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 |
|---|---|---|---|---|---|
96,385 | [
"https://cs.stackexchange.com/questions/96385",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/40409/"
] | Set <span class="math-container">$I_n = \{0,\ldots,n-1\}$</span>.
Given integers <span class="math-container">$v_0,\dots,v_{n-1} \in \mathbb{N}$</span>, find an integer <span class="math-container">$t>0$</span>, a map <span class="math-container">$f:\mathbb{N} \times I_n \to \mathbb{N}^t$</span>, and a well-founded ... | Yes. This is possible. $t=1$ suffices. Take
$$\begin{align*}
f(m,n-1) &= Cm + D\\
f(m,n-2) &= f(m+v_{n-2},n-1) + 1 = Cm + C v_{n-2} + D + 1\\
f(m,n-3) &= f(m+v_{n-3},n-2) + 1 = Cm + C v_{n-3} + C v_{n-2} + D + 2\\
&\ldots\\
f(m,i) &= Cm + C v_{i} + \dots + C v_{n-2} + D + n-1-i
\end{align*}$$
w... | I have to post this answer since it is probably what I will implement in practice because it is more extendable to other settings and it can be well encoded in my system by logical formulas. However, I will still refer to D.W.'s approach since is mathematically more appealing and for me as a mathematician opens a lot o... | https://cs.stackexchange.com |
665,412 | [
"https://math.stackexchange.com/questions/665412",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/126586/"
] | Formula for binary sequences of length $m$ with no $n$ consecutive $1$s?
I know The number of binary strings of length $m$ without consecutive $1$s is the Fibonacci number $F_{m+2}$.
But how about no $n$ consecutive $1$s?
Any help will be appreciated! Thank you
| The same idea will work to make a recurrence. To make a sequence of length $m$, you can take one of length $m-1$ and add a zero, one of length $m-2$ and add $01$, one of length $m-3$ and add $011$ on up to $m-n$ adding a zero and $n-1\ \ 1$'s
| This formula should work-
Total sequences possible $=2^m=s(let)$;
Sequences with no $n$ consecutive $1$'s $= \frac{(m-n+1)(m-n+2)}2=t(let)$
Answer$=s-t$
| https://math.stackexchange.com |
64,139 | [
"https://biology.stackexchange.com/questions/64139",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/5009/"
] | I'm translating a document from Russian:
<blockquote>
The mean retention time for the first four injections of RNase should be (40.8± 2) min. If the mean RT is beyond this range, adjust the gradient system (change the content of acetonitrile within the 20% - 32% range) and <strong>chromatograph</strong> the RNase so... | I would say simply:
<blockquote>
repeat the chromatography four times
</blockquote>
or less formal, but quite acceptable:
<blockquote>
re-run the column (or whatever it is) four times
</blockquote>
This puts the emphasis on the process.
But I’m not exactly sure what’s happening. You have four injections of RN... | I would continue to use <code>inject</code> to describe loading samples into the liquid chromatography system and replace
<blockquote>
chromatograph the RNAase solution four times.
</blockquote>
with
<blockquote>
inject the RNAase solution another four times.
</blockquote>
| https://biology.stackexchange.com |
494,882 | [
"https://physics.stackexchange.com/questions/494882",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/222840/"
] | I am not talking about the distinction between mass and weight, just the concept of 'weight'.
In University physics (book by Young & Freedman, 14th Ed.) it is given that
<blockquote>
the weight of an object is the total gravitational force exerted on it
by all other objects in the universe.
</blockquote>
Foll... | Hardly anyone calls the Sun’s gravitational force on the Earth the Earth’s “weight”. But for historical reasons everyone calls the Earth’s gravitational force on you your weight.
The general rule is that people use the word “weight” when you can put an object on a scale and weigh it. The usage comes from everyday life... | <blockquote>
In University physics, they wrote, " weight of an object is the total gravitational force exerted on it by all other objects in the universe."
</blockquote>
I think this definition is wrong, or, at the very least, generalizes the notion of weight as applied to everyday objects in an unhelpful and potent... | https://physics.stackexchange.com |
2,751,178 | [
"https://math.stackexchange.com/questions/2751178",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/555389/"
] | Let $U$ be the harmonic lift of a subharmonic function $u$ on $B \Subset \Omega \subset_{\mathrm {domain}} \Bbb R^n$. Then
$$
U(x) = \left\{
\begin{array}{ll}
\bar {u} (x) & \quad x \in B \\
u(x) & \quad x \in \Omega \setminus B
\end{array}
\right.
$$
where $\bar ... | You have done almost everything. The remaining part can be tackled using set theory.
First note that $\overline {B \cap B'} \subset \overline B \cap \overline B' \subset \overline B'$. So
$\partial (B \cap B') = \overline {B \cap B'} \setminus (B\cap B') \subset {\overline {B'}} \setminus {(B \cap B')} = (B' \cup \... | Note that subharmonicity ( like harmonicity) is a local condition. That is: if there exists an open cover of the domain of the function such that the restriction to each piece is subharmonic, then the function is subharmonic. ( in fact, if the function is $C^2$, then the condition is $\Delta f\ge 0$)
It's better to us... | https://math.stackexchange.com |
248,670 | [
"https://physics.stackexchange.com/questions/248670",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/102985/"
] | What are the exact definitions of pure translational , pure rotational and rolling motion? I am a class 11th student ... I find it difficult to exactly make a distinction between translational, rolling and rotational motions in my dynamics questions. So I want definitions that can fit in any situation.
| Theese concepts usually arise in rigid body mechanics. So consider a rigid body which is a set of points in which the distance between any two points do not change. If this is too abstract you can just think of a piece of rock.
One talks of <strong>translational motion</strong> when the body moves along a straight lin... | I haven't given the exact definitions, but instead given examples on what each of the three are. This will help you get your head around the topic, and be able to get more understanding when you encounter the problem again later.
Translation is when the centre of mass of a body moves from one point to another. An exam... | https://physics.stackexchange.com |
16,151 | [
"https://physics.stackexchange.com/questions/16151",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5473/"
] | I hope this question is simple and can be quickly cleared up.
In a 1D conservative dynamical system, I've always been taught that the potential function is the function $V(x)$ such that:
$$F=-\frac{dV}{dx}$$
That makes sense to me, simply derived from the definitions of work and conservation of energy.
However, ju... | While Jonathan's answer is correct, it is very general. I would like to explain the reason for the terminology in this specific problem.
When dealing with second order equations, like Newton's laws, the notion of potential is designed to give a conserved energy. This definition is natural in the inertial domain--- in ... | Keep in mind that the definition of potential is dependent on context. There is nothing deep going on here. If he wishes to define the potential of the system $\dot{x}=f(x)$ to be a function $V$ such that $-\frac{dV}{dx}=f(x)$, he is free to do so. Now of course, because the system itself is different, you can't exp... | https://physics.stackexchange.com |
3,484 | [
"https://engineering.stackexchange.com/questions/3484",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/2170/"
] | I am trying to find the enthalphy of Helium if its internal energy is 200 kJ/kg. The answer is given as 333.42 kJ/kg, but I keep getting the wrong answer.
I've tried the following:
$\begin {align}
H &= U + PV \\
H &= U + mRT \\
\end {align}$
Universal Gas Constant, $R_u = 8.314 \:\mathrm{\dfrac{J}{K \cdot mo... | First, notice that the problem statement does not specify a temperature.
The internal energy and enthalpy are given by:
$$ U = m c_vT $$
$$ H = m c_pT $$
Therefore:
$$ H = \frac{c_p}{c_v}U $$
For a monatomic gas, such as helium, the ratio $c_p/c_v$ is very nearly $5/3$. It follows that:
$$ H = \frac{5}{3} \times ... | Following your method: You can't assume that temperature of Helium at that particular state is $273.15\ K$, but we can calculate it as follows:
$$u = C_{v}\Delta T$$
$$\Delta T = \frac{u}{C_v} = \frac{200}{3} = 66.66667\ K$$
$$h = C_{p}\Delta T = 5*66.66667 = 333.3 \ kJ/kg$$
As John said, Values from your text book o... | https://engineering.stackexchange.com |
3,012 | [
"https://dba.stackexchange.com/questions/3012",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/44/"
] | For example
<pre><code>SQL> create table dates(d date);
Table created.
SQL> insert into dates select sysdate from dual;
1 row created.
SQL> select * from dates;
D
---------
28-MAY-11
SQL> insert into dates (d) values (select sysdate fom dual);
insert into dates (d) values (select sysdate fom dual)
... | If you want to use a SELECT statement where only a single value is allowed you need to put that SELECT statement into brackets:
<pre><code>insert into dates (d)
values
( (select sysdate from dual) )
</code></pre>
That could be extended for multiple columns:
<pre><code>insert into dates
(
id,
d,
other_column
... | I <em>think</em> without knowing (I don't do Oracle so don't have a box to try this on) that the problem is here:
<pre><code>insert into dates (d) values (select sysdate fom dual)
^^^^^^ <- this isn't a date; it expects a date here
</code></pre>
Try this instead:
<pre><code>insert in... | https://dba.stackexchange.com |
4,480,709 | [
"https://math.stackexchange.com/questions/4480709",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/456519/"
] | Given a Hilbert space <span class="math-container">$H$</span>, a projection <span class="math-container">$P\in B(H)$</span> and a compact operator <span class="math-container">$T\in B(H)$</span> how does one conclude that <span class="math-container">$P\leq T$</span> implies <span class="math-container">$P$</span> comp... | Notice that if <span class="math-container">$P \le T$</span> then
<span class="math-container">$$ \|Pu\|^2 = (Pu,Pu)= (Pu,u) \le (Tu,u) \le \|Tu\| \|u\|, \tag 1 $$</span>
for all <span class="math-container">$u \in H$</span>. Let <span class="math-container">$(u_n)$</span> be a bounded sequence in <span class="math-con... | More general statement is true. If <span class="math-container">$0\le B\le A$</span> and <span class="math-container">$A$</span> is compact, then <span class="math-container">$B$</span> is compact. Indeed, the assumption is equivalent to <span class="math-container">$$\|B^{1/2}x\|^2\le \langle Ax,x\rangle $$</span> Thi... | https://math.stackexchange.com |
173,586 | [
"https://dba.stackexchange.com/questions/173586",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/107357/"
] | DatabaseBackup - USER_DATABASES - LOG: This job fails saying "Executed as user: Domain\XXXX-SVC. Unable to open Step output file. The step failed."
The error is only with LOG backup job.<br/>
The other DatabaseBackup jobs (FULL, DIFF) works just fine with same SVC account. So the service account have appropriate perm... | It turns out that the person migrated the jobs from old server to new server edited the jobs manually.<br/>
One of the edit was to <code>"Output File: (Job Step properties-->Advanced)"</code>
this was set to default log location <code>C:\Program Files\Microsoft SQL Server\MSSQL11.MSSQLSERVER\MSSQL\Log</code> on ol... | Try to change Type in <code>Job Step Properties</code> to <code>Transact SQL Script</code> and then change the script itself by removing <code>sqlcmd -E -S $(ESCAPE_SQUOTE(SRVR)) -d master -Q "</code> and quotes at the end of the script.
