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
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446,940 | [
"https://physics.stackexchange.com/questions/446940",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/747/"
] | We are all familiar with the typical example of statistical physics; <span class="math-container">$N$</span> particle of gas in a box of average volume <span class="math-container">$\overline{V}$</span> and average energy <span class="math-container">$\overline{E}$</span>.
The equation of state of of the canonical ens... | First, we have to address a misconception in the premise of your question.
When you say "The quantities <span class="math-container">$T$</span> and <span class="math-container">$p$</span> do not have thermal fluctuations, but the quantities <span class="math-container">$\overline{E}$</span> and <span class="math-conta... | <ol>
<li>Suppose we fix <span class="math-container">$T$</span>, <span class="math-container">$P$</span> and <span class="math-container">$N$</span>. Imagine the gas to be inside a very elastic balloon in thermal and mechanical equilibrium with the surroundings (say, the atmosphere). Neither the energy nor the volume o... | https://physics.stackexchange.com |
108,641 | [
"https://physics.stackexchange.com/questions/108641",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/28924/"
] | Why is $SU(3)$ chosen as the gauge group. Why not $U(3)$? Why does it even have to be unitary?
| Let me first make a general remark about internal symmetry groups, unrelated to our problem of the correct symmetry group for QCD.
<blockquote>
<em>The symmetry must act on Hilbert space as a unitary operator for the
conservation of probability.</em>
</blockquote>
Now let us turn to the strong interaction. The m... | Proving, that <span class="math-container">$N_c=3$</span> is not enough to verify, that the transformations are governed by <span class="math-container">$SU(3)$</span>. Imagine a SU(2) color triplet <span class="math-container">$\phi \to \phi^\prime=W\phi$</span>.
A meson would be color neutral, because
<span class="m... | https://physics.stackexchange.com |
168,964 | [
"https://physics.stackexchange.com/questions/168964",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/74611/"
] | So recently I have became interested in quantum physics. However when I read up on quantum physics Feynman diagrams appear everywhere, and I do not understand them!
Here is a Feynman diagram that is annoying me:
<img src="https://i.stack.imgur.com/DxvSt.png" alt="enter image description here">
So, How do I know if th... | The energy levels of a diatomic molecule are $E = 2B, 6B, 12B$ and so on, where $B$ is:
$$ B = \frac{\hbar^2}{2I} $$
Most of the mass of the molecule is in the nuclei, so when calculating the moment of inertia $I$ we can ignore the electrons and just use the nuclei. But the size of the nuclei is around $10^{-5}$ time... | Just an addition to John Rennie's answer. The equipartition theorem can only be derived in classical statistical physics. In quantum statistics it is not correct. For each degree of freedom there is a characteristic temperature below which the quantum effects are significant. This temperature is very high for rotation ... | https://physics.stackexchange.com |
184,685 | [
"https://dba.stackexchange.com/questions/184685",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/60677/"
] | This query: <code>select count(*) from planner_event</code> takes a very long time to run - so long, I gave up and killed it before it finished. However, when I run <code>explain select count(*) from planner_event</code>, I can see a column in the output with the number of rows (14m).
How come explain can get the numb... | Explain is using previously gathered statistics (used by the query optimizer). Doing a <code>select count(*)</code> reads EVERY data block.
Here's a cheap way to get an <strong>estimated</strong> row count:
<pre><code>SELECT table_rows
FROM information_schema.tables
WHERE table_name='planner_event';
</code></pre>
Even ... | Explain gets the number from some "statistics" that are used to estimate things for the Optimizer. That number can be far from correct -- I sometimes see it being more than a factor of 2 (higher or lower) than the exact value.
Performing the <code>COUNT(*)</code> on an InnoDB table must scan the table to avoid miscou... | https://dba.stackexchange.com |
1,117,082 | [
"https://math.stackexchange.com/questions/1117082",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/210154/"
] | The problem: show that $x \le x+(1-x) \sin^2(x) \le 1$ for $x \in (0,1)$
I tried to solve it with the derivative and the inequality $\sin(x) \le x$ for $x>0$
thanks for helpers
| $$
0 \leq (1-x)\sin^2 x\leq 1- x
$$
Then you can see that
$$
0 \leq \sin^2 x \leq 1
$$ which is true.
| There is no need for derivatives. If $x\in (0,1)$, then $1 - x > 0$ and $\sin^2 x\ge 0$, thus $(1 - x)\sin^2 x \ge 0$. Consequently, $x \le x + (1 - x)\sin^2 x$. Since $0 \le \sin^2 x \le 1$ and $1 - x > 0$, $(1 - x)\sin^2 x \le 1 - x$. Hence $x + (1 - x)\sin^2 x \le x + (1 - x) = 1$.
| https://math.stackexchange.com |
194,820 | [
"https://softwareengineering.stackexchange.com/questions/194820",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/75283/"
] | I know there are similar questions to this one, and I've read most of them. Most of the answers to these questions are talking about "cost-effectiveness" and "time-saving" aspects of the frameworks, which are huge reasons in favor of using frameworks.
I'm a pretty new .NET developer and I'm trying to learn stuff like ... | <blockquote>
I'm a pretty new .NET developer and I'm trying to learn stuff like WPF, MVVM, layered architecture design, dependency injection, logging, database access, test-driven development, and many more different technologies/techniques.
</blockquote>
I've seen a great talks once about how to learn something qui... | Practicing doing a skill the wrong way doesn't help you learn it. You will have plenty of chances when you do it wrong by accident, or to maintain code that was done poorly by someone else.
I also find it fascinating that in these sorts of questions people only worry about the highest layer of abstraction. You're bu... | https://softwareengineering.stackexchange.com |
12,098 | [
"https://dba.stackexchange.com/questions/12098",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/6370/"
] | I am having a problem connecting sql developer to my Oracle 10g database. sqlplus is able to connect fine, but when I try to open the connection in sql developer, I get 'ORA-12514 TNS does not know of service' error. I have tried modifying my tnsnames.ora file. It has the following:
<pre><code>COTT3 =
(DESCRIPTIO... | Try this:
<pre><code>COTT3 =
(DESCRIPTION =
(ADDRESS = (PROTOCOL = TCP)(HOST = localhost)(PORT = 1521))
(CONNECT_DATA =
(SERVER = DEDICATED)
(SERVICE_NAME = COTT3)
)
)
</code></pre>
If that doesn't work, replace "SERVICE_NAME" with "SID".
Put this in $ORACLE_HOME/network/admin/listener.ora:
<pre><cod... | here is my listener.ora:
<pre><code>SID_LIST_LISTENER =
(SID_LIST =
(SID_DESC =
(SID_NAME = PLSExtProc)
(ORACLE_HOME = C:\oraclexe\app\oracle\product\11.2.0\server)
(PROGRAM = extproc)
)
(SID_DESC =
(SID_NAME = CLRExtProc)
(ORACLE_HOME = C:\oraclexe\app\oracle\product\11.2.0... | https://dba.stackexchange.com |
9,389 | [
"https://biology.stackexchange.com/questions/9389",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/4053/"
] | Verging on the realm of science fiction, my question is that is there any theoretically possible way, biologically/chemically, with which the entire human race can be killed without affecting the rest of the biosphere at all? I am only curious about theoretically possible no matter how unlikely. If we encounter a suffi... | Infectious diseases is probably the only way I can think of. Viruses for example may have tropisms based on receptors to which they attach. These receptors may be and often are unique to a species, and thus an infection could target humans very specifically. Differences between humans and animals present the weaknesses... | Trick question. By driving humans to extinction, you almost certainly will be driving all human-specific parasites and pathogens to extinction as well.
| https://biology.stackexchange.com |
90,490 | [
"https://mathoverflow.net/questions/90490",
"https://mathoverflow.net",
"https://mathoverflow.net/users/15606/"
] | Let $X$ be a noetherian scheme and let $Y$ be a closed subscheme of $X$.
What relation is there between $\mathrm{Bl} _ {Y}(X)$ and $\mathrm{Bl} _{ Y _{\mathrm{red}}}(X)$ ?
Thanks.
| There is no map from one blow up to the other, and definitely not an isomorphism. Please see my comments to J.C. Ottems answer.
<em>However</em>, if you replace radical by integral closure, then everything is fine.
