to distribute power. I have made sure that my power supplies will never exceed 90% of its capacity, but the normal operating will be around 40-50%.
I tri... | <blockquote>this supply says: 230V (170-264V) 1.5A. However my calculations for 240V is 0.416A.</blockquote>
You are comparing two different things. The supply spec gives you the absolute maximum current it will ever draw under any conditions of output load, input voltage, temperature, phase of the moon, and what you... | You can't calculate AC power by multiplying effective voltage and effective current as put on the label. The voltage is there so you can pick the right device for an input voltage and the current is there so you don't overload the circuit, power strips etc.
On the label, there may be two addional values, first is ...V... | https://electronics.stackexchange.com |
59,018 | [
"https://mathoverflow.net/questions/59018",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5100/"
] | The following question feels to me like a standard sort of 'fact' in birational geometry, but I can't seem to write down a correct set of details. Hopefully someone can point me to a reference and not a counter example!
Suppose $X$ is a variety (reduced and irreducible over an algebraically closed field, perhaps of ... | <em>Credit</em>: This answer came out of trying to understand why auniket's answer (a.k.a. counterexample) works.
1) auniket is correct that for dimension reasons $T$ cannot surject onto $S$, so in particular my comment about $X$ being normal possibly helping is irrelevant. So is $T$.
2) It seems to me that there is ... | Note that $T := \tilde \phi(f^{-1}(Y))$ is a proper Zariski closed subset of $S$. Therefore, for generic $v_1, \ldots, v_s \in V$, $Z(v_1) \cap \cdots \cap Z(v_s) \cap T = \emptyset$. Consequently, in this case $P \cap Y = \emptyset$ and your question boils down to whether $v_1, \ldots, v_s$ generate the ideal of $Y$ (... | https://mathoverflow.net |
48,656 | [
"https://quant.stackexchange.com/questions/48656",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/34825/"
] | I understand the aspect that central clearing reduced counterparty risks. From the valuation side, am I right that cash flows for both trades will be discounted at the OIS rate?
The party that holds the collateral will need to pass back the interest, but if you pay into the margin account, the money is "gone" and you... | For both cleared and OTC swaps you need to post margin. If you are delivering cash then you will receive OIS in generally in either case. As OTC trades are bespoke you might have a different agreement with your particular counterparty - but that would be unusual.
The main advantage of a central clearer is the recyc... | A cleared swap faces the clearing house. As a centralised trade depository the clearing house imposes margin requirements, as a kind of insurance for their perceived lower credit risk. Margin is nowadays remunerated at local currency OIS I believe. The collateral is posted in local currency (or USD depending upon produ... | https://quant.stackexchange.com |
129,866 | [
"https://mathoverflow.net/questions/129866",
"https://mathoverflow.net",
"https://mathoverflow.net/users/33751/"
] | Assume we have a centrally symmetric convex set $K \subset \mathbb{R}^n$ such that Vol(K)=1. In addition, assume that for every direction $u$ we know that $Vol(K \Delta R_u(K)) < \epsilon$, where $A \Delta B$ is the symmetric difference and $R_u(K)$ denotes the reflection of $K$ with respect to $u^\perp$.
Does this ... | Let $r$ be the radius of the maximal ball contained in $K$ and $R$ the radius of the minimal ball containing $K$. I claim that $\frac rR>1-2\epsilon^{1/n}$. It follows that the Hausdorff distance from $K$ to a ball is bounded by $C_n\epsilon^{1/n}$. The argument does not use symmetry (although the constant can be im... | For convex closed sets with uniform upper-diameter and lower-volume bounds,
the Nikodym distance is equivalent to Hausdorff distance.
Your condition for the Hausdorff distance, implies that $K$ is close to any ball which does not contain $K$ and is not contained in $K$. Hence the statement follows.
| https://mathoverflow.net |
80,732 | [
"https://physics.stackexchange.com/questions/80732",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/31031/"
] | From time to time I see safety warning about keeping loose items in your car. The last warning used a 2kg object, and claimed that if a collision occurred at $50{km\over h}$ it would have a weight equal to 80kg. At $90{km\over h}$ it would have a weight of 256kg.
How are these "new weights" calculated?
| From $dp/dt\simeq \Delta p/\Delta t=F$. A 2 kg object at 50 km/hr has an initial momentum of
$$
p=mv = 2\,{\rm kg}\cdot13.9\,{\rm m/s}=27.8\,{\rm kg\,m/s}
$$
If we naively assume that the crash is over the course of a 0.05 seconds, then the force is $F=556\,{\rm N}\to m_{eff}\simeq58\,{\rm kg}$ (final momentum being 0 ... | I'd guess it's probably some heuristic where they assume the object decelerates from the car speed to stationary in some time interval characteristic of impact times during car crashes (ie, the time it takes to decelerate when it hits you). If that's the case, the formula is
$$gm_e =a m$$
where $m_e$ is the calculated... | https://physics.stackexchange.com |
161,737 | [
"https://security.stackexchange.com/questions/161737",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/149372/"
] | So today I was about to download cheat engine to access some hidden mini games on PvZ Game of the year edition, and I want to know; is it safe?
| There is no way to know if what you have downloaded is actually safe. But, a common way to distribute malware are social attacks, where the user itself is downloading and executing the malware and thus implicitly helps the malware to bypass safe guards which are only effective against unintended downloads.
For example... | It's difficult to be 100% sure if anything is safe. You can check the file with your own antivirus and you can also submit the file to the virus total website which will run it through multiple antivirus engines. By that time of course it's too late as you've downloaded the file and potentially infected your machine.