Then try to execute the job and inform us if it worked.
| https://dba.stackexchange.com |
2,033,443 | [
"https://math.stackexchange.com/questions/2033443",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/393640/"
] | I need to check if this function is continuous:
$$f(x)= \lim_{n\to\infty}\sqrt[n]{4+x^{6n}}$$
So I did this:
$$f(x)= \lim_{n\to\infty}\sqrt[n]{4+x^{6n}} = \lim_{n\to\infty}(4+x^{6n})^{1/n} =\lim_{n\to\infty} \left(x^{6n}\cdot \left(\frac{4}{x^{6n}}+ 1 \right) \right)^{1/n}$$
$$f(x) = \lim_{n\to\infty}x^6 \cdot \lef... | <strong>Hint</strong>
Your function $f$ is defined by
$f(x)=1$ if $|x|\leq 1$ and
$f(x)=x^6$ if $|x|>1$.
so, it is continuous at $\mathbb R$.
| When you did the $$\lim_{n\to\infty}({4+x^{6n})^{1/n}} =\lim_{n\to\infty}(x^{6n}\cdot({\frac{4}{x^{6n}}+ 1))^{1/n}}$$
step, you introduced a discontinuity at $f(0)$, due to the $\frac4{x^{6n}}$ which is a div$/0$ error that was not accounted for. See if you can find a different way around this issue.
| https://math.stackexchange.com |
25,408 | [
"https://dba.stackexchange.com/questions/25408",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/10832/"
] | I have several databases on a production server that are in the hundreds of gigabytes, and have many thousands of transactions running through them on a daily basis.
Almost all these databases are mirrored using SQL Server Mirroring.
Even though we have carefully planned the physical log file sizes to match expected ... | Here is a slightly simpler approach that avoids the cursor and nested exec:
<pre><code>SET NOCOUNT ON;
CREATE TABLE #to
(
DBName SYSNAME,
FileCount INT
);
DECLARE @v INT;
SELECT @v = CONVERT(INT, PARSENAME(CONVERT(VARCHAR(32),
SERVERPROPERTY('ProductVersion')), 4));
DECLARE @sql NVARCHAR(MAX);
SET @sql = N'... | You can create a temp table and use it inside the dynamic SQL. I didn't go based off your code but this shows the concept:
<pre><code>create table #mainTab
(
DatabaseName varchar(max)
,FileId int
, FileSize nvarchar(255)
, StartOffset nvarchar(255)
, FSeqNo nvarchar(255)
, Status int
, Pa... | https://dba.stackexchange.com |
4,916 | [
"https://dba.stackexchange.com/questions/4916",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/136/"
] | Which is the best way to implement a canceled attribute in a database table, provided that less than say 3 % of the rows are canceled.
For canceled data I want to store the additional information
<ul>
<li>by whom</li>
<li>when</li>
<li>why</li>
</ul>
In about 95 % of the queries I only want to select the non cancele... | You have 97% active rows and 95% of queries on this 97%.
A WHERE clause that selects 97% of rows won't be helped by indexing: it isn't selective enough
I'd consider 2 tables for your "Things": ThingActive and ThingCancelled
For the 5% where you query cancelled rows, you read either the Cancelled table only or a UNIO... | I'm not sure I like <code>NULL</code> for lack of being cancelled. I think I'd rather have an Active flag that is 1 by default, and set to 0 when something is cancelled. Now your checks are simply WHERE active = 1 or WHERE active = 0, instead of dealing with all the <code>OR IS NULL</code> or <code>OR IS NOT NULL</code... | https://dba.stackexchange.com |
253,133 | [
"https://softwareengineering.stackexchange.com/questions/253133",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/146037/"
] | In our organization, we are using various data access/persistence technologies in different projects. The ones used till now are Hibernate, JPA, Spring Data JPA, JDBC, Spring JDBC, MyBatis, and QueryDSL.
How do I find out what is the industry usage of these technologies? i.e. which is used more widely than others - o... | I guess most of this information is not freely available on the internet. So the best approach is probably to make a survey, call or email 100 top IT companies and just <em>ask</em> them. However, if you don't have a name like "Forrester" or "Gartner" on your business card, it is likely you won't get much response. Alt... | <ol>
<li>why do you even care?</li>
<li>you won't get a response from most companies as they'd consider it a company secret what they use</li>
<li>what are your criteria? Many companies would have investigated a lot of things, before maybe adopting one or two of them. And then they may no longer be used in new projects... | https://softwareengineering.stackexchange.com |
251,250 | [
"https://softwareengineering.stackexchange.com/questions/251250",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/121368/"
] | If I write a C program and compile it to an <code>.exe</code> file, the <code>.exe</code> file contains raw machine instructions to the CPU. (I think).
If so, how is it possible for me to run the compiled file on any computer that runs a modern version of Windows? Each family of CPUs has a different instruction set. S... | Executables do depend on both the OS and the CPU:
<ul>
<li><strong>Instruction Set:</strong> The binary instructions in the executable are decoded by the CPU according to some instruction set. Most consumer CPUs support the x86 (“32bit”) and/or AMD64 (“64bit”) instruction sets. A program can be compiled for either of ... | 99% of current PCs running Windows have a 64 bit processor, which also is capable of running 32 bit software. The other one percent has 32 bit processors. So software built for 32 bit processors runs everywhere. Software built for 64 bit processors runs on every PC that the creator of the software cares about.
MacOS ... | https://softwareengineering.stackexchange.com |
572,978 | [
"https://electronics.stackexchange.com/questions/572978",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/220456/"
] | I am trying to read and understand on what device would be a better switching element - BJT or MOSFET.
From what I have read and my understanding is that:
If the application requires faster switching, we need to go for the BJT because, the capacitance between the base and emitter is very less when compared to the capac... | I'll address your first point first:
It's true that the parasitic capacitances of a MOSFET are significantly higher than those of a BJT. However, the BJT suffers from an effect known as saturation, where a buildup of charge carriers prevents the BJT from turning off for a fairly long time after you try to turn it off--... | I can offer a very simple way of thinking about using one of the two common areas, discrete circuits for <strong>switching</strong>. (The discrete MOSFET pretty much isn't used for analog audio voltage amplification.)
For switching, the BJT <em>looks like</em> a voltage source/difference between its collector and emitt... | https://electronics.stackexchange.com |
254,205 | [
"https://softwareengineering.stackexchange.com/questions/254205",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/136829/"
] | Okay, I know first-class functions are cool, closures even better, etc. But is there any language with first-class methods?
In my mind, I see a first-class method as an "object" that has both a function pointer and a pointer to a specific instance of the class/object, but the implementation doesn't matter. I just want... | In typical OO parlance, methods belong to objects. If methods were themselves objects, then these objects would of course have methods. But those are objects, too, so they have methods. Which are objects which have methods which are objects which have methods which are objects which have methods …
There are ways to de... | Yes, in javascript. That's because in javascript methods are functions and functions are full-fledged objects.
Example:
<pre><code>// Here's a "class" with method foo.
// Note that javascript don't really have classes,
// we use constructors instead:
function FooTeNator () {
this.text = "foo";
}
FooTeNator.protot... | https://softwareengineering.stackexchange.com |
1,507,365 | [
"https://math.stackexchange.com/questions/1507365",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/248588/"
] | Part of solving a bigger problem, I discovered that when dividing $1$ with a prime number $p$ > 11, the results has $p-1$ repeating decimals.
Examples: $\dfrac 1{23} = 0.\underline{0434782608695652173913}0434782608695...$
As far as I could tell, this happens for all primes I tested.
I can't at this time see the logi... | When you divide p into 1 you get a remainder. When you divide p into that remaineder you get a second remainder. There are only p - 1 possible remainders. Once you go through them all they will repeat.
The only thing you need to figure out is why you will always have a remainder (because p, except 2 and 5, don't d... | If $p=3$ you get $0.333333\ldots$, and you could say it has $p-1=2$ repeating digits and the part that repeats is $33$.
If $p=11$ you get $0.0909090909\ldots$, and you could say it has $p-1=10$ repeating digits, and the part that repeats is $0909090909$.
If $p=37$, you get $0.027027027\ldots$, and you could say it ha... | https://math.stackexchange.com |
59,309 | [
"https://cs.stackexchange.com/questions/59309",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/53223/"
] | This site is full of Pumping Lemma questions, and I do admit I've not read them all. I've tried some proofs myself and they seem to work, but I can't find anywhere what is the (general) exact structure of a proof where you show a language is not regular or context-free?
Wikipedia and most proofs start with "Suppose $L... | <blockquote>
this is not context-free/regular because I can come up with a counterexample which fails the pumping lemma
</blockquote>
You are missing that in order to construct this counterexample you have to <em>assume</em> that $L$ is regular. Then you <em>apply</em> the Pumping lemma, which yields the Pumping len... | The formulation of the Pumping Lemma, with explicit quantifiers, is as follows:
$$\forall L\in REG, \exists p>0, \forall w\in L,|w|>p\Rightarrow \exists x,y,z\in \Sigma^*, w=xyz\wedge c_1\wedge c_2\wedge c_3$$
where $c_1,c_2,c_3$ are the conditions of the lemma.
Thus, a proof that a language is not regular is i... | https://cs.stackexchange.com |
164,924 | [
"https://math.stackexchange.com/questions/164924",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/17537/"
] | Suppose $d \ge 2$ and $S$ is a finite simplicial complex of dimension $2d$, such that
(1) $S$ is simply connected, i.e. $\pi_1 ( S) = 0$, and
(2) all the homology of $S$ is in middle degree, i.e. $\widetilde{H}_i ( S, \mathbb{Z}) = 0,$ unless $i = d$, and
(3) homology $\widetilde{H}_d(S, \mathbb{Z})$ is torsion-free... | Your space is what is called a Moore space (a space with a unique nontrivial homology group), and these are determined up to homotopy by the nontrivial homology group $G$ and the nontrivial dimension (see Hatcher Example 4.34). It follows that your space is homotopy equivalent to a wedge of spheres whenever its nontriv... | I will also assume that $S$ is connected, as is usually implied by simply connected, though your definition does not explicitly state this. Since $S$ is a finite simplicial complex, $H_d(S, \mathbb Z) \cong \bigoplus_{i=1}^k \mathbb Z$. By the Hurewicz theorem, the Hurewicz map $\pi_d(S) \to H_d(S)$ is an isomorphism, ... | https://math.stackexchange.com |
3,327,786 | [
"https://math.stackexchange.com/questions/3327786",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/693516/"
] | Compute the area of that part of plane <span class="math-container">$x+y+z=2a$</span> which lies in the first octant and is bounded by the cylinder <span class="math-container">$x^2+ y^2 =a^2$</span>
Now
<span class="math-container">$z = 2a -x -y$</span> ,
<span class="math-container">$\dfrac{\partial{z}}{\partial... | As <span class="math-container">$f' = -\frac 1k\left(f^2+c\right)$</span> we have
<span class="math-container">$$
-\frac{df}{f^2+c}=\frac{dx}{k}
$$</span>
then for <span class="math-container">$c > 0$</span>
<span class="math-container">$$
-\frac{\arctan(\frac{f}{\sqrt c})}{\sqrt c} = \frac xk + C_0
$$</span>
et... | <strong>Hint</strong>
The easiest (at least to me) is to rewrite
<span class="math-container">$$f^2+\frac k {x'}+c=0$$</span> which is separable and quite simple.
When you have <span class="math-container">$x(f)$</span> just inverse it.
| https://math.stackexchange.com |
13,204 | [
"https://mechanics.stackexchange.com/questions/13204",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/3279/"
] | A while back I stopped my 2000 Ford Ranger (V6 4WD) and all of a sudden there was white smoke pouring out from under the hood, indicating that something was leaking radiator fluid. When I opened the hood, I found that a part connected to 4 cooling hoses and one wire had broken:
<img src="https://i.stack.imgur.com/6RAX... | This is the heater valve. It's Motocraft part# YG350:
<img src="https://i.stack.imgur.com/dCiWV.jpg" alt="Pulled from Rockauto.com">
| This is your Heater Control Valve
But I am going to explain what it does.
First of all the "wire" you see is actually a vacuum line, it's a hollow (hopefully) air-tight tube that passes vacuum to the Heater Control Valve.