Here's what I mean, if $I$ is an ideal and $J$ is its integral closure, then you always have an ev... | In general they can be very different. For example take the subscheme $Y$ of $\mathbb{A}^2$ given by the ideal $(x^2,y)$. Here the blow up is covered by the two open subsets
$$U = \mbox{Spec} k[x, y][t]/(y − x^2t),\qquad V = \mbox{Spec} k[x, y][s]/(ys − x^2)$$
In particular the blow up of $Y$ is singular, whereas th... | https://mathoverflow.net |
442,746 | [
"https://physics.stackexchange.com/questions/442746",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/213851/"
] | we studied that antimatter can be stored in the large hadron collider. what i dont get is that the collider is used to collide particles and antiparticles together right? so how is antimatter stored in the collider without it interacting with the accelerating matter and causing pair production? also in our book its wri... | Often it does not matter, because surface is so thin its energy is negligible. For example, gas in a thin walled metal cylinder has energy that is orders of magnitude higher than energy of the metal cylinder.
In case energy of the surface is important, one has to decide if it counts towards the system, or the environm... | <strong><em>Okay, if the surface of that object gained some energy, is the system who gained? or the environment or neither?</em></strong>
When applying these concepts in thermodynamics, generally speaking the boundary between a system and its surroundings provides the mechanism for transferring work and/or heat betwe... | https://physics.stackexchange.com |
3,617,274 | [
"https://math.stackexchange.com/questions/3617274",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/176213/"
] | Urn contains <span class="math-container">$w$</span> white and <span class="math-container">$b$</span> black balls. We draw balls with the following procedure:
<ol>
<li>We draw ball and put it aside.</li>
<li>We draw another ball. If its color is different than last drawn ball then we put it back to urn and go to stat... | The coefficient by <span class="math-container">$x^{n-1}$</span> of <span class="math-container">$T_n(x)$</span> is <span class="math-container">$0$</span>. One can use induction:
<ul>
<li><span class="math-container">$n=0$</span> and <span class="math-container">$n=1$</span> are clear.</li>
<li>Assume it is true for... | <em>Hint:</em> Prove by induction that the degree of <span class="math-container">$T_n$</span> is <span class="math-container">$n$</span> and that the coefficient of <span class="math-container">$x^{n-1}$</span> in <span class="math-container">$T_n$</span> is zero.
Actually, <span class="math-container">$T_n$</span> h... | https://math.stackexchange.com |
2,064,996 | [
"https://math.stackexchange.com/questions/2064996",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/399584/"
] | One obvious method to show $C_{S_4}(V_4)=V_4$ is to directly check that each element of $S_4$ that is not in $V_4$ fails to commute with some element of $V_4$. But is there a more efficient way to showing this true?
By $V_4$, I meant $\{(), (1 2)(3 4), (13)(24),(14)(23)\}$.
| If you mean the normal $V_4$ inside $S_4$, (the one generated by the three elements with cyclic structure $(**)(**)$), you can use the fact that the centralizer of a subgroup is a normal subgroup of the normalizer (in this case, the whole $S_4$). So the centralizer is either $V_4$ itself, $A_4$ or $S_4$. A quick check ... | Remember that the action of $S_4$ on its elements is by relabeling. We will concentrate on elements of order $2$:
<ul>
<li>Those of the form $(1,2)$:</li>
</ul>
The only way to relabel this element while preserving it is to swap $1$ and $2$, or to swap $3$ and $4$, this gives us the group $\{(), (1,2), (3,4), (1,2)(3... | https://math.stackexchange.com |
1,180,055 | [
"https://math.stackexchange.com/questions/1180055",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/221620/"
] | Let $f$ be increasing on $D$ ($D$ is dense in $\mathbb{R}$), and define $\tilde{f}$ on $(-\infty,\infty)$ as follows: $$ \forall x: \tilde{f}(x) = \inf_{x<t\in D} f(t).$$
Show that continuity of $f$ on $D$ does not imply that of $\tilde{f}$ on $(-\infty,\infty),$ but uniform continuity does imply uniform continuity... | Suppose that $D = \mathbb R \setminus \{0\}$ and that $f : D \to \mathbb R$ is given by $$f(x) = \left\{ \begin{array}{cl} x & \text{ if }x < 0, \\ x+1 & \text{ if }x > 0. \end{array} \right.$$
Then $f$ is continuous on $D$, but
$$\tilde f(x) = \left\{ \begin{array}{cl} x & \text{ if }x < 0, \\ x+... | Let $q_n$ be an enumeration of the rationals (since they're countable) and define $g(q_n) = 1/2^n$, and define $f(x) = \sum_{q_n \leq x} g(q_n)$. Then this should give you your increasing function which is continuous on a dense subset but not continuous anywhere else when you extend to ${\mathbb R}$. In a certain sense... | https://math.stackexchange.com |
360,354 | [
"https://stats.stackexchange.com/questions/360354",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/152542/"
] | I am an old dog (DB guy) trying to learn new tricks (stats) and was hoping someone here could tell me if this is a good approach:
I have to analyse extremely right skewed counts of events over a period of observation, pre vs post. I have N=1213 pre and N=1138 post intervention datasets. Minitab rates Skewness at 5.3 a... | If you have count data and are interested in the percentage change due to the intervention, you might want to run a negative binomial regression with the counts as the outcome variable and the intervention condition as the predictor. Taking $exp(\beta_1)$, where $\beta_1$ is the coefficient on the intervention variabl... | I think the taking the log and then comparing medians is odd, and might sound like shenanigans to your audience.
You can use Mann-Whitney on the original data (with or without the zeros, depending on what makes sense). Just understand that it isn't a test of medians. It is a test of stochastic equality. That is, H... | https://stats.stackexchange.com |
19,313 | [
"https://security.stackexchange.com/questions/19313",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/1957/"
] | I would like to at first be clear that this is for poor site owners who can't afford the SSL option but require logins to their site, potentially from a public kiosk, and need a secure method of allowing such. All I'm looking for is a public vetting of the process I have drawn up, if there are any attacks I may have mi... | In short: Just go to startssl.com and get your SSL certificate for free.
The protocol is not specific enough. If you aim to implement this yourself, you will likely introduce flaws in the signing and encryption steps. How are users going to validate the server's public key here? Do you expect them to compare hex-digit... | Your method is trivially vulnerable to a Man in the Middle (MitM) attack. There are two benefits of using SSL:
<ol>
<li>Sensitive traffic over the wire is sent encrypted (which your method effectively accomplishes) and </li>
<li>you can cryptographically verify that you are going to the right website and not a fake v... | https://security.stackexchange.com |
117,815 | [
"https://softwareengineering.stackexchange.com/questions/117815",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/36465/"
] | Currently working on a complete front-end and back-end overhaul of our webapp. We did this because a lot of changes needed to be made to the database schema as well as the user experience.
Now we are almost done with the overhaul and I'm thinking if we could have taken a more incremental approach? We started a new cod... | You are right to fear the complete rewrite, nothing is ever scarier in the world of refactoring. There are many strategies for breaking down the rewrite into digestible chunks, and it depends on what's wrong with the code base to begin with. Was it spaghetti? Was it inherently unstable? Or, based on deprecated services... | Small is always better than big!
An incremental approach, dividing the upgrade into several small releases is usually the best approach, though its a hard sell to management.
It sound like splitting your project up into:--
<ul>
<li>presentation code updates to enable the fancy stuff, plus an implementation of some o... | https://softwareengineering.stackexchange.com |
54,268 | [
"https://mathoverflow.net/questions/54268",
"https://mathoverflow.net",
"https://mathoverflow.net/users/12713/"
] | <ul>
<li>Let $X$ be some uncountable standard Borel space (e.g., the real line).</li>
<li>Let $D$ be the set of Borel probability measures on $X$.</li>
<li>Let $M$ be the set of signed Borel measures on $X$</li>
<li>Now let $p_1,...,p_N$ be a finite sequence of linearly independent probability measures in $D$.</li>
<li... | Something is wrong in the statement of the question. If $X$ has four points, then a measure on $X$ is a list of four non-negative numbers that sum to 1. But if you take the plane subtended by $(1,0,1,0)$, $(1,0,0,1)$, and $(0,1,1,0)$, then it also contains $(0,1,0,1)$, and these four measures are the four extremal on... | Here is a counterexample.
Take $X=\mathbb S^1=\mathbb R/2{\cdot}\pi{\cdot}\mathbb Z$ and
$$p_i=\tfrac1{2{\cdot}\pi}{\cdot}[1+\cos(x-\alpha_i)]$$
for $\alpha_1=0$, $\alpha_2=\pi/2$.