... | https://security.stackexchange.com |
2,902 | [
"https://dsp.stackexchange.com/questions/2902",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/1658/"
] | I recently started playing with the Fourier transform (after spending a few weeks learning about the mathematics behind it). I decided to try hacking together a low-pass filter on the following sound bite:
<div class="soundcloud-embed">
<iframe src="https://w.soundcloud.com/player/?url=http://api.soundcl... | Two potential issues:
<ol>
<li>Doing filtering in the frequency domain (using an FFT) requires overlap-add, overlap-save, or a related algorithm. This is caused by the difference between linear and circular convolution. Otherwise you get time-domain aliasing</li>
<li>Some of the noise sounds like simple clipping. Filt... | First just a note, fourier transforms are not ideal for low/high pass filters. Butterworth filters are a good place to start and following that Chebyshev/Elliptical filters if you get more ambitious.
It looks like your are trying to implement an ideal filter. There is no way we can implement these 'brick-wall' filters... | https://dsp.stackexchange.com |
43,332 | [
"https://physics.stackexchange.com/questions/43332",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/9845/"
] | I wanted to know why there is a hole in the ball (basketball, volleyball, handball) to fill the ball with air. Why can't the ball come with filled in air and fully sealed so that there is no loss of air?
| Large inflatable balls such as soccerballs, footballs and basketballs have an internal rubber bladder which needs to be inserted by hand into the carcass of the ball and inflated to the desired pressure to suit the user (eg: basketballs can be inflated to the produce the desired bounce height for the individual user).
... | The ball will slowly leak air because it's skin isn't perfectly impermeable to air molecules. Unless there is some way to refill the ball it will slowly deflate.
| https://physics.stackexchange.com |
12,972 | [
"https://electronics.stackexchange.com/questions/12972",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2062/"
] | Let's say I have a signal where 1v is digital 0, and 4v is digital 1.
I am a little lost how can I use PNP+NPN transistor to have +11..12(for 1) or -11..12V(for 0) output, provided that I have +12/-12 PSU?
UPDATE: This is for low-power MOSFET driver, which has to be done in discreet transistors.
| Is this what you mean?
<img src="https://i.stack.imgur.com/QUA47.png" alt="enter image description here">
| My attempt at a solution.
R5 and R6 are only there to model source resistance and are not part of the circuit. C1 and R4 are used as load for simulation.
V4: input source (10MHz 0.5 duty ratio 0-to-5V square wave for simulation)<br>
V3: reference source (2.5V for simulation)<br>
V1: +12V supply<br>
V2: -12V supply
... | https://electronics.stackexchange.com |
326,832 | [
"https://math.stackexchange.com/questions/326832",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/30330/"
] | <strong>Problem</strong>
Let $P(z) = z^n + a_{n−1}z^{n−1} + \cdots + a_1z + a_0$ be a polynomial of degree $n > 0$. Show
that if $\lvert P(z) \lvert \le 1$ whenever $\lvert z \rvert = 1$ then $P(z) = z^n$.
<hr>
I have tried to see $\dfrac{P(z)}{z^n}$, but nothing happens. I wonder which theorems should I use to ... | <strong>Hint:</strong> let $Q(z):=z^nP(z^{-1})$, which is a polynomial. Then $|Q(z)|\leqslant 1$ when $|z|=1$ and $Q(0)=1$ so by maximum modulus principle...
| Hint: Schwarz lemma and maximum prinicple
| https://math.stackexchange.com |
291,511 | [
"https://mathoverflow.net/questions/291511",
"https://mathoverflow.net",
"https://mathoverflow.net/users/69037/"
] | <strong>Definition.</strong> Let $X\subset \mathbb R^n$ be a locally Euclidean subset. Say it has a tangent space at $p\in X$ if there exists a linear subspace $V\leq \mathbb R^n$ satisfying the following conditions.
<ol>
<li>$\dim V=\dim_pX$.</li>
<li>There exists a neighborhood $U\subset X$ of $p$ in $X$ for which
$... | By invariance of domain, the condition $\dim V=\dim_pX$ implies that the local injectivity is locally a bijection to a neighborhood of $p.$ So there are open sets $V_0\subseteq V$ and $X_0\subseteq X$ with $V_0$ containing $0,$ and a function $g:V_0\to X_0$ such that $\pi_V(g(v)-p)=v$ and $g(0)=p.$ By condition 2 we ha... | This is a long comment, rather than a complete answer. It shows, for any subset $X$ near $0$ and any dimension of the tangent(s), that if there are two tangent spaces in the sense of the OP then they must have nonzero intersection.
<strong>Lemma.</strong> Let $\{0\}\neq X\subseteq\mathbb{R}^n$ be any subset that has t... | https://mathoverflow.net |
131,575 | [
"https://security.stackexchange.com/questions/131575",
"https://security.stackexchange.com",
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] | When it comes time for the internal phase of a white box or red-team audit, where you've locked yourself in a mop-closet in an office building of a Fortune 500 company, I would think that the last thing you'd need is Burp Suite attempting to connect to portswiggerDOTcom to check for a new version or noisy traffic gener... | Welcome to Security.SE.
First, a brief explanation of hashing versus encryption, because that's important here.
<h2>Hashing and encryption</h2>
When talking about hashes, it is impossible to decrypt. Hashes are one-way and cannot be reversed to retrieve the plaintext. This matters because how you go about getting th... | In short, no. By definition, hashes are one way encryption and can't be de-hashed. That is why the best way to crack a hash is to pseudo-randomly encrypt strings of texts and compare the encryption output to the hash you already have.
If brute forcing the hash isn't working, you can try the following:
<ul>
<li>Check ... | https://security.stackexchange.com |
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