The heater control valve is a vacuum actuated valve that in the open position allows fluid to pas... | https://mechanics.stackexchange.com |
527,480 | [
"https://physics.stackexchange.com/questions/527480",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/98414/"
] | We all know heat transfer occurs via energy carriers (electrons, photons, bulk flow of molecules, phonons, etc.).
In many materials, phonons are the major contributors to heat transfer.
Classic texts describe phonons as plane waves of atomic displacements in crystals, which can travel at some group velocity <span cla... | The physics definition of work is <span class="math-container">$W=Fd$</span>, where <span class="math-container">$W$</span> is work, <span class="math-container">$F$</span> is force, and <span class="math-container">$d$</span> is displacement. Only the component of force that acts in the direction of the displacement ... | <blockquote>
Why do we need it to describe the physical world and how is it useful
to us?
</blockquote>
@David White has answered the first and third bulleted questions. This pertains to the second.
How useful is it? Consider that in 2015 (according to Wikipedia) 16.6% of the world's total electricity and 70% of ... | https://physics.stackexchange.com |
5,043 | [
"https://mechanics.stackexchange.com/questions/5043",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/2552/"
] | I'm trying to change the engine oil but running into difficulties removing the oil drain plug. One of the instructions I followed to change the engine oil was to give the car a short drive prior to the oil change; this would heat up the oil so that it would flow more readily into an oil drain pan.
Since I am having di... | I agree with Dan's comment - the right sized socket and a bigger bar.
I'd allow the car to cool, then using a 6-sided socket of the correct size on a 12" solid bar, crack off the seal on the plug. As with any stuck bolt, a short, sharp shock (e.g. kicking the end of the bar with your boot) is usually better than prol... | Are you using the right wrench? The proper wrench will not damage the plug regardless of the temperature, and if using the wrong wrench, you could be stripping the plug. If the plug is already stripped, you might want to let it cool so you can work on the problem and not burn yourself. The plug could have also been ove... | https://mechanics.stackexchange.com |
664,272 | [
"https://physics.stackexchange.com/questions/664272",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/297424/"
] | In books the derivation of pressure exerted by a gas on a closed container is derived for a cubical geometry, but since it contains number of molecules per volume (denote it by <span class="math-container">$n$</span>) the books say it's independent of geometry. My question is how they say it's independent of geometry b... | Here is a version of a derivation given by J H Jeans. It doesn't consider any specific shape of box, but concentrates on the molecules that are about to hit a small patch of wall.
Consider the molecules that will hit a small area, <span class="math-container">$A$</span>, of wall of a container of any shape in time <spa... | You said it yourself , it depends on the number of molecules per volume not the total number of molecules. And by saying so it means you are only considering about the density of gas contained in the closed objest whatever it may be. And also density of gas will not change by changing the shape of container.also the ma... | https://physics.stackexchange.com |
257,713 | [
"https://softwareengineering.stackexchange.com/questions/257713",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/150750/"
] | We've been working on a networked online game project which will run in near future and
looking for a satisfying solution for our distributed game database. We didn't take networking costs
into account so far.
We have following constraints:
1) We planned to use MySql but we can review alternatives if offered soluti... | I would avoid any ad-hoc, on-demand, database replication. Ideally you want a single consistent, logical user database across all of your nodes, for disaster purposes.
@Wardy's recommendation of a service bus is a good one.
I won't discuss different cluster architectures, but will address the issue of network bandwid... | Sounds like a typical use for a service bus based solution.
I solved exactly this problem but for keeping running servers live and interconnected and in sync with each other in my MMO server framework.
The simple answer is "don't try and sync the data once its in the database use an event and handle it in multiple lo... | https://softwareengineering.stackexchange.com |
678,755 | [
"https://physics.stackexchange.com/questions/678755",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/124750/"
] | For a spacecraft in orbit with radius <span class="math-container">$r$</span> with speed <span class="math-container">$v$</span> around a planet, centripetal force <span class="math-container">$F_C$</span> is provided by gravity:
<span class="math-container">$$\frac{GmM}{r^2}=\frac{mv^2}{r},$$</span>
which simplifies t... | The equation you have written there applies only for circular orbit but the orbit is not circular during the time the spacecraft is climbing to higher orbit. As the spacecraft climbs towards the higher orbit its initially increased velocity slows down as kinetic energy is transformed to potential energy.
| A simple way to calculate moving from one circular orbit to a larger one: Start by increasing the speed. The orbit becomes an ellipse. As Kirby points out, the speed decreases as the satellite moves out. At the far side of the ellipse, increase the speed again to put the satellite into a larger circle. (Calculate usi... | https://physics.stackexchange.com |
343,926 | [
"https://softwareengineering.stackexchange.com/questions/343926",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/265149/"
] | When writing block code in languages like C++ and Java, people usually argue over whether brackets at the end of a line should have their own line.
<pre><code>if (condition) {
if (condition)
{
</code></pre>
However, I have never seen anyone even suggest the second format below. Are the following equivalent, and if s... | <h2>It's all about the indents</h2>
It's not really about the brackets, it's about indenting and vertical alignment.
<strong>Not indented</strong>
You <em>can</em> put brackets on the same line when indentation is not in play.
Example in lambda expression:
<pre><code>list.ForEach( a => { a.Init(); a.DoSometh... | One reason I can think of is that putting the closing brackets on individual lines makes it easier to (un)comment the whole block using <code>//</code> without breaking the syntax.
| https://softwareengineering.stackexchange.com |
17,615 | [
"https://mathoverflow.net/questions/17615",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1464/"
] | As the title says.
In particular, I am interested in the story for a general reductive group $G$, say defined over $\mathbb{Q}$. I can imagine that mod-$\ell$ (algebraic) automorphic representation should correspond to conjugacy classes of homomorphisms from the motivic Galois group into $\widehat{G}(\overline{\mathb... | This is in my mind a central open problem.
Here is an explicit example which I believe is still wide open. Serre's conjecture (the Khare-Wintenberger theorem) says that if I have a continuous odd irreducible <span class="math-container">$2$</span>-dimensional mod <span class="math-container">$p$</span> representation o... | If $G$ is a connected, linear, reductive group over $\mathbb Q$, let $q_0$ be the dimension so denoted in Borel--Wallach, i.e. $q_0 = (d - l_0)/2,$ where $d = \text{dim } G_{\infty} -
\text{ dim } A_{\infty}K_{\infty}$ and $l_0 = \text{rank } G_{\infty} -
\text{ rank } A_{\infty}K_{\infty},$ where $G_{\infty} = G(\m... | https://mathoverflow.net |
321,475 | [
"https://math.stackexchange.com/questions/321475",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/30195/"
] | Sorry for the simplicity of the question, but about which conditions we will
have
$Z(G)K/K=Z(G/K)$ where $1\not=K\trianglelefteq G$ and $G$ is not abelian? I
know that is always worth $Z(G)K/K\leq Z(G/K)$
$K\leq Z(G)\,\ $is enough?
| Let
$$
H / K = Z(G / K),
$$
then $H = \{ a \in G : [a, G] \subseteq K \}$.
Here $[a, G] = \{ [a, g] : g \in g \}$, and $[a, g] = a^{-1} g^{-1} a g$.
So to guarantee that $H = Z(G) K$ you have to assume the condition that there is no element $a \in G \setminus Z(G) K$ such that $[a, G] \subseteq K$.
At the moment I ... | Let $G=S_3$, $K=Z_3 <G$. Then $Z(G)K/K=1\ne Z(G/K)=G/K$.
"$K≤Z(G)$ is enough?" - No.
| https://math.stackexchange.com |
543,620 | [
"https://stats.stackexchange.com/questions/543620",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/334050/"
] | What is the difference between saying X is a random variable following normal distribution and X is normally distributed. Is the random variable implicit or is X in the second case some other entity?
| Only a random variable can follow a distribution. If “X is normally distributed” it needs to be a random variable. Those terms mean the same thing.
| Without more context "X is normally distributed" could either mean X is a variable taken randomly from a normal distribution or it could be referenced as an array or matrix in which the values in it are normally distributed.
It really depends on the context as far as I can tell.
| https://stats.stackexchange.com |
7,998 | [
"https://mathoverflow.net/questions/7998",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1354/"
] | Is there a sort of structure theorem for pairwise independent random variables or a very general way to create them?
I'm wondering because I find it difficult to come up with a lot of examples of nontrivial pairwise independent random variables. (by 'nontrivial', i mean not mutually independent)
<h1>one example (thre... | I'm sure that Gil's answer is wise and that it is a good idea to look at Alon and Spencer's book. Here also is a quick summary of what is going on.
Suppose that <span class="math-container">$X_1,\ldots,X_n$</span> are random variables, and suppose for simplicity that they take finitely many values. Suppose that you ... | One very useful construction: if $X_1,\ldots,X_n$ are i.i.d. RVs, uniform in $\{0,\ldots,q-1\}$ ($q$ prime), then two linear combinations $\sum a_i X_i$ and $\sum b_i X_i$ are independent iff the vectors $a$ and $b$ are linearly independent (all operations are modulo q).
If we take $q=2$, this means that using $n$ i.i... | https://mathoverflow.net |
108,591 | [
"https://stats.stackexchange.com/questions/108591",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/31466/"
] | What is the importance of hat matrix, $H=X(X^{\prime}X )^{-1}X^{\prime}$, in regression analysis?
Is it only for easier calculation?
| In the study of linear regression, the basic starting point is the data generating process
$ \textbf{y= XB + u} \quad $
where $ \textbf{u} \sim N(0,\sigma^2 \boldsymbol I) $ and $\textbf{X}$ deterministic. After minimizing the least squares criterion, one finds an estimator $ \widehat {\textbf{B} }$ for $\textbf{... | The hat matrix is very useful for a few reasons:
<ol>
<li>Instead of having $\widehat{y}=Z\widehat{\beta}$, we get that $\widehat{y}=Py$ where $P$ is the hat matrix. This gives us that $\widehat{y}$ is a linear mapping of the observed values.</li>
<li>From the hat matrix $P$, it is easy to calculate the residuals $\wi... | https://stats.stackexchange.com |
27,853 | [
"https://mathoverflow.net/questions/27853",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4526/"
] | The finite dimensional irreducible unitary representations of $SU(2)$ are labelled by $j$ which needs to be half-integer, the dimension of the representation is $2j+1$. This is well-known, all is good.
If we do not require finite dimension for the representation, is it possible to make sense of representations with an... | I just wrote this answer on your last question. To summarize, you can't have an irreducible representation of a compact group that is infinite dimensional, unless the representation space is very exotic.
By the Peter-Weyl Theorem, all irreducible Hilbert space representations of a compact group (e.g. SU(2)) are finite... | You have to distinguish between representations of a compact group $SU(2)$ and of its Lie algebra $su(2)$, which can be complexified to $sl(2,\mathbb{C}).$ By Peter-Weyl theorem, every irreducible representation of the group $SU(2)$ is finite-dimensional. However, you can let Lie algebra $sl(2)$ act on various infinite... | https://mathoverflow.net |
194,108 | [
"https://security.stackexchange.com/questions/194108",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/166497/"
] | I noticed some websites do this and I am not sure if this is normal or not. So for example, on some websites, I go into setting and can create an API key that will be visible in plain text. Also, seems like a lot of HTTP requests have an API key visible in the URL. Something like this <code>"https://www.myWebsite/user?... | "Normal" may be the wrong choice of words for your question. The real question is... "Is it secure?"
Breaking the question into different parts, here's my take at an answer:
<strong>1. Is it secure for a site to provide me with an API key?</strong>
Providing you with your own API key isn't a problem, since it's <em>... | It is standard to make the api key visible to you. And the end of the day, you can always extract the key from your browser no mater how it is protected. As for you mentioning "plaintext", it is not really possible to meaningfully encrypt the key if that is what you mean. At the end of the day, you are unlikely to abus... | https://security.stackexchange.com |
37,756 | [
"https://stats.stackexchange.com/questions/37756",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/13550/"
] | I did correlation tests between a number of variables consisting of both interval and categorical scales ($n = 1274$, one sample). I used $\chi ^2$ test for categorical vs ordinal and Spearman's $\rho$ for interval vs ordinal data.