In this case
$$A=\{\,\tfrac1{2{\cdot}\pi}{\cdot}[1+\lambda{\cdot}\cos(x-\alpha)]\mid \alpha\in \mathbb S^1, \ \lambda\ge 0\,\}$$
and
$$A... | https://mathoverflow.net |
263,890 | [
"https://dba.stackexchange.com/questions/263890",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/33246/"
] | When I create a new user in MariaDB, I cannot login as that user.
First I login to the database as root doing <code>mariadb</code> in a bash terminal.
I then run the following commands to create a database and a user:
<pre class="lang-sql prettyprint-override"><code>CREATE DATABASE mydb;
grant all privileges on myd... | The <code>-p</code> password prompt seems to be broken. Supplying the password on the command line works as it should.
<pre><code>mariadb -u myuser mydb --password="password"
</code></pre>
| Try granting to 'myuser'@'127.0.0.1', @'::1', or even @'%'. In your logs, you will see 'Access denied for user' and what IP address you were trying to connect from.
| https://dba.stackexchange.com |
110,271 | [
"https://electronics.stackexchange.com/questions/110271",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/41780/"
] | due to the "high cost" (at least from my point of view) of a thermal printer I was wondering whether it was possible/worth the effort to buy a compared cheaper device with it integrated already (a calculator for example). I was thinking of buying a "P1-DTSC, Canon" calculator for my "misuse". So would it be easier to r... | It would be essentially impossible for you to reprogram the microcontroller in a commercial product like a Canon calculator. First of all, the chip is probably propriety, and not something you could find documentation on. Even if you could, it is unlikely it is able to be reprogrammed within the device -- the chips a... | Possible sure. Worth the effort: doubtful. You're probably better off figuring out what kind of thermal printer is in the calculator and then sourcing that thermal printer as that would likely be cheaper.
I doubt you'd be able to reprogram the microcontroller. Replacing it with uC is the same thing as controlling it ... | https://electronics.stackexchange.com |
103,169 | [
"https://softwareengineering.stackexchange.com/questions/103169",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/6584/"
] | I am part of a small software company that specializes in small to medium-sized business applications and my experience with distributed architectures/SOA is limited. Please let me know if I'm going about this all wrong.
We often start development on small business applications, where a distributed architecture seems ... | You should think ahead which parts would be considered 'client-side' and which would be 'server-side'. The server tier would be exposed via a service layer, not necessarily using WCF or any tecnology. At first, would be just an interface (IService). In the client tier you would have a delegate layer that knows how to r... | You are not wrong about regarding the time factor. It will take longer to design and develop a partitioned application such as you are suggestng. However, given your past experiences you can see that the time will be well spent.
It seems to me that if you would partition the application much like a distributed applica... | https://softwareengineering.stackexchange.com |
65,291 | [
"https://biology.stackexchange.com/questions/65291",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/36077/"
] | I can't understand the difference be because both involvery the main cause that is an external stimuli, so how do they differ(
| If the sequence of the 26 kDa form is included within the sequence of the 28 kDa form then the answer is 'probably yes'.
However if the N- or C-terminus of the short form is an important/dominant epitope and it is masked in the long form (by being extended) then the activity of the serum against the long form could b... | As Alan said, it depends but I'd guess that, yes, it probably does.
Given that you are using polyclonal antibodies against a not so dramatic extension, I'd say it's even more likely that you'll see signal. The various antibodies within the polyclonal mixture will bind different parts of the smaller protein, so unless ... | https://biology.stackexchange.com |
613,788 | [
"https://electronics.stackexchange.com/questions/613788",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/310287/"
] | Need to rectify 3 phase 120V AC 250A using 3 Phase 200A bridge rectifier.
Details:
Input Voltage: 120V AC 3 Phase
Input Current: 250A
Problem: Only 3 Phase 200A bridge rectifier is available. Is this possible?
| <blockquote>
Is the motor always in regenerative mode when the it decelerates?
</blockquote>
The motor is only in regenerative mode if the deceleration rate is faster than the motor would decelerate if it were simply disconnected from power. In other words, if the losses in the motor and load use up all of the energy t... | <blockquote>
Is the motor always in regenerative mode when the it decelerates? isn't it dynamic braking if we don't purposely implement regenerative braking? If it is dynamic braking, why DC cap voltage increases?
</blockquote>
There's no such thing as regenerative mode on a motor. There is, however, generator mode and... | https://electronics.stackexchange.com |
1,256,581 | [
"https://math.stackexchange.com/questions/1256581",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/230976/"
] | Prove that if $x$ is a real number in the range $12 - 7x + x^2 \ge 0.$
Which type of proof should I use to solve this? At first I thought direct proof. Choosing a number between $0$ and $3$ and attempting to solve?
| Hints:
<ol>
<li>$$12-7x+x^2=\left(x-\frac{7}{2}\right)^2+12-\frac{49}{4}=\left(x-\frac{7}{2}\right)^2-\frac{1}{4}$$</li>
<li>$$0\leq x\leq 3\implies \frac{1}{4}\leq \left(x-\frac{7}{2}\right)^2\leq \frac{49}{4}$$</li>
</ol>
| Evaluate the endpoints. What happens when $x = 0$, $x=3$? Can the expression ever be negative? There would have to be a point where is moves from the positive side to the negative side, i.e, where the expression is zero. Compute where that happens, or show that it can't, using the quadratic formula.
| https://math.stackexchange.com |
711,523 | [
"https://physics.stackexchange.com/questions/711523",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/312912/"
] | We have all heard of the famous twin paradox, in which the twin traveling at relativistic speeds ages slower, and finds his twin brother is now years older than him.
What about the other way around?
Is it possible to move so slowly compared to the rest of the galaxy, that time moves faster for the twin in space than th... | Point particles do self-interact, sort of. Remember that the description of an electron as a “particle” is a semiclassical simplification which sweeps an awful lot of modern physics under the rug. In quantum field theory, “an electron” is a quantized excitation of a spinor field associated with a particular mass, cha... | In a nutshell, classical electrodynamics isn't suited to the description of self-interaction. In order to lift that restriction, you need to add a quantum ingredient to the soup, in other words switch to quantum field theory.
Although it isn't the whole story, a good picture could be the following.
As you get closer to... | https://physics.stackexchange.com |
282,286 | [
"https://physics.stackexchange.com/questions/282286",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/121464/"
] | So, I've been trying to teach myself about quantum computing, and I found a great YouTube series called Quantum Computing for the Determined. However. Why do we use ket/bra notation? Normal vector notation is much clearer (okay, clearer because I've spent a couple of weeks versus two days with it, but still). Is there ... | Indeed, I agree with you, standard notation is, in my personal view, already sufficiently clear and bra-ket notation should be used when it is really useful. A typical case in QM is when a state vector is determined by a set of quantum numbers like this $$\left|l m s \right\rangle$$
Another case concerns the use of th... | What is "normal vector notation"? I've seen angle brackets with commas, parentheses, square brackets, $\hat{x}$, $\hat{i}$, column matrices, row matrices ... which of those is "normal", $(x|y)$, ...?
Bras and kets are just another, with the particular benefit that it distinguishes the vector space from its dual ... | https://physics.stackexchange.com |
119,206 | [
"https://softwareengineering.stackexchange.com/questions/119206",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/25404/"
] | Often, when I am initializing something I have to use a temporary variable, for example:
<pre><code>file_str = "path/to/file"
file_file = open(file)
</code></pre>
or
<pre><code>regexp_parts = ['foo', 'bar']
regexp = new RegExp( regexp_parts.join('|') )
</code></pre>
However, I like to reduce the scope my vari... | <strong>Short answer:</strong> No, don't repurpose variables.
<blockquote>
The idea is that <em>by reducing the number of variables in scope I reduce
the chances to misuse them</em>.
</blockquote>
It sounds more like <em>you're misusing variables so that you can reduce the number of them</em>.
Variables are chea... | I believe having one variable with multiple meanings is <em>much more</em> confusing than having many variables in scope.
At any rate, if you feel overwhelmed by the number of variables in scope, chances are your method/function is doing too much and should be split.
So the answer is: No, do not reuse variables, part... | https://softwareengineering.stackexchange.com |
125,950 | [
"https://electronics.stackexchange.com/questions/125950",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/51720/"
] | I have a lamp that has LED driver producing 35 V (actually lamp driver says 16 - 28 V, but I've measured 35 V). On the lamp I have 7 LEDs (originally 5 + 2 I've added) with heatsinks that have burned and replaced a couple of times now. All LEDs are connected in sequence.