The correlation between climate zone (zone $1, 2, 3, 4$) and daily exposure to air-con... | Two small points:
1) As mentioned before - the two correlation measures are measuring different things, so a strict comparison of the two is risky.
2) If you also want to make a formal inference of the difference between the two, you will probably need to go with a permutation test, since (to my knowledge) there is n... | Up to a point. The closer you get to conditions of interval- or ratio-level variables with normal distributions, the greater the opportunity for correlations to reach high values if the underlying associations are linear and strong. With ordinal variables and distributions that are far from normal, correlations will ... | https://stats.stackexchange.com |
597,862 | [
"https://physics.stackexchange.com/questions/597862",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/260493/"
] | When a particle's position is measured, if one considers the wavefunction to collapse then one can assume it collapses into a delta function peaked at the measured position, and then after some finite time the wavefunciton 'evolves' outward away from this position.
Does a similar thing happen to spin?
From reading, it ... | Cliff notes: a spin up particle won't in general stay spin up, but in certain situations it will (for example, if it's free).
The standard way to describe a physical quantity (observable) whose value stays the same is to say that "it's conserved". Your question can be generalized as follows:
Which observables... | <blockquote>
One idea I had was that if we assume the wavefunctions only evolve due to the Hamiltonian in the TISE, if we assume a free particle Hamiltonian, this would indeed affect the spatial part of the wavefunciton but not the spin part.
</blockquote>
Exactly. The Hamiltonian of a free particle commutes with the a... | https://physics.stackexchange.com |
647,298 | [
"https://physics.stackexchange.com/questions/647298",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/304925/"
] | Consider a one-dimensional quantum-mechanical simple harmonic oscillator of mass <span class="math-container">$m$</span> and potential energy <span class="math-container">$\frac{kx^2}{2}$</span>. The energy levels of this system are <span class="math-container">$E_n=(n+\frac{1}{2})\hbar\omega $</span> for <span class="... | We know that <span class="math-container">$\hat{N}=\hat{a}^{\dagger}\hat{a}$</span> and
<span class="math-container">$$[\hat{a},\hat{a}^{\dagger}]=1 \implies \hat{a}\hat{a}^{\dagger}=\hat{a}^{\dagger}\hat{a}+1=\hat{N}+1$$</span>
You are confusing that <span class="math-container">$\hat{N}^{\dagger}=\hat{a}\hat{a}^{\dag... | You either didn't apply the operator to the bra correctly, or didn't take its adjoint correctly. Specifically, if we define
<span class="math-container">$B = a a^\dagger$</span>, then <span class="math-container">$B^\dagger = (a^\dagger)^\dagger a^\dagger = a a^\dagger$</span> (by the general rule that <span class="ma... | https://physics.stackexchange.com |
632,912 | [
"https://electronics.stackexchange.com/questions/632912",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/222856/"
] | I have a sensor that outputs a signal change between -4 to 4 V.
I want to use a bipolar ADC with a 3.3 V reference. I know that I should use a voltage divider, but what is the impact on resolution? I will use a 12-bit ADC (though even 8 bits will be enough).
Will an op-amp with 0.5 V/V gain do the job ? Or maybe a volt... | <blockquote>
<em>I know that I must be using some voltage divider but what is the
impact on resolution?</em>
</blockquote>
Well, if you don't use the voltage divider either your ADC will be destroyed or your signal range above 3.3 volts and below -3.3 volts is lost.
So, you need a voltage divider irrespective of how th... | It depends a bit on how the ADC is designed and specified.
If it's a 12-bit including polarity and it reads +/-3.3V then you can use a voltage divider to reduce the input by the ratio 3.3/4.0 = 0.825.
If it's a 3.3V single-supply ADC with differential inputs then you'd have to bias one input at 3.3V/2 (maybe with a cou... | https://electronics.stackexchange.com |
308,061 | [
"https://physics.stackexchange.com/questions/308061",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/143518/"
] | I have read in many books about induced current in a coil (Faraday's law), and also the motional emf across a moving conductor in a magnetic field. But somewhere I read about induced electric field due to a time varying magnetic field.
And I think that Induction of electric field is the fundamental phenomenon, and in... | You are right that a changing magnetic field creates (induces) an electric field, this is an actual law of nature.
Now if you put a conductor where the magnetic field is changing, you will get a current due to the produced electric field.
But in the case of the moving conductor moving through a magnetic field the reas... | Talking of "induced" fields is, again, yet more bad terminology and language that conveys a misleading notion - here, an impression of a kind of "causality" of one field upon the other - that is not part of our generally-used physical model.
What it means is this: In any case where that the magnetic field is changing ... | https://physics.stackexchange.com |
77,143 | [
"https://softwareengineering.stackexchange.com/questions/77143",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/25533/"
] | I've been thinking about this problem recently and it really doesn't seem like it's possible, but I figured that I'd ask just in case.
Assume a simple program, in pseudocode:
<pre><code>run hash on an executable we think is mimicing the true executable
check the value against the hash that's hard coded into this exec... | <blockquote>
what would be the most secure way to make sure that an executable is in fact the same executable that was distributed with a program and not some impostor executable trying to hijack the system?
</blockquote>
This has been solved.
You have to use a separate channel for the signature.
Any separate ch... | If the signature is bundled inside the executable, then nothing prohibits the adversary from modifying it to match the malicious executable. The only way to verify the executable is to compare with the hash fetched independently from a different source, or validate the signature using a verified public key.
| https://softwareengineering.stackexchange.com |
134,131 | [
"https://electronics.stackexchange.com/questions/134131",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/35113/"
] | I am new to the world of audio amplifiers however i am quickly trying to learn. I have built a simple circuit using a circuit based on what I read in the database. The circuit works however there is a lot of noise and the sound quality quickly decreases at higher volumes however that may just be the speaker I am usin... | Couple of suggestions, first, regarding the speaker. You didn't mention your speaker impedance, and with only a 6V supply, you'd certainly want to use an 8 ohm speaker as opposed to 16 ohms to get the most out of it. But that aside, you correctly point out that that the speaker may be the cause of at least some of your... | I adapted the "Amplifier with Bass Boost" from the data sheet by choosing different values for the resistor and the capacitor between "output" and the "gain1" pins. According to my simulation it doesn't really boost the bass. But, instead has an evenly distributed amplification from 0 Hz up to about 10 kHz where the am... | https://electronics.stackexchange.com |
70,848 | [
"https://quant.stackexchange.com/questions/70848",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/62109/"
] | Is it even possible without resorting to gradient descent methods? I can't see any way to algebraically reason around the cumulative normal functions involved in d1 and d2.
Any ideas?
| In most (all?) practical cases, Delta is a model-dependent measure; you need a model to compute it. Black-Scholes, Heston, ... each model has a formula for the (call) option price <span class="math-container">$C$</span> and its Delta <span class="math-container">$\Delta$</span> , and each model depends on a set of cont... | A number of models used in options pricing, but by no means all, are homogeneous of degree 1 in spot price and strike.
This means,
<span class="math-container">$$
C(\lambda S, \lambda K) = \lambda C(S,K)
$$</span>
If you differentiate the above wrt <span class="math-container">$\lambda$</span>, then
<span class="math-c... | https://quant.stackexchange.com |
127,876 | [
"https://softwareengineering.stackexchange.com/questions/127876",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/43388/"
] | Serious help needed here. I love programming. I've been reading bunch of books(such as K&R) and articles/forums online for C language lately. Even tried looking into Linux code(although, i was lost where to start but peeking into small libraries helped?).
I started as a Java programmer and in Java it's pretty cut... | I have 20+ years of embedded systems, mostly 8 and 16 micros. The short answer to your question is the same as any other software development - don't optimise till you know you need to, and then don't optimise till you know what you need to optimise. Write you code so it's reliable, readable and maintainable first. Pre... | Your question ("without wasting resources") is too general, so it's hard to give much advice. Taken literally, if you don't want to waste resources, maybe you should take a step back and evaluate whether you need doing anything at all, i.e., whether you can solve the problem in other ways.
Also, useful advice is very ... | https://softwareengineering.stackexchange.com |
31,437 | [
"https://mathoverflow.net/questions/31437",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7466/"
] | Let X ad Y be two vectors in R<sup>4</sup>, and define the inner product of X and Y as:
(X*Y) = g<sub>ik</sub>X<sub>i</sub>Y<sub>k</sub> (summation convention for repeated indicies)
Then we consider the 4x4 matrix g whose components are g<sub>ik</sub>. I am of course interested in the case that g is NOT positive de... | You don't need to diagonalize. You are looking at the group of those $A$ such that $A g A^T = g$. Putting $A=1+ \epsilon B$ for some small $\epsilon$, you want $(1+\epsilon B)g(1+\epsilon B^T) = g$ or $\epsilon(Bg+g B^T) = O(\epsilon^2)$. So the Lie algebra you want is $\{ B : Bg+gB^T=0 \}$. Since $g=g^T$, this can a... | (1) There is no difficulty in diagonalizing the quadratic form $g$, regardless of its signature. However, you must be careful: either $g = B^{-1} \eta B$, where $B$ is an orthogonal matrix and $\eta$ is an arbitrary diagonal matrix of signature (3,1), or $g = B^T \eta B$, where $B$ may not be orthogonal, but $\eta$ is... | https://mathoverflow.net |
102,714 | [
"https://mathoverflow.net/questions/102714",
"https://mathoverflow.net",
"https://mathoverflow.net/users/15289/"
] | To be specific, suppose $M$ is a closed oriented manifold, $g$ is a Riemannian metric of $M$.
Let $\Delta_g$ be the Laplace-Beltrami operator w.r.t. $g$.
<strong>Prove</strong>: Suppose $f\in C^\alpha(M)$ satisfies $\int_M f\, dVol_g=0$, then there exists a function $u\in C^{2,\alpha}(M)$ such that $\Delta_g u=f$ in... | Careful. C^\infty is not dense in C^{\alpha}. Nonetheless you can first produce an L^2 solution then use Schauder estimates to show that the solution is C^{2,\alpha}. This last step is localizable -- you can multiply by a smooth cutoff function (and use some preliminary
estimates to say that the solution is C^2, for ex... | Elliptic regularity in Hölder spaces is precisely what you need here.
If you want to prove it along the lines you described, using $L^2$-theory, then you can first establish that smooth $f$ leads to smooth solution $u$. Then you approximate $f$ in the $L^2$-norm by smooth functions with uniformly bounded $C^{\alpha}$-... | https://mathoverflow.net |
34,041 | [
"https://mathoverflow.net/questions/34041",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1483/"
] | Hi--
Where can I find a proof of this theorem: For each $r \in \mathbb{Z}_{+}$,
there exists a complex entire function $f(z)$ such that $f(r) \neq 0$ but
$f(r+1)=f(r+2)=\cdots =0$,
i.e. $f(z) \in I_{r+1}$ but $f(z) \neq I_{r}$, where
$I_{r}= \{ f \in R \ | f(r)=f(r+1)= \cdots =0\}$
where $R$ is the ring of complex ... | Why don't you start with a function with zeros at the integers,
for instance $\sin\pi z$, and then somehow eliminate the zero at $r$?
| Since your question title has Weierstrass, presumably you know about Weierstrass products. You should use them! They let you build an entire function having zeros at any discrete set. (The more refined Hadamard product construction can be used when the chosen zeros are spread out enough, which is the case for your si... | https://mathoverflow.net |
58,963 | [
"https://chemistry.stackexchange.com/questions/58963",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/34292/"
] | While I was reading about the chemical reactions of ozone, I came across this reaction.
$$\ce{PbS + 4O3 -> PbSO4 + 4O2}$$
Though the reaction seems well balanced, but when I attempted to balance it myself, I did this as $$\ce{PbS + 2O3 -> PbSO4 + O2}$$
I understand that there must be some reason that the 1st re... | This is a semi-standard example of why 'naive' balancing does not work.
Ozone is a source of atomic oxygen, producing free oxygen molecules. So, in 'mild' conditions only one oxygen per ozone molecule would react as a strong oxidizer, and the remaining molecular oxygen would require elevated temperatures to react. Thu... | Because remember ozone always gives nascent oxygen, that O single atom, which is a very strong oxidizing agent. Your mistake here is that you are involving all 3 oxygen atoms in the reaction which isn't the case.
| https://chemistry.stackexchange.com |
73,079 | [
"https://physics.stackexchange.com/questions/73079",
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"https://physics.stackexchange.com/users/27736/"
] | Suppose we create very large spherical body by using gamma rays generator and they will concentrate on a single point at the centre of sphere.We will place this spherical body thousands of kms above the sun so that it can draw energy from sun.Can the centre of the sphere create a Mini Black hole by the energy from the ... | Yes, taking any object and decreasing its volume, while keeping the mass constant, will result in creating a black hole - the question is how long is it going to "live", because there is such thing as evaporation due to Hawking's radiation. For example, turning Earth into a black hole requires squeezing it down into a... | What you propose is theoretically but not practically possible. Or rather, we can not really tell the difference. Shining a bunch of lasers at a common point is a good example of a rather complicated scattering experiment. You're creating huge numbers of photons which all have the same energy and bouncing them off e... | https://physics.stackexchange.com |
4,218 | [
"https://mechanics.stackexchange.com/questions/4218",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1574/"
] | I have a 2008 Mazda 3 car with a semi-automatic transmission (i.e. it is automatic with the ability to switch to a manual mode).
On the weekend, it was driven by somebody else who accidentally put it into manual mode without realising. They drove it for about 100 metres, probably not getting far above 40 km/h. It wo... | <blockquote>
I have heard that most modern cars have rev limiters which prevent
damage - is this just to prevent damage to the engine, transmission or
both?
</blockquote>
The rev limiter is there to protect the engine, often to prevent problems caused by the transmission (or the human operator's use thereof).
... | It's doubtful that any damage was done. The rev limiter should have prevented any damage from occurring to the engine and driving in a lower gear won't hurt the transmission.
| https://mechanics.stackexchange.com |
268,872 | [
"https://electronics.stackexchange.com/questions/268872",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/129685/"
] | I'm trying to decide whether to order components direct from manufacturers in China or from distributors in the US. If I have to test each component either way, I'm not sure it matters to me if it's a knock-off or the "certified" one, especially when prices are 100x more expensive from distributors.
It's very importan... | If you are talking about IC's, yes, manufacturers (not distributors) normally test 100% of the IC's as part of the production process. As far as I know, this applies regardless of country of manufacture. Distributors don't test anything. That is not their job.
Manufacturers may not test 100% of the features in a produ... | It is very unlikely that even a premium US distributor tests every component before shipping it. And if they did, you would be paying an extraordinary premium price for the privilege. OTOH, ordering anything from Asia is even a bigger gamble.
That said, are you creating products from components (even pre-TESTED compo... | https://electronics.stackexchange.com |
54,374 | [
"https://mechanics.stackexchange.com/questions/54374",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/21790/"
] | I have an old Honda n600 from the 70s, but no one makes a filter for it anymore. The word from the n600 forums is that if you want a new filter you have to use one meant for a Honda motorcycle that's about 5mm shorter than the original. The n600 basically has a motorcycle engine, so that's fine, but it being short has ... | Practically speaking, cleaning a filter is impractical. The filter absorbs particles, generally to about 10 microns, which become embedded into the media. Even if one could "wash" it, much of the particulates would remain embedded into the media. (The media actually filters finer as it loads up.)
In addition to a s... | If the filter fits, but is only 5mm shorter in length, you are better off using that than trying to clean the old filter.
Reason being, the filter is what catches all the contaminates. In 5mm you will not lose that much filter area.
| https://mechanics.stackexchange.com |
363,847 | [
"https://softwareengineering.stackexchange.com/questions/363847",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/293110/"
] | I have a website that allows users to be "tracked" and track their time/work. This involves the users being able to update their account with my site at most every minute, but typically users do it only a few times per day. However, there is nothing stopping other people from updating your account.
Each update creates... | Your scoping requirements (300K+ users, 100K+ bytes per user) suggest the use of a <strong>relational database</strong> such as MySQL, or a <strong>document data store</strong> like MongoDB, not a JSON array. JSON is primarily a data transfer mechanism, not a storage mechanism, and it lacks the necessary tools (indexe... | From my perspective, there might be a number of things here I would do differently. Firstly, when you have a system with a potentially large number of concurrent users, it's pretty important to make sure you aren't updated shared resources, because this makes the users' operations all convoy on a single lock.
Secondly... | https://softwareengineering.stackexchange.com |
227,686 | [
"https://softwareengineering.stackexchange.com/questions/227686",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/30814/"
] | has there ever been a proposal for establishing a formatting style file for programmers? In web programming, we have CSS files that help separate style from 'code', so two people can see the same code while each can see it in his/her preferred way.
I was thinking something like this could theoretically be achieved for... | Yes - but not the way you're thinking.
What has been done for decades now is 'beautifying' code. You supply your code to a program that has a set of configuration options, and it formats your code accordingly.
A VS plugin that reformatted your code when you checked it out would be interesting, but... the huge problem... | In some way, syntax highlighting, as it is done in most editors and IDEs, could be seen as a form of CSS for program text. It seems however that most programmer do not customise the syntax highlighting according to their needs (if it is possible).
| https://softwareengineering.stackexchange.com |
3,662 | [
"https://astronomy.stackexchange.com/questions/3662",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/1863/"
] | Per the Big Bang Theory, the universe was formed from a dense singular point which existed 13 billion years ago and has been expanding ever since. This suggests that the point should have existed somewhere in space implying an outer universe. If we call this point the "Universe", then what do we call the space that hel... | You are making the mistake of thinking that there was a single spot in space that everything expanded from. Rather, the expansion was not of things in space, it was space that expanded. It was an expansion OF space, not IN space. There wasn't "space" around the singularity.
| This has not been answered yet for sure I guess. For example string theory (M-Theory?) suggests that our Universe lies on a higher dimensional "membrane" that "colided" with another one and thus created the big bang.
This implies stuff like extra dimensions, strings, multiverses and other yet not proven theories.
Even... | https://astronomy.stackexchange.com |
266,681 | [
"https://electronics.stackexchange.com/questions/266681",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/82396/"
] | Suppose we have a small box with a circutry and a set of sensors in it. Box is lying on the table, but it is light enough to be lifted into the air.
What I want to achieve is to switch off the circutry in a box if anybody lifts the box, and switch it on back when box is returned to the table.
<ul>
<li>Is it possible ... | Accelerometers will tell you if it moves, gyroscopes will tell you if it's rotated. Both of those can tell you if it's picked up - but will probably give you a false positive if someone picks up or bangs the table.
Have you considered a simple contact microswitch on the bottom of the object?
| An optical reflection using 5mm IR emitter and detector are most sensitive in the small gap controlled by narrow beam width and angle.
This pulse "signal" reduces by 2x inverse squared with distance.
Sensitivity with daylight blocking PD is tuned by voltage gain of the Load R and logic level.
<ul>
<li>there are ... | https://electronics.stackexchange.com |
12,558 | [
"https://cogsci.stackexchange.com/questions/12558",
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"https://cogsci.stackexchange.com/users/6493/"
] | Suppose, hypothetically, that I wanted to do a blind taste test into preference for Coke or Pepsi. I organize hundreds of volunteers and find that a certain group prefers one and another group the other.
As I work for some marketing company, they ask me to account for this. After all, they reason, preference for Coke... | You use the words "experiment" and "correlate" somewhat loosely in your question, but there are various ways that we can address the general idea in a more rigourous way. Let's consider two possible situations:
(1) You randomly put people into two groups and found that group A likes pepsi much more often than group B.... | Researchers are trained to address this problem by using literature reviews to isolate the specific variables that should be of most interest. At the start of research you generally examine the knowns and unknowns in the particular area of interest, so as to determine the state of the art in that area. Once you know th... | https://cogsci.stackexchange.com |
87,657 | [
"https://electronics.stackexchange.com/questions/87657",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/29600/"
] | I am using a STM32 Cortex M3 microcontroller and have configured the ADC. I have verified that the ADC works by measuring different voltages on the micro controller eval. board.
When I connect my ADC to the output of the op amp (MCP6002) the signal gets distorted. A picture showing how the signal looks at the output b... | I am again amazed by myself. The same pin has been configured as a digital push-pull somewhere else in code, but no longer used by this module. This code has been present for over a year, but since it probably always have been initialized before the ADC, the ADC have been overwriting the pin configuration and everythin... | A few things to make sure of:
<ul>
<li>Make sure you have decoupling capacitors (e.g. 100nF) on all opamp power pins.</li>
<li>As a unity gain configuration is sensitive to capacitive load (the ADC input pin), try isolating it using a series resistor (between opamp output and ADC input), value say between 220Ω a... | https://electronics.stackexchange.com |
3,523,028 | [
"https://math.stackexchange.com/questions/3523028",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/156887/"
] | If <span class="math-container">$\mathcal{O}$</span> is the ring of integers of some number field and <span class="math-container">$I$</span> is some nonzero ideal in <span class="math-container">$\mathcal{O}$</span>, the ideal norm <span class="math-container">$N(I)$</span> can be defined via
<span class="math-contain... | The natural idea to find a counterexample is to take a non maximal order. Let <span class="math-container">$R=\mathbb{Z}[i\sqrt{3}]$</span>. Set <span class="math-container">$\alpha=i\sqrt{3}$</span>, so <span class="math-container">$\alpha^2=-3$</span>.
<strong>Fact 1.</strong> If <span class="math-container">$I\neq 0... | The simplest non-Dedekind domain example is <span class="math-container">$\Bbb{Z}[2i]$</span>, then <span class="math-container">$(2,2i)^2=(4,4i)$</span> and
<span class="math-container">$$|\Bbb{Z}[2i]/(2,2i)|=2,\qquad |\Bbb{Z}[2i]/(4,4i)|=8.$$</span>
| https://math.stackexchange.com |
231,109 | [
"https://math.stackexchange.com/questions/231109",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/46007/"
] | I have no idea with $\min_{\{a, b, c\}}\int^{\infty}_0|x^3-a-bx-cx^2|^2e^{-x}\,dx$, especially the $e^{-x}$ part.
| Let $V$ be the inner product space whose elements are polynomial functions on $[0,\infty)$, with inner product defined by $\langle f,g\rangle =\int_0^\infty f(x)\overline{g(x)} e^{-x}dx$. You are trying to find (the square of) the distance from $x^3$ to the subspace $P_2$ of polynomials of degree at most $2$. One w... | $$F(a,b,c) = \int_0^{\infty} \left(x^3 - a -bx - cx^2\right)^2 \exp(-x) dx$$
$$\dfrac{\partial F}{\partial a} = \int_0^{\infty} -2\left(x^3 - a -bx - cx^2\right) \exp(-x) dx = 0$$
$$\dfrac{\partial F}{\partial b} = \int_0^{\infty} -2x\left(x^3 - a -bx - cx^2\right) \exp(-x) dx = 0$$
$$\dfrac{\partial F}{\partial c} = \... | https://math.stackexchange.com |
425,836 | [
"https://physics.stackexchange.com/questions/425836",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/185612/"
] | What I mean by this question is, as we say that the electric field energy around a charge is the self energy of the charge, similarly can we say that the magnetic field energy around a current carrying wire is the Self Energy of the current? If yes, then following questions arise :
<ol>
<li>Why the current is associat... | It would be inappropriate to say that a current carrying wire would have Self Energy, in form of Magnetic Field Energy. Self Energy of charges are different from this concept.