LEDs specs:
<ul>
<li>LED Emitter: 3W </l... | <h2>Your "LED Driver" is most likely bad</h2>
The driver is clearly out of spec and mostly likely internally damaged. From you photos it isn't clear how the rest of your lights and power sources are connected, but you may have made an error here (I've even seen people connect the AC power line to the DC output side of... | According to the data printed on the driver, it's a constant-current supply and it's rated to supply about 600mA into a load that can drop anywhere between 16 and 28 volts with 600mA through it, which is a load resistance range of from about 27 to 47 ohms.
Your LEDs are spec'ed to drop a nominal 3.7 volts each with 70... | https://electronics.stackexchange.com |
11,415 | [
"https://quantumcomputing.stackexchange.com/questions/11415",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/11581/"
] | I want to create a parameter dependent gate in qiskit and I need to compute some complex operations as <code>sympy.atan2</code> or <code>sympy.sin</code> over the parameters but I don't know how
I've tried
<pre><code>from qiskit import *
from qiskit.circuit import Parameter
import sympy as sy
x=Parameter('x')
theta=... | As a general rule, just because you can produce controlled-<span class="math-container">$U$</span>, it does not mean that you can produce controlled-<span class="math-container">$U^{2^k}$</span> with the same complexity. Modular exponentiation is a very special case where it turns out that you can.
It is probably wort... | <strong>Partial answer:</strong>
If a operator <span class="math-container">$U$</span> is a single qubit rotation around axis <span class="math-container">$a$</span> for angle <span class="math-container">$\theta$</span> (denote <span class="math-container">$R_a(\theta)$</span>) you can use additivity of such operator... | https://quantumcomputing.stackexchange.com |
299,723 | [
"https://physics.stackexchange.com/questions/299723",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/106713/"
] | When I am on earth, the weight of my body is countered by the reaction of the ground. So, there is no net force acting on me.
But I am spinning with earth. But if there is no centripetal force then why am I spinning? And the equal air pressure on both side of my body won't be enough for me to stay in the same angular ... | It is easier to consider you standing on the Equator.
Assume that the gravitational field strength at the Equator is $g$. This would be the acceleration of free fall at the Equator with no air resistance if the Earth was not spinning.
If the reaction of the Earth is $N$ then assuming down is positive and using N2L... | Actually, this is rather insightful. The normal force from the ground does <em>not</em> quite cancel out the effect of gravity. The difference between them is precisely the centripetal force that keeps you rotating around with the Earth's surface.
Of course, you won't notice this because the centripetal force is so sm... | https://physics.stackexchange.com |
257,881 | [
"https://softwareengineering.stackexchange.com/questions/257881",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/150936/"
] | I'm writing some test code for a feature which processes PDF files. The basic idea behind the tests is that I point them towards some PDFs I've selected specially, they process them and I check that the output is what I expect.
My question is: where should I be storing these large-ish PDFs? Should I check them into ... | Your version control system should contain everything it needs to build, compile, <strong>test</strong>, and package an application for distribution (e.g. MSI, RPM). I would also argue build configurations and other scripts should also be in version control.
I should be able to check out a project and have a complete ... | If the tests are useless without the setup files that you have prepared, then it makes sense to include the files in your VCS along with the test code.
While the files used in the test aren't code, you can view them as a dependency that the code relies upon. So there is merit in keeping everything together.
<hr>
As... | https://softwareengineering.stackexchange.com |
15,600 | [
"https://mathoverflow.net/questions/15600",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4056/"
] | There is an algorithm that give us cuboids in $\mathbb{R}^3$, say $Q_1,Q_2,\ldots$, such that $\cup_{i=1}^{\infty} Q_i$ is the simplex with vertices $(0,0,0), (1,0,0) , (0,1,0), (0,0,1)$, and the $Q_i$'s are almost disjoint (i.e $\lambda(Q_i\cap Q_j)=0$ if $i\neq j$)?
In $\mathbb{R}^2$ there are many easy ways to fil... | OK, since we finally have figured out what Andres is asking and since 600 characters is a bit too restrictive, I'll post this as an answer.
The following Asymptote code will draw the filling except I used the size 4 simplex instead of size 1 one here:
<pre>
size(400);
import three;
import graph3;
pen[] q={red,green... | Here's a (highly nonoriginal) method: overlay a finite hyperplane grid onto the region of interest. For R^2 this divides the plane into rectangles, for R^3 into cuboids (a.k.a rectangular parallelipipeds), and into higher dimensional intervals for the space of your choice. Now, mark all those bounded grid areas which... | https://mathoverflow.net |
452,783 | [
"https://electronics.stackexchange.com/questions/452783",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/226870/"
] | I am using ATmega32 AVR microcontroller. I am confused about bitwise operation in embedded C. I understand (AND, OR, XOR, NOT) logic gates very well, but there is something that I don't understand:
<ol>
<li>I understand this block of code:
<pre><code>if ((PINB&(1<<PB0))==0x01) //if button pressed
{
//Do... | The example number 1 is not a good pattern to follow because it will work only if PB0 equals 0. Example number 2 is a better pattern to follow because it will work for all values of PB0. Example 1 can be edited to work for all values of PB0 like this:
<pre><code>if ((PINB & (1<<PB0)) == (1<<PB0)) //i... | The first expression shows a common error in embedded programming. Note that the expression <code>PINB&(1<<PB0)</code> has two variables, <code>PINB</code> and <code>PB0</code>. Exxentially the result of this expression will be equal to <code>1 << PB0</code> if and only if bit number <code>PB0</code> in... | https://electronics.stackexchange.com |
300,296 | [
"https://electronics.stackexchange.com/questions/300296",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/128492/"
] | In my power engineering course, we were introduced to reactive power. I believe I understand what reactive power is in essence: there is energy transfer between the source and inductor/capacitor. This makes sense to me, and I can do many calculations just fine. However, I am failing to understand what the value of reac... | Let's ignore the power aspect for a second, and think about what reactance really is.
You know a math and theory, you can talk about things in abstract theoretical constructs using complex numbers, phasors, and all that. But abstract models are exactly that: abstract models. The math can model a thing, but it won'... | When you have a complex load, its associated power can be modeled with a complex number:
$$S = P+jQ$$
Where S is the complex power, usually measured in VA, P is the real power, measured in W, and Q is the reactive power, measured in VAR.
As op noted, the only "useful" power is the real power P, since it is the only ... | https://electronics.stackexchange.com |
34,515 | [
"https://electronics.stackexchange.com/questions/34515",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/9877/"
] | I have some 3.3V Arduino Pro Mini boards and they require either an FTDI cable or breakout board to be programmed from a USB port.<br>
So far I've been using a board, but it's annoying to have to either solder headers in place or hold the boards carefully every time I make a modification to the code. Also, switching be... | Your <code>clk</code> pin is driving some non-clock pins (LUT inputs by the look of it). This is almost always a bad idea.
Open your design in the technology viewer and look at the "non-clock load pins" listed in the logfile (<code>< PIN: sync_apbinterface_0/pclk_test_select[15]_AND_253_o4.A4; ></code> is the... | Generally speaking you should not be writing dividers like this. You are creating a clock signal out of logic, which as ISE is telling you, is not a recommended design practise. Not only are you consuming (often scarce) clock routing nets, but you can also end up with jittery, glitchy clocks as the logic blocks ripple ... | https://electronics.stackexchange.com |
2,132,470 | [
"https://math.stackexchange.com/questions/2132470",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/74414/"
] | I need to prove this equation:
$$\lim_{r\to0}\left((1+\frac{r}{1})^1-(1+\frac{r}{n})^n\right)=\frac{1-n}{2n}r^2$$
Lecturer gave us a hint: $$\lim_{x\to0} \frac{\sin x}{x}=1$$
I was thinking about expanding $(1+r/n)^n$ with Taylor series, but that gave me nothing.