In electrical circuits, for a very small duration of time, when current was growing in the circuit, the current was variable, due to which th... | Potential energy is a book-keeping device. Only <em>differences</em> in potential energy correspond to real energy. Since the electric and magnetic vector fields are defined by changes in potentials, any electromagnetic field with non-zero $\mathbf{E}$ or $\mathbf{B}$ has a (real) energy density, and this energy densit... | https://physics.stackexchange.com |
444,283 | [
"https://electronics.stackexchange.com/questions/444283",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/197393/"
] | I was wondering why almost all USB cables that exist are USB-A to (Micro-USB | USB-C | USB-B | etc.)
Why was USB-A to USB-A not a popular thing? Is there a technical reason this cannot work?
| USB-A male to USB-A female is fine. They exist, and are relatively common. They work just fine as USB extension cables, provided the overall length is not too long. For longer distances, active cables exist that contain an internal repeater or USB hub to regenerate the signal. However, you may run in to power deliv... | Because it's against the standard. The USB standard says that type A is for hosts, and type B is for devices.
In practical terms, a device with a type A connector is expected to provide power, so if you connect two of them together, they will attempt to power each other, leading most likely to Bad Things Happening. Ty... | https://electronics.stackexchange.com |
531,922 | [
"https://physics.stackexchange.com/questions/531922",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | I'm taking my first course in thermodynamics, so my apologies if this is a rather silly question.
I'm a bit confused about the pressure term in the formulation of the first law. The first law states that: <span class="math-container">$$ dU_{system} = \delta Q - p_{int}dV $$</span>
I "understand" this formulation if ... | <span class="math-container">$dU$</span> usually refers exclusively to the change in internal energy of the system, though you do bring up a common point about internal and external pressures. I will use the convention that positive work <span class="math-container">$W$</span> means work done on the gas by the surround... | The work done by the gas on its surroundings is determined by the force that the gas exerts on the piston integrated over the piston displacement. If the deformation is quasi static (slow), then this force is equal to the pressure calculated from the ideal gas law times the area of the piston. But, if the gas deforma... | https://physics.stackexchange.com |
125,631 | [
"https://math.stackexchange.com/questions/125631",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/8390/"
] | This is Exercise 2.20 in Atiyah-Macdonald.
<blockquote>
How can we prove that $\varinjlim (M_i \otimes N) \cong (\varinjlim M_i) \otimes N$ ?
</blockquote>
Atiyah-Macdonald give a suggestion, they say that one should obtain a map $g \colon (\varinjlim M_i )\times N \longrightarrow \varinjlim (M_i \otimes N)$, but... | One way is to use the adjunction property of the tensor product. For any $R$-module $P$, we have the following sequence of canonical $R$-module isomorphisms:
$$\begin{eqnarray}\hom(\varinjlim(M_i \otimes N), P) \cong&& \varprojlim \hom(M_i \otimes N, P) \\ \cong && \varprojlim \hom(N, \hom(M_i, P)) \\ ... | Here's an idea for a proof that doesn't involve Yoneda:
To show $(\varinjlim M_n) \otimes N \cong \varinjlim(M_n \otimes N)$ it is enough to verify that $(\varinjlim M_n) \otimes N $ satisfies the universal property of $\varinjlim(M_n \otimes N)$. This means that if $(M_n, f_{nm})$ is the direct system with limit $(\v... | https://math.stackexchange.com |
431,146 | [
"https://softwareengineering.stackexchange.com/questions/431146",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/400519/"
] | Assume we are building a Progressive Web App(as everyone does these days) that communicates with the server through a rest API. Now I need to show a list of world countries to the user to choose from.
I have a table with valid world countries in the backend that I use to validate requests, but the problem is, it seems ... | The decision between offline/online storage is a balance between volatility (data change rate) and efficiency (bandwidth/performance from network call).
As you're dealing with low volatility, there's little issue with storing these details offline. This mean that when the data does change, you either:
<ul>
<li>Deploy a... | On the client, store the list of countries and a version number. Then have a request to the server “give me the list of countries, but I have version X”. The request returns the last version number on the server, but only returns the country list if the caller passed a different version number than the current one. Gua... | https://softwareengineering.stackexchange.com |
232,183 | [
"https://softwareengineering.stackexchange.com/questions/232183",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/78439/"
] | Let's take a server-side WebServices app, we need to make sure that all function applies every security rules, and keep the code clean.
In such a case, I usually prefer to place my security checks on the upper layers. As soon as the user call a function, I check if he has the rights to access it or not. But this strat... | Treating security as a separate concern, and handling it in a layer above application logic is a good practice.
One project I was on was a great example. It involved a family of web services. The evolution of our authorization check went like this (it's a bit Java-centric, but hopefully the idea is clear):
<ul>
<li>F... | There are two facets to this problem and both should be satisfied for a good application to work:
<ol>
<li><strong>Fail Fast</strong> - having the user fill all the data, press the action button, wait 5 seconds, only to fail since some text at the beginning of the form should be at least 3 characters, or a dash has be... | https://softwareengineering.stackexchange.com |
87,468 | [
"https://softwareengineering.stackexchange.com/questions/87468",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/23632/"
] | It may be a personal quirk of mine, but I like keeping code in living projects up to date - including the libraries/frameworks that they use. Part of it is that I believe a web app is more secure if it is fully patched and up to date. Part of it is just a touch of obsessive compulsiveness on my part.
Over the past s... | The issue isn't unique to open source. The same issues occur with commercial projects. Maybe even more so because you don't have source you can maintain yourself if the company drops support.
End user type open source projects have rapid upgrade cycles and old versions lose support very quickly. On the other hand, ... | I don't always do it. A lot of open source projects have active maintenance branches maintained for previous major releases. Sometimes those are maintained by people who need that version to be maintained. A lot of projects stay on a major release until they themselves are ready for a major release.
| https://softwareengineering.stackexchange.com |
446,888 | [
"https://math.stackexchange.com/questions/446888",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/54609/"
] | I need to construct a 3-regular connected planar graph with a planar embedding where each face has degree 4 and 6. In addition, each vertex must be incident with exactly one face of degree 4.
<img src="https://i.stack.imgur.com/VPIRb.gif" alt="enter image description here">
seems to fit the description well if extend... | <img src="https://i.stack.imgur.com/M0AJq.png" alt="Graph drawing">
The colours show the order in which I constructed the graph. Every vertex must be part of one face of order 4, so I start with a square (black, centre).
Now, each vertex is of order 3, and the four vertices have order 2, so extend one edge out from e... | Let $f_4, f_6$ be the number of quadrangles and hexagons.
Then we get the restrictions (count vertex-edge incidences, count face-edge incidences, Eulre's polyhedra formula, vertex-quadrangle incidences)
$$\tag13v=2e$$
$$\tag24f_4+6f_6=2e$$
$$\tag3v+f_4+f_6=e+2$$
$$\tag4 v=4f_4$$
By combining these ($6\cdot(3)-2\cdot(1)... | https://math.stackexchange.com |
97,802 | [
"https://physics.stackexchange.com/questions/97802",
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"https://physics.stackexchange.com/users/39943/"
] | i tried to find it in books but i was unable to do so and i am not able to understand this and I couldn't think of a better example. i repeat. its just an example. if i punch someone's face with my arm having constant velocity, it will mean that the acceleration of my arm is zero. F=ma, therefore force exerted by my ar... | For simplicity's sake, let's start with punching a concrete wall. Let's assume you are not strong enough to actually damage the wall. So (again for simplicities sake) if your fist is traveling at 1 m/s, when it hits the wall it will be moving zero, so it DECELERATES as part of the process of colliding with the wall, an... | This is an example in which one needs to be careful to make the distinction between net force, which may vanish, and one of the individual, nonzero interaction forces that contributed to the net force
The fact that your knuckles are not accelerating does <em>not</em> mean that the contact force with the person's face ... | https://physics.stackexchange.com |
113,650 | [
"https://stats.stackexchange.com/questions/113650",
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] | Let's say you have $X$ coins, each with a differing probability of landing heads (e.g. coin 1 has 10% chance of landing heads, coin 2 has 20% chance of landing heads, etc.).
Now, let's say that you flip coin $i$ coin $Y_i$ times (each coin has a differing amount of flips). We know how many times each coin was flipped.... | Sorry for the delay, I was going to code this up as an example, but basically my method was going to agree with @Aniko's comment about using a linear regression.
So basically you can run a multiple linear regression where the outcome variable is number of heads and the predictors (or covariates) to the model is the nu... | Starting with the case of two coins, we know that $$E\{T_k \}=m_k\theta_A+n_k\theta_B.$$
If $k=2$, we can solve
$$t_1 = m_1\hat{\theta}_A +n_1\hat{\theta}_B$$
$$t_2 = m_2\hat{\theta}_A +n_2\hat{\theta}_B,$$
which is uniquely solvable if and only if $m_1n_2-m_2n_1 \neq 0$.
This yields Method of Moments (MoM) estimators... | https://stats.stackexchange.com |
41,313 | [
"https://security.stackexchange.com/questions/41313",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/30040/"
] | What does capture filter means in wireshark? Is it same as display filter?
| There are two type of filter in wireshark:
<ol>
<li>Display Filter</li>
<li>Capture Filter</li>
</ol>
Display filter is filter introduced by wireshark. It's user friendly, powerful and many things to filter. It has modular form. For example,filter to display HTTP Post is:
<pre><code>http.request.method=POST
</code><... | Capture filters work when the capture is taking place. It tells Wireshark <em>which</em> packets to capture and save to a pcap file.
Display filters works on already captured network traffic. It's simply a filter to that tells Wireshark which packets to <em>display</em>.
| https://security.stackexchange.com |
158,316 | [
"https://dba.stackexchange.com/questions/158316",
"https://dba.stackexchange.com",
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] | Consider a seat booking database. There is a list of n seats, and each one has an attribute <code>is_booked</code>. 0 means it isn't, 1 means it is. Any higher number and there is an overbooking.
What is the strategy for having multiple transactions (where each transaction will book a group of y seats concurrently) wi... | Because you're not telling us much of what you need, I'll guess for everything, and we'll make it moderately complex to simplify some of the possible questions.
First thing about MVCC is that in a highly concurrent system you want to avoid table locking. As a general rule, you can't tell what does not exist without lo... | I think this can be accomplished by the use of a little fancy <em>double table</em> and some constraints.
Let's start by some (not fully normalized) structure:
<pre><code>/* Everything goes to one schema... */
CREATE SCHEMA bookings ;
SET search_path = bookings ;
/* A table for theatre sessions (or events, or ...) *... | https://dba.stackexchange.com |
364,208 | [
"https://physics.stackexchange.com/questions/364208",
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] | Let's say I have eigenstates $|x\rangle$ associated with measurement of position. I know that the eigenstates corresponding to their respective eigenvalues form a basis, let's call it $A$. Now let's say I want to expand a generic state vector $|ϕ\rangle$ in that basis formed by eigenstates. Now, what does it mean when ... | If you think of kets $\vert\psi\rangle$ as vectors, i.e. elements of a vector space in the sense that you can take linear combination of them, and you think of these vector as column vectors, then you can think of $\langle\psi\vert$ as a row vector so that $\langle\phi\vert\psi\rangle$ is a scalar product since it give... | I think that what you are asking is not completely a mathematical problem but a physical trick...