Do you have any ideas/suggestions? Thank you.
| $$
\begin{align}
\phi^2 &= \phi+1 \\[4mm]
\color{red}{S} &= \sum_{n=1}^{\infty}\left(\frac{\phi^2+\gamma}{n+1}-\frac{\phi+\gamma}{n}-\log{\frac{n+1}{n}}\right) \\[2mm]
&= \sum_{n=1}^{\infty}\left(\frac{\phi^2+\gamma}{n+1}-\frac{\phi\color{red}{+1}+\gamma\color{red}{-1}}{n}-\log{\frac{n+1}{n}}\right) \\[... | $\newcommand{\bbx}[1]{\,\bbox[8px,border:1px groove navy]{\displaystyle{#1}}\,}
\newcommand{\braces}[1]{\left\lbrace\,{#1}\,\right\rbrace}
\newcommand{\bracks}[1]{\left\lbrack\,{#1}\,\right\rbrack}
\newcommand{\dd}{\mathrm{d}}
\newcommand{\ds}[1]{\displaystyle{#1}}
\newcommand{\expo}[1]{\,\mathrm{e}^{#1}\,}
\newc... | https://math.stackexchange.com |
388,357 | [
"https://electronics.stackexchange.com/questions/388357",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/194748/"
] | I have this subwoofer that turns on and off based on if there is signal on the input. It's real annoying that I will be watching something quiet, it will turn off, and then later it will turn on again when something happens with bass. It takes a couple of seconds to kick on, so it misses what it supposed to come throug... | It seems like the easiest way will be to remove C601 and connecting the R601 "upper" leg to pin 8 of a Q301 or short Q603 to ground.
| Jumpering P631 will disable auto standby.
| https://electronics.stackexchange.com |
76,158 | [
"https://stats.stackexchange.com/questions/76158",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/31420/"
] | <strong>Theorem</strong>
Suppose $X_n \stackrel{P}\to X\quad \text{and}\quad Y_n \stackrel{P}\to Y $. Then $X_n+Y_n \stackrel{P}\to X+Y $.
<strong>Proof</strong>
Let $\epsilon >0 $ be given. Using the triangle inequality, we can write $$ | X_n-X|+|Y_n-Y| \geq |\left( X_n+Y_n \right) -\left( X+Y \right) | \geq \ep... | The meaning of <em>$P$ is monotone relative to set containment</em> is this:
<blockquote>
If $A \subseteq B$ then $P(A)\leq P(B)$.
</blockquote>
Now here for every $\omega\in\Omega$, we have
$$\begin{align*}
A &= \left\{\omega : \left| (X_n(\omega) + Y_n(\omega)) - ( X(\omega) + Y(\omega) ) \right| \geq \epsil... | If you're aware of an equivalent characterization of convergence in probability, the proof is really short. It is known that $X_n \rightarrow X$ in probability if and only if, for any subsequence $\left \{a_1, a_2, \ldots \right\}$, there exists a sub-subsequence $\left\{a'_1,a'_2,\ldots \right \}$ such that $X_{a'_n}... | https://stats.stackexchange.com |
482,763 | [
"https://physics.stackexchange.com/questions/482763",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | why work done by a battery in circuit is potential diffrence across plates times charge flown through body.
<strong>W=Qε(ε is emf of battery)</strong>
although there are heat and other loses ? and another that my text book has not mentioned from which point till which point in circuit Q is being transffered?
| Batteries use a chemical reaction to do work on charge in the battery to generate a voltage across its terminals giving the charge potential energy. If the battery is not connected to a circuit that voltage is called an emf which means the voltage across its terminals when there is no current flow (the open circuit ... | The key here is that the potential comes from the fact that there are losses. Consider a circuit element like a resistor; If instead this was an ideal wire, then the work needed to move a charge (neglecting external fields such as gravity) is 0 because there is no force applied to the charge. Now if we replace this ide... | https://physics.stackexchange.com |
435,548 | [
"https://math.stackexchange.com/questions/435548",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/61493/"
] | When is was making some exercises I encountered the following exercise:
$Exercise$:
Let $P(A)$ denote the set of all subsets of an arbitrary set $A$.
List first the elements of $P(\emptyset)$, then the elements of $P(P(\emptyset))$.
Finally, check in two steps whether you have listed the correct number of elements... | $P(\{x\}) = \{\emptyset,\{x\}\}$ for any $x$. Then take $x=\emptyset$. Then note that $\emptyset \neq\{\emptyset\}$.
So $P(\emptyset) = \{\emptyset\}$. And $P(P(\emptyset))=\{\emptyset,\{\emptyset\}\}$.
| <strong>Hint:</strong> for every set $A$, $P(A)$ <strong>always</strong> contains among its elements the empty set $\emptyset$ and also the total set $A$, since both are always subsets of $A$.
So, if $A\neq \emptyset$ then you can count at least two elements in $P(A)$.
| https://math.stackexchange.com |
19,171 | [
"https://cs.stackexchange.com/questions/19171",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/11155/"
] | I'm trying to understand decidable languages. In particular, I would like to show that
$$B = \lbrace \langle D \rangle \mid \exists k \geq 0 \,.\,\text{DFA $D$ accepts $a^k b^k$}\rangle.$$
I don't quite understand the process of proving these. I know that $a^kb^k$ is not regular, so then no DFA accepts it. I also know ... | Hint: Let $s_0$ be the starting state, $F$ the set of accepting states, and $q$ the transition function. The mapping $k \mapsto q(s_0,a^k)$ is eventually periodic and can be determined explicitly. The predicate $(s,k) \mapsto q(s,b^k) \in F$ is eventually periodic and can be determined explicitly. So the predicate $k \... | Hint. The language $\{a^k b^k \mid k \in \mathbb{N}\}$ is context-free. So, can you construct a context-free grammar or pushdown automaton for it? What do you know about the closure properties of context-free languages and regular langauges? If you take the <code>_____</code> of a regular language and a context-fre... | https://cs.stackexchange.com |
553,277 | [
"https://electronics.stackexchange.com/questions/553277",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/43685/"
] | Is there any standard or common numbering system for PCB layer numbers? I'm using Altium.
I imported a few different components from a couple of libraries and found that they put things like designators, 3d bodies etc. all over different layers.
I'd like to settle on a standard 'put designator on layer XX, put 3d body ... | That 'EMC circuit' is simply a passive filter to avoid propagating switching noise upstream on the power line. Search for "common mode input filter" for details.
For various reasons (entire books have been written on the subject) the DC/DC converter generates electric noise. If it in not suitably suppressed (... | It's purpose is for reducing conducted RF emmissions for Electro-Magnetic Compliance (EMC) purposes.
Basically if you want to pass compliance testing (e.g. CE mark, UL, etc), it may help reduce noise levels conducted out of your device onto the mains or DC power input.
Whether or not it is necessary is for you to deter... | https://electronics.stackexchange.com |
20,800 | [
"https://physics.stackexchange.com/questions/20800",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7607/"
] | If we consider a ball moving at an acceleration of <span class="math-container">$5\ \mathrm{m\ s^{-2}}$</span>, over a time of 4 seconds, the distance covered by the ball in the first second is <span class="math-container">$5\ \mathrm m$</span>. In the 2nd second will <span class="math-container">$5\ \mathrm m+5\ \math... | You say:
<blockquote>
If we consider a ball moving at an acceleration of <span class="math-container">$5\ \mathrm{m/s^2}$</span>, over a time of 4 seconds, the distance covered by the ball in the first second is <span class="math-container">$5\ \mathrm m$</span>. etc
</blockquote>
But that's not true. Why do you th... | It seems to me you have confused velocity and acceleration.
<blockquote>
If we consider a ball moving at an acceleration of 5m/s^2
</blockquote>
This doesn't really make sense, acceleration is change of rate of movement. Movement is defined physically by 'velocity' in units of $ms^{-1}$. I think you have this m... | https://physics.stackexchange.com |
312,963 | [
"https://softwareengineering.stackexchange.com/questions/312963",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/218837/"
] | I'm writing a camera control program which uses many methods for each of the different commands.
One example is:
<pre><code>public void CameraPan(int Id, string Direction, int Speed)
{
StringBuilder sb = new StringBuilder();
sb.Append(_cameraRamp); //command to camera - start moving
sb.Append(_camID);
... | Instantiate a <code>StringBuilder</code> for each method.
Here's why:
<ol>
<li><strong>Encapsulation.</strong> Because each method has its own <code>StringBuilder</code> object that it controls, it does not have to worry about anything else monkeying with its <code>StringBuilder</code> state. </li>
<li><code>String... | Use a new StringBuilder whenever you need a new StringBuilder.
Anything else is probably breaking encapsulation and leaves you open to the undesired side-effects of sharing an object.
Also, I'd suggest using AppendFormat() instead of plain Append().<br>
You're constructing a fairly complex (and, I assume, format-se... | https://softwareengineering.stackexchange.com |
336,413 | [
"https://physics.stackexchange.com/questions/336413",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/140152/"
] | If we throw something upwards with some initial velocity (of course), then it's the same whether the acceleration upward is considered positive or negative, right?
But by convention, the upward direction is considered positive. That's good, but see-
In that case, if initial velocity is 20m/s and g=10m/s², then the dis... | Suppose we adopt the convention that a distance upwards is positive and a distance downwards is negative. Velocity is given by:
$$ v = \frac{dx}{dt} $$
So if the object is moving upwards its position increases, i.e. gets more positive with increasing time so $dx \gt 0$ and $dt \gt 0$. That means an object moving upwa... | Yes ... It matters .. If u take the positive y axis upward then acceleration due to gravity is downwards .. And vice versa... Because if we take the +y axis upwards .... When we throw a ball upwards velocity is positive... and as we know that the gravity acts downwards it stops the motion of the ball in the sense .. It... | https://physics.stackexchange.com |
140,401 | [
"https://security.stackexchange.com/questions/140401",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/128172/"
] | Currently I am developing an SSO system with CAS. CAS uses an ticket granting ticket (TGT) that can be seen as the SSO-session. CAS by default will encrypt the TGT. And by default you also have HTTPS among the nodes.
Since HTTPS already deals with encryption I don't get why I need to encrypt the value of the cookie (T... | Its correct that usually in accessing ssl encrypted website you don't need encrypt cookies normally , But its about even if someone somehow hijacked your ssl connection , the TGT should be unusable to that person.
As in the SSO scenarios things changes a lot .
<strong>Authentication Process / Request Flow</strong>
... | Cookies stay in the browser. And if they have some sensitive information stored, they should be encrypted. Though I will argue that any sensitive information should not be stored in the cookies.<br>
And encrypting session ID(which is already a random value) doesn't make sense at all. And if you are using some user info... | https://security.stackexchange.com |
220,740 | [
"https://mathoverflow.net/questions/220740",
"https://mathoverflow.net",
"https://mathoverflow.net/users/15242/"
] | I've encountered a strange situation while thinking about modular curves... Consider the modular curve $Y(3)$ parametrizing elliptic curves with a symplectic basis for their 3-torsion. This curve has degree 12 over the $j$-line $Y(1)$. Let $y\in Y(1)$ be a $\mathbb{Q}$-rational point, then its fiber in $Y(3)$ has degre... | $\newcommand{\QQ}{\mathbb{Q}}$
$\newcommand{\ZZ}{\mathbb{Z}}$
Okay, so the solution appears to be this (Thanks to Ari Shnidman, Joseph Silverman, nfdc23, and eric for their comments)
Fix an $N\ge 3$. Let $y\in Y(1)$ be a $\QQ$-point, then the fiber $Y(N)_y$ of $Y(N)$ above $y$ is a $\QQ$-algebra $A$ of degree $d_N :=... | I think there are two issues. One, as Ari noted, your triple $(E^d/K,P(d),Q(d))$ is not really defined over $K$, since the action of Galois is twisted by the character of $K(\sqrt d)/K$. But more importantly, you're not really getting different points on $Y(3)$, because the points of $Y(3)$ classify up to $\overline K$... | https://mathoverflow.net |
2,851 | [
"https://chemistry.stackexchange.com/questions/2851",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/1031/"
] | I can understand redox equations of the following form, I break these down into half equations and combine them.
$$\ce{MnO4^- + C2O4^{2-} -> Mn^{2+} + CO2}$$
Where I have issue is with the following (unbalanced) equation:
$$\ce{H2 + NO -> NH_3 + H2O}$$
I am asked to show balanced half equations and the final ... | <strong>Assuming this reaction is taking place in aqueous phase</strong>, you can follow the conventional 7 steps for balancing redox reactions although this one does require some extra thoughts.<br>
I will be writing the equation as it should be after each step.
<hr>
$$\ce{H2 + NO -> NH3 + H2O}$$
<h3>Step 1: Ion... | I sympathise with your problem using electron half equations when one of the reactants produces two different products. For this reason and the fact that (as the previous answer points out) there are no ionic compounds invoved, I prefer to use oxidation number half equations.
<strong>Oxidation half equation:</strong> ... | https://chemistry.stackexchange.com |
501,758 | [
"https://stats.stackexchange.com/questions/501758",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/305435/"
] | Suppose <span class="math-container">$X \sim N(\mu, \sigma^2)$</span>, is there a general way to describe the distribution (i.e. mean, variance, ...) of <span class="math-container">$Y=X^n$</span> for some constant <span class="math-container">$n$</span>?
(assume <span class="math-container">$\mu \in (0,1)$</span> and ... | Let <span class="math-container">$Z_n := Z := g(X) := n X^n$</span>. The relation between <span class="math-container">$Z$</span> and <span class="math-container">$Y$</span> is quite simple (one is a scaled version of the other). Let's figure out the distribution of <span class="math-container">$Z$</span>. Assume for s... | Far from an answer in general, but there is a formula for <span class="math-container">$\text{E}[X^n]$</span> if <span class="math-container">$\mu=0$</span>. Then we have
<span class="math-container">$$
\text{E}[\text{X}^n] = \begin{cases}0\,, & n \text{ odd }\\ \sigma^n(n-1)(n-3)\cdot\ldots\cdot 1\,, & n \te... | https://stats.stackexchange.com |
208,325 | [
"https://dba.stackexchange.com/questions/208325",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/147416/"
] | I have the following table in my database:
<pre><code>create table [dbo].[tb_StatusLog](
[RequestID] [int] not null,
[statusID] [int] not null,
[startTime] [datetime] not null,
[endTime] [datetime] null,
)
</code></pre>
with the following non-clustered index
<pre><code>create nonclusteredindex [index1] on [dbo].[tb_... | Because you have an equality predicate on <code>where statusID=2</code>.
With the reversed order it is able to seek into exactly the rows matching the status and these can then feed into a stream aggregate to do the grouping.
Your original index supports the <code>group by requestID, statusID</code> but not the <code... | Somewhat simplified, but you can think of a composite index as if rows are ordered first by the first column, second by the second column and so forth. Your first example would be:
<pre><code>requestID statusID
----------------------
-> A 1
| A 2
v A 3
B 1
... | https://dba.stackexchange.com |
7,761 | [
"https://security.stackexchange.com/questions/7761",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/396/"
] | There seems to be some misconceptions regarding what a switched network will protect us from, and what technologies/precautions a secure environment requires when segmenting trusted users from hostile users.
Can anyone elaborate on what the real risks of switched networks, and if there are any real benefits from a se... | <strong>Switches are not meant for security.</strong> A switch differs from a hub in that it observes packets to deduce where each host is, so that a packet aimed at a given host will be written only on the physical cable leading to that host. This is a <em>performance optimization</em> in that it allows more traffic t... | There are three networking devices: a hub, a switch, and a router. They operate at Physical, Data access, and Network layers respectively. Nodes connected to a hub are in the same network domain, and in the same collision domain. Nodes connected to a switch are in the same network domain, but not in the same collision ... | https://security.stackexchange.com |
498,630 | [
"https://electronics.stackexchange.com/questions/498630",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/249622/"
] | What is the relation between the impedance of lumped components and the characteristic impedance of transmission lines?
I have noticed that in some cases transmission lines are loaded with lumped components (e.g. for matching) and in some other cases they are loaded with other transmission lines (characteristic impedan... | <blockquote>
I have noticed that in some cases transmission lines are loaded with lumped components (e.g. for matching) and in some other cases they are loaded with other transmission lines (characteristic impedances).
</blockquote>
In that case, you have seen cases where the designers were trying to do specific thi... | trivially, Zo = [sqrt ( L / C)
which comes from constants needed in the wave equations.
In early work (the 1880s) Oliver Heaviside and his brother showed loading coils, placed in parallel between the two wires of a telegraph system, would usefully expand the bandwidth.
| https://electronics.stackexchange.com |
348,049 | [
"https://softwareengineering.stackexchange.com/questions/348049",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/13382/"
] | I work on a large software program in financial services. (15 project managers, 20 technical leads, 15 environments, 150 people on the technical side).
We do lots of Bankwide integration to hundreds of systems (insurance, bill payment, mutual funds, insurance, tax reporting, equities trading etc), which are frequentl... | It depends what kind of issues you are facing. "Fixing the environment" is somewhat vague, and lack of precision in describing the problem might in itself be a reason it is hard to get solved. If the problem is unclear it is also unclear who is responsible for fixing it.
You have to break the perceived problems into ... | The best strategy I have seen is an old fashioned one.
Hire an OPs dept and make it their job to keep the servers up.
Sure this doesn't work in a startup, where devs have to, and want to, do everything. But it works very well in a large company with large systems where you want to hire 'unit of work' devs who just wr... | https://softwareengineering.stackexchange.com |
251,794 | [
"https://security.stackexchange.com/questions/251794",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/260506/"
] | I would like to provide some free tokens to users on registration, I don't want bot accounts to register and get free tokens. Is there any way to prevent this?