Since I think that you got stuck around eq. (19) of the document you uploaded, I'll try to explain what's going on there.
<strong>The aim is to expand our state <span class="math-container">$|\psi \rangle$</span> in terms ... | https://physics.stackexchange.com |
12,861 | [
"https://mathoverflow.net/questions/12861",
"https://mathoverflow.net",
"https://mathoverflow.net/users/493/"
] | Let G be a finite group and let F be an algebraically closed field. If the characteristic of F is 0, then the number of irreducible F-representations of G is given by the number of conjugacy classes of elements of G. A paper I'm reading says that if the characteristic of F is p>0, then the number of F-irreps of G is ... | Yes, you are correct. The point is that a $p$-group acting in char. $p$ always has
a fixed point (and so acts trivially on an irrep.). So <I>every</I> irrep. of $G$
in char. $p$ factors through $G'$, as you anticipated.
The proof of the claim about $p$-groups is not hard. One approach (in general,
even when $P$ is n... | The fact that the number of isomorphism types of irreducible $FG$ modules is the number
of conjugacy classes of elements of $G$ of order prime to $p$ (or number of $p$-regular conjugacy classes) when $F$ is an algebraically closed field of characteristic $p$ is a theorem of Richard Brauer. Proofs can be found in almost... | https://mathoverflow.net |
55,526 | [
"https://mathoverflow.net/questions/55526",
"https://mathoverflow.net",
"https://mathoverflow.net/users/12992/"
] | I know the definition of $K_X$ on a normal, singular variety, but I don't have a good set of examples in my mind. What's an example of a variety where $K_X$ is $\mathbb Q$-Cartier but not Cartier? Are there any conditions under which an adjunction formula lets me compute the canonical class of a singular divisor?
| <strong>Note:</strong> I added an addendum below in response to <em>quinque</em>'s comment and the subsequent discussion of the issue (s)he raised on math.stackexchange (see the link in <em>quinque</em>'s comment).
<hr>
An easy way to produce a $\mathbb Q$-Cartier but not Cartier canonical divisor is by a quotient. F... | Probably the easiest example is $X = \operatorname{Spec} k[x^3, x^2y, xy^2, y^3]$. In this case, $K_X$ is not Cartier, but $3K_X$ is Cartier.
In what way do you have in mind computing the canonical class of a singular divisor? The adjunction formula basically always works assuming things are sufficiently normal.
I... | https://mathoverflow.net |
210,159 | [
"https://electronics.stackexchange.com/questions/210159",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/96473/"
] | i want to calculate the uptime of LPC 1768 from when it begins running. for example a function like millis(); in arduino.
| I suggest that you setup a hardware timer that increments a counter every milisecond. By reading this value you will know your uptime.
| I use the following code which uses the RIT peripheral (Repetitive Interrupt Timer). This is a very simple timer peripheral. This will let you use the full featured timers and the ARM system tick timer for other uses:
<pre><code>volatile uint32_t rit_high = 0;
static void rit_irq_handler()
///////////////////////////... | https://electronics.stackexchange.com |
164,420 | [
"https://softwareengineering.stackexchange.com/questions/164420",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/63991/"
] | My boss wants to recruit testers based on their testing efficiency (number of bugs identified). So, he's shortlisted 5 people and I need to give them an app full of bugs and see how they fare in reporting obvious bugs, and hidden bugs. I know.... it kind of sounds weird. I guess, this is just like the coding world, whe... | I actually did this. I created a buggy calculator. It's just HTML and JavaScript. I created it originally to help my father (a QA professional) practice testing. And because it was fun. I then used it when interviewing.
I don't just look for # bugs found though. I look for:
<ul>
<li>What bugs are found</li>
<li... | If you want to do this, create your own buggy app. When I was hired into my current position, I was given an app to test and find bugs that was based on actual software the company worked on. Some of the bugs were pretty obvious, some were more subtle, but mostly here were plenty of bugs or arguably buggy behaviour. My... | https://softwareengineering.stackexchange.com |
510,149 | [
"https://math.stackexchange.com/questions/510149",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/40209/"
] | Why does the sequence $\frac 1n$, where $n$ is a natural number , does not converge when R is endowed with the discrete metric ?
| Sequence $1/n$ converges to $0$ iff for every $\varepsilon>0$ there is $n\in\mathbb{N}$ so that for every $k > n$ $$d(\frac1k,0) < \varepsilon.$$ Since $d$ is the discrete metric and $\frac1k > 0$, $d(\frac1k,0) = 1$. So if you take for example $\varepsilon=\frac12$ there is no $n$ as required above.
| The sequence fails to be Cauchy because the distance between any two terms in the sequence is $1$.
| https://math.stackexchange.com |
1,987,689 | [
"https://math.stackexchange.com/questions/1987689",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/299168/"
] | <blockquote>
Let $k$ be an integer. Show that
$$\gcd(3k+2,5k+3)=1$$
</blockquote>
I know that I can use the Euclidean algorithm, but the $k$ is bugging me. Should I use induction or something?
| You can do it just like normal.
$$ 5k+3 = 1(3k+2) + (2k+1)$$
$$ 3k+2 = 1(2k+1) + (k+1)$$
$$ 2k+1 = 1(k+1) + (k)$$
$$ k+1 = 1(k) + (1)$$
Since we see $1$, we're done.
| Suppose, there is a $d \in \Bbb N$ such that $d|(3k+2)$ and $d|(5k+3)$
$\therefore d|\{5(3k+2)\}$ and $d|\{3(5k+3)\}$
$\implies d|(15k+10)$ and $d|(15k+9)$
$\implies d|\{(15k+10)-(15k+9)\}\implies d|1$.
Now, do you get it?
| https://math.stackexchange.com |
168,718 | [
"https://physics.stackexchange.com/questions/168718",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/8916/"
] | If I may summarize something I told a friend in a pub...
"We don't get heat from the sun at all. Heat requires matter to move through and there's too much vacuum between the sun and us for any heat to get here. What we get from the sun is light - photons - and some of those photons become heat when they fall on the Ea... | In a physics lab there is a (more or less) unambiguous definition of the word <em>heat</em>. In a pub there is not. In general usage, the word can mean different things. For example, it might mean "thermal energy". It might mean "thermal energy transfered by conduction". It might mean "infrared radiation".
From... | they are 3 ways to exchange heat : conduction, convection, and radiation.
When we touch an object, the heat is transferred from the hot body to the cold body thanks to electrons collisions within the mediums. The speed at which this heat is transferred depends on the thermal conductivity.
The convection is a similar ... | https://physics.stackexchange.com |
442,423 | [
"https://physics.stackexchange.com/questions/442423",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/210069/"
] | I am currently working with Harvey Reall's notes on Black holes, and I have 2 questions concerning the interpretation of the Einstein-Rosen bridge.
After some algebra, we are faced with the metric:
<span class="math-container">$$ds^2 = \left(1+\frac{M}{2 \rho}\right)^4 (d\rho^2 + \rho^2d\Omega^2)$$</span>
with <span cl... | First I would like to stress that you cannot infer the topology of a manifold from its metric. Reasons:
Topology is a global property, metric is a local property
You can squeeze and stretch a manifold without changing the topology, but these actions will definitely change its metric, so metric and topology are largel... | That is indeed why it is called Riemannian (Riemannian just means the signature is all plus).
The topology of <span class="math-container">$\mathbb{R}^3$</span> with a truncation of the radius is <span class="math-container">$\mathbb{R} \times S^2$</span>. In general, spherical coordinates only cover a manifold of th... | https://physics.stackexchange.com |
1,154 | [
"https://electronics.stackexchange.com/questions/1154",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3/"
] | A customer has asked:
<blockquote>
I want to slow down a small hobby
sized DC motor to a user variable
range that runs from slow to zero
RPM. I would simply use a wall wart
for a power supply and a potentiometer
to set the speed but the load on the
motor might change slightly. Although
the drag on the ... | DC motors don't work well at low RPMs. They stall and have horrible torque. (i.e. they can't turn very hard) So people have created gear motors: motors with integrated gearing. The result looks like a slightly bulkier motor, but one that has low RPMs and high torque. If you were to take apart a running a gear motor... | Generally speaking, a potentiometer will <em>not</em> be a good choice for controlling the speed of a DC motor, unless it's a very small one (think a few 100 mA draw) as the pot must be rated for the current drawn by the motor. Additionally, as you restrict current, you're also sapping power from the motor. So, at slo... | https://electronics.stackexchange.com |
197,590 | [
"https://softwareengineering.stackexchange.com/questions/197590",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/63589/"
] | So I'm finishing up refactoring some code to remove a number of previously-mutable objects and add a better generic processing for all the classes in the domain. Just as I thought I was finishing I eralized that there is one sub-class that has some additional state.
The additional state is a link to other classes tha... | There's nothing inherently wrong with mutable subclasses provided you don't make assumptions about mutability in other parts of your code.
As an example, the Foundation framework that's part of Cocoa and Cocoa Touch frameworks (MacOS X and iOS respectively) has a number of immutable data containers that have mutable ... | It is legitimate, and sometimes useful, to have a subtype of a mutable type which includes additional <em>immutable</em> information not present in the base. It is also legitimate to have a subtype add mutable members to a type whose base members are immutable, provided that the base type makes no promises about the i... | https://softwareengineering.stackexchange.com |
84,586 | [
"https://softwareengineering.stackexchange.com/questions/84586",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/27998/"
] | What do you do to stay focused when learning a new language with so many other interesting languages out there?
| <strong>Build something.</strong>
Decide what you want to build and what language you want to learn and do it. You'll learn more about the language by using it. And you get the joy of writing code, and seeing a finished product when you're done....which is what will keep you coming back for more.
For me, it's not wh... | I generally focus on projects rather than languages. That is, when I'm learning a language I really focus on a concrete project I can implement in that language.
Of course it's pretty common for people to abandon projects without finishing, but still I think you will be more motivated by a project to focus on than the... | https://softwareengineering.stackexchange.com |
466,365 | [
"https://electronics.stackexchange.com/questions/466365",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/232634/"
] | I'm learning about the RGMII interface of ethernet. Can anybody please tell me What IO standard does the TX and RX line of RGMII interface support? Please help. I'm just a beginner
| The two RGMII reference designs I have are both 2.5V LVCMOS. You should check the datasheet of the PHY chip you're using to confirm.
| Depends on RGMII version, but either 2.5V CMOS or 1.5V HSTL
| https://electronics.stackexchange.com |
4,542,502 | [
"https://math.stackexchange.com/questions/4542502",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1100163/"
] | <blockquote>
At a restaurant, customers can choose up to four side dishes and up to two main courses. If a customer must have at least 1 side dish and 1 main course, how many distinct dinner plate combinations are possible?
</blockquote>
The answer is 45. I can only calculate 12.
Call the four side dishes A,B,C,D.
Call... | Possible combinations of side dishes: <span class="math-container">${4 \choose 1}+{4 \choose 2}+{4 \choose 3}+{4 \choose 4}=4+6+4+1=15$</span>.
Possible combinations of main courses: <span class="math-container">${2 \choose 1}+{2 \choose 2}=2+1=3$</span>.
Thus the total number is <span class="math-container">$15\times3... | If any number of side dishes are allowed, then you may note that there are in total <span class="math-container">$2^4 - 1 = 15$</span> combinations of side dishes and <span class="math-container">$2^2 - 1 = 3$</span> combinations of main dishes, so a total of <span class="math-container">$15 \cdot 3 = 45$</span> total ... | https://math.stackexchange.com |
609,723 | [
"https://physics.stackexchange.com/questions/609723",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/113889/"
] | I have quite a basic question in hydrostatics that's bugging me and would be happy to get some help.
Suppose I have a tube inside a water tank (the tube's opening is inside the water) and say the water inside of the tube raises to some height <span class="math-container">$h$</span> above the water surface inside the ta... | The correct (and more meaningful) term is <em>relative density</em>.