I would like to use phone verification, but I am not sure if it's obsolete. I was able to find services that provide virtual numbers such as Twilio. So not sure... | No. There are no guarantees.
There are lots of things that can make it more difficult for bots to register, but as you said, you have to balance that against the inconvenience to your users.
The better option is to be ok with some bots getting free tokens or to change your business model so that this is not an issue fo... | Many users are reluctant to provide a phone number - for good reasons. Unless this is part of the registration process and already accepted by the users.
Indeed virtual/disposable phone numbers are readily available, even for free. Phone verification is not foolproof.
Have you tried available options like captcha ? Unl... | https://security.stackexchange.com |
631,469 | [
"https://electronics.stackexchange.com/questions/631469",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/320055/"
] | I'm a novice who's looking for a very basic oscilloscope. I found some on Ebay. Probably I'm much too careful, but I'm wondering if cathode ray screens from oscilloscopes of the 80s may leak dangerous levels of X-rays or if a broken case could increase the radiations.
| That's not "very old" in terms of CRTs, but anyways:
your concerns aren't unfounded. CRTs <em>do</em> leak X-rays. However, the amount and hardness of the radiation scales with size of the CRT. And with an oscilloscope display, you're at the least end of all this, so, even if the protection isn't as good as i... | The anode voltage in a cathode ray oscilloscope is a few thousand volts. X-rays aren't produced until the that voltage exceeds 20 kV or more. That only happened in color televisions. Your oscilloscope will not produce X-rays.
| https://electronics.stackexchange.com |
544,678 | [
"https://physics.stackexchange.com/questions/544678",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/236734/"
] | When we study we usually refer to quantities in terms of differentials, why is this?
Secondly how do we get an intuitive idea of how to deal with the infinitesimal quantities involve? Like what is the right perspective to look at these things from? It is quite different from most physics I have encountered so far.
| Great question! I remember being mystified with the elusive nature of thermodynamics and its formalism. But the fact of the matter is that like most (if not all) of physics, at the core of it, they’re just differential equations.
To look at this the first and fundamental thing to note is that thermodynamics is a stud... | I guess most of the time you are interested in understanding how a system's, for example, internal energy change as you change the volume. On the other hand, some quantities such as internal energy or enthalpy are independent of the way you change the system so therefore like gravitational potential energy they only de... | https://physics.stackexchange.com |
291,336 | [
"https://softwareengineering.stackexchange.com/questions/291336",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/29411/"
] | I have two web applications, say Application_1 and Application_2.
<code>Application_2</code> has a database table named <code>table_2</code>, which changes infrequently, and needs to be accessed by <code>Application_1</code>.
Does it make sense to create a <code>table_2</code> table in <code>Application_1</code> and ... | Since you tagged the question with SOA, I suspect that you're thinking the right answer might be using a service interface. Such a service interface should not expose the data, but the functionality you want to provide as a contract to be exposed by one application and consumed by the other application.
As the ques... | The best way is to make the REST api but copy data over in a scheduled job. Sharing databases should always be avoided between solutions. Remember we don't share toothbrushes and connectionstrings.
By exposing the inner workings of the db you lock the cadance of both apps to each other and neither of them can have the... | https://softwareengineering.stackexchange.com |
113,414 | [
"https://electronics.stackexchange.com/questions/113414",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/30084/"
] | I'm working with the DYP-ME007Y ultrasonic sensor for a project and I bought two off eBay. Both seem to work however they have this 'unknown' twistable part which is in a different position of rotation on both. I have a suspicion it is a trim pot of some description, but I would like to make sure. It could possibly be ... | Looks like a variable inductor to me. The black circle is the top of a ferrite core that changes position within the coil.
| This is variable transformer. Primary winding goes from frequency generator, secondary winding forms resonance circuit with piezo element (ultrasound transducer).
| https://electronics.stackexchange.com |
5,380 | [
"https://bioinformatics.stackexchange.com/questions/5380",
"https://bioinformatics.stackexchange.com",
"https://bioinformatics.stackexchange.com/users/260/"
] | I have an output from vcfutils.pl vcf2fq with specified minimal depth, and it means that nucleotides with not enough depth are lowercase.
I would like to change them to gaps. I could do it in higher language but I would like to know the solution in bash.
I have found simple solution to replace all lowercase to upperc... | The following <code>sed</code> command will do the trick.
<code>sed -e '/^[^>]/ s/[a-z]/\-/g' in.fna > out.fna</code>
Lines starting with <code>></code> will be escaped and the lowercase characters will be replaced with <code>-</code> .
| You could try it with <code>sed</code>.<br>
Replace all lower-case chars with <code>-</code> in lines not starting with <code>></code>:
<pre><code>sed -e '/^>/!s/[a-z]/-/g' in.fa
</code></pre>
| https://bioinformatics.stackexchange.com |
1,943,733 | [
"https://math.stackexchange.com/questions/1943733",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/349576/"
] | Find the number of integers $1\leq x \leq 2010 $ such that the expression
$\sqrt[3]{x+(x+8)\sqrt\frac{x-1}{27}}-\sqrt[3]{x-(x+8)\sqrt\frac{x-1}{27}}$
is a rational number
NOTE -> I <strong>LITERALLY</strong> do not understand where to start !! HELP ME!!
| In case it's required, it's not too hard to show Abdallah's identity:
\begin{align*}
\lim_{x\to 0} \frac{1-\cos x}{x^2}
&= \lim_{x\to 0} \frac{1-\cos x}{x^2}\cdot \frac{1+\cos x}{1+\cos x} \\
&= \lim_{x\to 0} \frac{1-\cos^2 x}{x^2}\cdot \frac{1}{1+\cos x} \\
&= \lim_{x\to 0} \frac{\sin^2 x}{... | Using the follow formula:
$$\cos 3x-\cos x=-2\sin 2x \sin x$$
\begin{align}
\lim_{x\to 0}\frac{\cos 3x-\cos x}{x^2}=\lim_{x\to 0}\frac{-2\sin 2x \sin x}{x^2}=-4
\end{align}
Or,you can use L'Hospital directly.
| https://math.stackexchange.com |
19,538 | [
"https://electronics.stackexchange.com/questions/19538",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5764/"
] | I am trying to make a very simple BUTTON (simple wire RED/YELLOW only). Now if the Button is pressed (RED touch YELLOW) i want to receive input signal in my Java application (that button was pressed).
In which ports of RS233(DB9) i should patch the RED/YELLOW wire? So that any button pressed i get in my application in... | At best this is going to be a kludge. RS-232 is for serial communication, not for digital input lines. However, if you want a single input line that can be read by the software then the modem line intended to tell the computer there is a incoming call could work. Depending on what access your software has to the ser... | If you connect one side to RTS (pin 4) via a large resistance (e.g. 47k or 100k) and to RX (pin 3), and the other side to +9V, you'd probably get a "break" signal when the button is pressed, which can be detected in software.
Unfortunately, there's no pin on the RS-232 connector which normally has a valid positive RS-... | https://electronics.stackexchange.com |
537,859 | [
"https://physics.stackexchange.com/questions/537859",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/132956/"
] | According to my book the spring constant is given by <span class="math-container">$k=V''(X_o)$</span>. Where <span class="math-container">$V(X)$</span> is the potential energy function. if I use the function <span class="math-container">$V(X)=X^6+X^4$</span> the spring constant is zero at <span class="math-container">$... | <blockquote>
But in low speeds occasions the effects of relativity should be incrediblely small, why we still have to consider it?
</blockquote>
The effects of relativity are very small but the effects of electromagnetism are huge! It takes only a very small excess of charge to have an enormous electrostatic effect.... | 1.Special Relativity doesn't fully explain the relation between electric fields and magnetic fields. It explains some occasions.
2.Relativistic effects are neglible but the electrostatic force is just very strong with little effects we can see consequences.
3.No mass and charge are not even close to similar. Charge i... | https://physics.stackexchange.com |
1,523,842 | [
"https://math.stackexchange.com/questions/1523842",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/284696/"
] | I was wondering how the ordinary expectation value $E(X)$ is related to $E(X|\mathcal{F})$ where $\mathcal{F} \subset \mathcal{E}$ where the latter is supposed to be the sigma algebra on our probability space.