It measures the ratio of two densities, where one is a reference one (usually water). So the specific gravity (SG) of a substance <span class="math-container">$x$</span> with respect to water is
<span class="math-container">$$SG=\rho_x / \rho_{water}$... | Relative density is a better name that is in common use.
"Specific" usually means per unit mass in thermodynamics nomenclature; for example specific volume or specific internal energy. However, for "specific gravity" I think "specific" means per unit volume. "Weight" typically ... | https://physics.stackexchange.com |
13,766 | [
"https://dba.stackexchange.com/questions/13766",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/2445/"
] | Background: a user had her name changed in Active Directory from Domain\oldname to Domain\newname and successfully logged into the network with Domain\newname and yet Domain\oldname appears in columns LoginName and NTUserName in Profiler.
User's SQL Server permissions are granted via a group set up in SQL Server sec... | I guess I can't comment on your question since this is the first time I've used stack exchange but is this an AD group that the user is in? Sometimes people say group when they mean SQL role so I just wanted to get some clarification.
The reason I ask is because if the user has a login on the server of domain\oldus... | I ran into the same problem in a SQL Server 2012 instance (SP2 applied). I haven't found the root cause yet, but we will be looking at the AD caching mechanism, as suggested by StanleyJohns.
By accident I have found a simple solution that worked for me without rebooting the server. I created a Windows Authenticated lo... | https://dba.stackexchange.com |
14,266 | [
"https://dba.stackexchange.com/questions/14266",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1514/"
] | I have a calendar date dimension backed by a physical table of dates (originally created on SQL Server 2000, hence the datetime instead of date):
<pre><code>CREATE TABLE [dbo].[PostDate_Dimension](
[post_date] [datetime] NOT NULL PRIMARY KEY,
[day_of_year] [int] NOT NULL,
[day_of_month] [int] NOT NULL,
... | Based on your edit, all writes lock exclusively.
No other process can read the row(s) being written unless
<ul>
<li>you've been silly and are using NOLOCK</li>
<li>you have snapshot isolation where the last committed row is read</li>
</ul>
There is usually no need to add lock hints in day to day code.<br>
As to why... | The <code>ROWLOCK</code> isn't locking the table, but your <code>TRANSACTION</code> is.
You should be able to do the update from within the same transaction. If you are trying to do the <code>UPDATE</code> from another session it won't work.
| https://dba.stackexchange.com |
319,036 | [
"https://softwareengineering.stackexchange.com/questions/319036",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/229154/"
] | I'm reading Yung-Hsiang Lu's book, Intermediate C Programming, and I'm working through the chapter on stack memory. When defining the value address he provides this code example:
<pre><code>int f1(int k, int m)
{
return (k + m);
}
void f2(void)
{
int u;
u = f1(7, 2);
// RL A
}
</code></pre>
He goe... | The author sounds as if he doesn't understand what he is talking about - though the problem may be in translation rather than in the author's thinking. Or perhaps he is over-simplifying for the purposes of exposition, confusing people who (like you) actually think about what they are reading.
Any description of what h... | ..., except that a modern C compiler would turn your <code>f2()</code> into this:
<pre><code>void f2(void)
{
int u = 9;
// RL A
}
</code></pre>
And if <code>f1()</code> was declared static, the compiler would not even emit it to the output file.
All of that is assuming that your comment, <code>// RL A</code... | https://softwareengineering.stackexchange.com |
104,404 | [
"https://stats.stackexchange.com/questions/104404",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/20148/"
] | I have been thinking about how to use regression to prove whether X factor is a necessary or a sufficient condition for Y. I am employing these terms in the traditionally logical sense, i.e.
<ul>
<li>If no X, then no Y --> X is necessary for Y</li>
<li>If X, then Y --> X is sufficient for Y</li>
</ul>
The reason I'm ... | Qualitative Response models, logistic regression being the most widely known, could in principle provide you with a way to arrive at a conclusion on these matters, in a regression framework.
The usual logistic regression model is specified as
$$P(Y=1\mid X=1) = \frac 1{1+\exp\{-\alpha-\beta X\}}$$
where both $Y$ a... | Articial Neural Networks developed in the machine learning community can learn highly complex boolean functions (and necessary/sufficient statements are very simple boolean functions). See for example chapter 11 of Hastie, Trevor, et al. The elements of statistical learning. New York: Springer, 2009.
| https://stats.stackexchange.com |
349,514 | [
"https://softwareengineering.stackexchange.com/questions/349514",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/222705/"
] | I was working in a story and in last minute, I have been asked to hide something from UI and we will used it next release.
<ul>
<li>Should i remove it or comment it </li>
<li>Should i remove or comment anything related to this part from code or leave it if it won't effect in anything.</li>
</ul>
| If you value clean work practices, I would suggest that instead of commenting out code (which is an OK enough practice in the very short term, i.e. when we're talking a few weeks or less), prefer to use a source control system (Git, Mercurial, Subversion, etc.) instead:
Move the feature's code, and all that's specific... | Alternatively, if your code is self-contained and this measure is temporary, you may get away by wrapping the code inside an <code>if</code> statement and set a boolean flag to disable the code block. Whether this is good practice though...
| https://softwareengineering.stackexchange.com |
92,916 | [
"https://mathoverflow.net/questions/92916",
"https://mathoverflow.net",
"https://mathoverflow.net/users/49/"
] | Let $(C,W)$ be a category equipped with a subcategory of weak equivalences. Its "classification diagram" or "bisimplicial nerve" $N(C,W)$ is a bisimplicial set, for which $N(C,W)_n$ is the nerve of the category of functors $[n]\to C$ and natural weak equivalences between them. If we fibrantly replace $N(C,W)$ in the ... | It seems to me that the answer is yes. Here is a sketchy argument.
Let us fix some notations. I will write $i(X)$ for the maximal Kan subcomplex of a quasi-category $X$ and $Hom(A,B)$ for the internal Hom of simplicial sets $A$ and $B$. If $B$ is a quasi-category, then so is $Hom(A,B)$ for any simplicial set $A$, and ... | Yes, this follows easily by combining the results of Barwick-Kan and Toen. One way to rephrase your question is the following:
<blockquote>
Given a relative category $(C,W)$ (i.e. just a category with a subcategory weak equivalences containing the identities) is the <em>classification diagram</em> $N(C,W)$ weakly eq... | https://mathoverflow.net |
623,051 | [
"https://physics.stackexchange.com/questions/623051",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/181235/"
] | In all of the images I've seen from a spectrometer, there's always a collimating element that places an image at infinity so as to have parallel rays hitting a diffraction grating. But why do we need that? I understand that the theory behind gratings is based on a plane wave hitting the grating, but if that were not th... | If the beam wasn't collimated then light with different wavelengths but from different parts of the source, arriving at different incidence angles, would be diffracted in the <em>same</em> direction.
This would spoil your wavelength discrimination, contradicting the whole purpose of a diffraction grating.
| I completely disagree with the answer by @ProfRob. If a beam is focused beyong the grating, it forms the focused image of a spectrum at the distance of the undiffracted focused beam. As long as the incoming beam has high spatial coherence, the wavelengths are well separated at that spectrum image. Of course aberrati... | https://physics.stackexchange.com |
34,724 | [
"https://stats.stackexchange.com/questions/34724",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/13455/"
] | I have a set of data that has $n$ samples described by $m$ variables. I do a PCA to reduce it to just 2 dimensions so I can make a nice 2D plot of the data. I understand that the $x,y$ coordinates (i.e., the PCA scores) for the plot are calculated by basically summing the products of the original data (after centering)... | Yes. Basically, what you did was to do:
$$\mathrm{PC}=\mathbf{V}X,$$
where $\mathrm{PC}$ are the principal components, $X$ is your matrix with the data (centered, and with data points in columns) and $\mathbf{V}$ is the matrix with the loadings (the matrix with the eigenvectors of the sample covariance matrix of $X$). ... | I have a doubt about the above answers. Since after dimension reduction, we only know 2 principal components, and the rest principal components are abandoned. The projection matrix V is not a square matrix (not completely orthonormal, it is a semi-orthogonal matrix). Suppose n is the number of samples and m is the numb... | https://stats.stackexchange.com |
31,865 | [
"https://physics.stackexchange.com/questions/31865",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5374/"
] | At least if $\vec v$ is really only a one dimensional parameter, measuring all the moments $\langle v^n \rangle_f$ seems to give me all the information to compute $\langle A \rangle_f$ with $A(v)$ being a function of $v$. So integer powers of the generator of the function algebra $v$ are special functions.
I wonder i... | In addition to the polynomial moments, people often consider the Fourier transform of a probability distribution. This is the expected value
$$ \int \rho(V) e^{ikV} dV $$
These exponential moments are clearly enough to reconstruct the distribution completely.
The polynomial moments are not always enough, but the cou... | ''is there e.g. a statistical significance to $⟨f⟩_f$?''
No but $\langle -\log f\rangle_f$ is the entropy.
| https://physics.stackexchange.com |
109,126 | [
"https://security.stackexchange.com/questions/109126",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/95452/"
] | Everywhere it is mentioned that <code>SSL/TLS</code> must be used because of the high security and privacy they provide.
My question is: if this is true then why terrorists and other people use other alternatives such as tox.chat instead?
Why <code>SSL/TLS</code> is not enough for them? does not this mean they are no... | The question here is whom you want to be protected from. Using SSL/TLS with signed certificates is not that secure for someone who is messing with almost every state on earth. This is because the CA's can be forced to give the private key they issued to a specific website to the authorities. This enables the countries ... | SSL/TLS is a solution to a specific problem in security and is not the all-in-one solution to all security problems one might have.
The scope of SSL/TLS is limited to securing the direct connection between two endpoints, i.e. client and a server. In protocols like HTTP the data exchange will be done this way, but in p... | https://security.stackexchange.com |
13,741 | [
"https://physics.stackexchange.com/questions/13741",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/930/"
] | We all can agree that UV lasers are extremely useful, but we (poor majority) are still struggling with 355nm DPSS ones, while excimer lasers being prohibitively expensive (let's say at 1-10W average power, or 100Hz @ 0.1J pulse).
What is the reason for this? What is the complexity, making excimer lasers (namely, 248nm... | Interestingly exicmer laser development was originally funded, in part, due to interest in inertial confinement fusion.
Original excimer lasers required: rare-gas atoms (e.g., Xe) at high pressures, 10 atm; very high voltages, 400 keV, were required to create an electron beam through a metal foil; high current densiti... | This laser is a type of ultraviolet laser often used in UV photolithography in eye surgery.
The term excimer comes from excited dimer English (excited dimer)
This uses a combination of inert gas such as argon, krypton or xenon, with reactive gas. Under appropriate conditions of electrical stimulation, a pseudo-mole... | https://physics.stackexchange.com |
352,831 | [
"https://physics.stackexchange.com/questions/352831",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/166432/"
] | Some say that astronauts use special space pens which uses pressurized nitrogen to write at space (zero gravity) and the normal gel pens does not write at space as there is no gravity for the gel to flow.
But, some others say that due to surface tension in the nip, the gel stays there and it is possible to write with ... | If pens required gravity to pull the ink to the tip, then you wouldn't be able to write upside down or sideways. Perhaps you could perform an experiment?
<hr>
If you were to do so, you would find that pens do indeed work (ish) upside down and sideways, and therefore do not require gravity for their operation. Howev... | Well, I would say no. Gel pens have pigments suspended in gelled water based carrier. The tip has a very fine hole that allows this thick gel to flow if the tip contacts a solid surface and moves along it. For this to happen, it's necessary that the pen is tip side down (at Earth) so that the ink is attracted towards t... | https://physics.stackexchange.com |
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