My first thought was that $E(X|\mathcal{E}) = E(X),$ but this is clearly wrong, as $X$ is $\mathcal{E}$ measu... | Assume $a>0$ and think like this: $$x^2 = a \stackrel{\sqrt{\cdot}}{\implies} \sqrt{x^2} = \sqrt{a} \implies |x| = \sqrt{a} \implies x = \sqrt{a} \text{ or } x = -\sqrt{a}.$$
| even simpler $x^2=a\Rightarrow (\pm x)^2=a\Rightarrow \pm x=\sqrt{a}\Rightarrow x=\pm \sqrt{a}$
| https://math.stackexchange.com |
169,244 | [
"https://stats.stackexchange.com/questions/169244",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/71358/"
] | I would like to assess a single time-series for a changing variance structure that might be leading to spurious variance estimates when that time-series is used in regression.
In my head two terms come to mind: (1) Heteroscedasticity and (2) Volatility Clustering
Here are my <em>related</em> questions on this:
<ol>... | <strong>1.</strong> I would say, heteroskedasticity can characterize original series, too. Suppose the variance of the original series was $\sigma_1^2$ from time $t_1$ to $t_k$ and turned to $\sigma_2^2$ since $t_{k+1}$. I would call that heteroskedasticity. Conversely, volatility clustering can characterize model resi... | 1) Heteroscedasticity is related to non-constant variance of the errors GIVEN that Volatility Clustering does not exist or has been remedied via Level Shift Detection Procedures ( Intervention Detection Procedures ) and model parameters are found to be inavariant over time and that other error mean-adjustment procedure... | https://stats.stackexchange.com |
5,513 | [
"https://softwareengineering.stackexchange.com/questions/5513",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/2926/"
] | In the past I have worked with designers, BAs and project managers, all who regularly produce project artifacts, yet very really do they understand the concept of versioning. When I try to explain it to them (even in its most simple form of multiple differently named files) they seem to have some kind of mental block.... | This is because the human has difficulties projecting himself in time.
Use the time machine analogy. Your life is versionned. Every day you have a new version of your life: new things and lost things. Hopefully more assets, less debts,... but more fat, less hairs, ... hopefully more knowledge, less doubts, ....
Then ... | Because, in the non-programming world, to change a competed product is very hard. Intentional changes, which are thought through, are not easy—take buildings, for example. And once the changes are made, it's hard to "revert" to previous version.
Contrary to that, changing software is very easy (easier than even othe... | https://softwareengineering.stackexchange.com |
273,006 | [
"https://physics.stackexchange.com/questions/273006",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/125265/"
] | The following are facts of the prevailing cosmological model.
<ol>
<li>The age of the universe is about 13.772 billion years.</li>
<li>Nothing with mass can exceed the speed of light.</li>
<li>The diameter of the observable universe is 28.5 gigaparsecs, i.e. 93 billion light-years.</li>
</ol>
How could two particles... | Lets assume you have to explain the truth without any complications to your friend.
Firstly, give your friend some introduction and draw some analogy between physics terms and some nicer terms.
"Space is like a piece of cloth, a fabric which can stretch. There are some godly powers, forces which keep stretching the ... | <blockquote>
Is it possible to explain this seeming contradiction in a way that appeals to reason and doesn't require a pencil and paper?
</blockquote>
I think so, but it does require some imagination/visualization (and perhaps a better explanation than I can provide).
<blockquote>
How could two particles never e... | https://physics.stackexchange.com |
142,951 | [
"https://security.stackexchange.com/questions/142951",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/15194/"
] | I was considering setting up my own mail server and one of the things I've read about is that I must setup reverse DNS to do not get caught by a spam filter.
Is that really a must? Aren't SPF and DKIM enough to prevent be labeled as spam?
| Your question,
<blockquote>
"Is having a PTR record a must for sending mail servers?"
</blockquote>
is not that easy to answer fully.
<blockquote>
Is it an requirement to be able to send mail?
</blockquote>
No, you can send mail from any address.
<blockquote>
"Can SPF and DKIM can replace a PTR record?"
</b... | Standards don't require PTR to send mail, but the real servers that receive mails quite frequently require valid PTRs. Why? To partially eliminate botnets' spam. PTRs are quite hard to obtain with some inexpensive network providers and by conjecture, many botnet members wouldn't have a valid PTR.
All the other DNS rec... | https://security.stackexchange.com |
3,958,915 | [
"https://math.stackexchange.com/questions/3958915",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/865124/"
] | I have to prove that the sequence <span class="math-container">$a_{k+1}=\frac{5a_k}{2+a_k}$</span> with <span class="math-container">$a_0=1$</span> is convergent.
I think I can use the Monotone Convergence Theorem for this, but I can't show that it is bounded and convergent inductively.
| Note that <span class="math-container">$\frac{a_{k+1}}{a_k}=\frac5{2+a_k}$</span> is greater than <span class="math-container">$1$</span> when <span class="math-container">$-2<a_k<3$</span>. Since <span class="math-container">$a_0=1$</span>, it’s clear that <span class="math-container">$a_k>0$</span> for all <... | <span class="math-container">$$\dfrac{1}{a_{n+1}}=\dfrac{2+a_n} {5a_n}=\dfrac{2}{5a_n}+\dfrac{1}{5}$$</span>
Let <span class="math-container">$b_n = \dfrac1{a_n}$</span>. Then <span class="math-container">$$b_n = \frac25 b_{n-1} + \frac15$$</span> with <span class="math-container">$b_0 = 1$</span>, so
<span class="mat... | https://math.stackexchange.com |
82,889 | [
"https://mathoverflow.net/questions/82889",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9342/"
] | <blockquote>
Does there exist an infinite order element $\phi\in Out(F_n)$, for some or all $n\geq 3$, which is not iwip but has finite index in its centralizer? How about an element such that all its non-zero powers have this property?
</blockquote>
Motivation: iwip elements are Morse (i.e., roughly speaking, all q... | There is a Nielsen-Thurston type method due to Feighn and Handel which is useful for approaching this question. The method is laid out in the papers arXiv:math/0612702 and arXiv:math.GR/0612705 by Feighn and Handel, "The recognition theorem for $Out(F_n)$ and "Abelian subgroups of $Out(F_n)$". It is an outgrowth of the... | The mapping class group question has a solution using Nielsen-Thurston theory, which goes like this. If $\phi \in MCG(S)$ is pseudo-Anosov and if $\Lambda$ is the stable or unstable lamination of $\phi$ then the subgroup of $MCG(S)$ that preserves $\Lambda$ and has stretch factor 1 on $\Lambda$ is a finite group (there... | https://mathoverflow.net |
485,552 | [
"https://electronics.stackexchange.com/questions/485552",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/162422/"
] | I have a question when designing a circuit.
I want to power two sensors with a 3.3V LDO.
My question is the following, in the LDO datasheet they recommend me to place a 10uF capacitor at the output of this one, but in the datasheet of each sensor, they recommend me to use 10uF and 0.1uF capacitors.
My question is, do... | The datasheets tend to play safe and show a typical circuit that should work in most cases. The datasheets can't know what other components there are, what their requirements are and what is the distance between components.
As you don't mention either what components you have and what is the distance between them, the... | Put a 100nF as close as possible to each pin that requires one, if that means multiple parallel capacitors then so be it. For larger capacitors like 10uF where high frequencies are less important, you can usually use a single capacitor for multiple devices and then put them a little further out of the way.
| https://electronics.stackexchange.com |
52,946 | [
"https://security.stackexchange.com/questions/52946",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/41624/"
] | We are planning to deploy HSM with our application.
The solution we are thinking is :
<hr>
<ul>
<li>Mobile applications talks to server application, </li>
<li>Server application talks to HSM for authentications, encryption, decryption</li>
</ul>
Clients are mobile application(Android, J2ME etc.) which communicates... | Using OpenPGP smartcards, the key will be generated <em>on the smartcard</em> using its own cryptoprocessor. The key never needs to leave the card (you might do so for backup purpose).
If it leaks, there are two possibilities:
<ol>
<li>It is a subkey. You revoke it using your main key and create a new one. Barely nob... | When using a smartcard, this is usually a bad idea to generate a <strong>signature</strong> key with an external device. It dramatically increases the risk of key leaking. Of course you can mitigate these risks by using an offline computer or storing the backup into a safe but it is always more secure to generate the k... | https://security.stackexchange.com |
201,529 | [
"https://softwareengineering.stackexchange.com/questions/201529",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/87835/"
] | I took a test recently and found that I could touch type comfortably at around 100 wpm... and if given some sort of autocorrect/intellisense then that would be even faster (who knows maybe 150 wpm?)...
I definitely do not program anywhere near that speed... This led me to wonder how exactly does one become faster at p... | Some very pessimistic answers here. I can speak from personal experience that it is absolutely possible to touch-type programming. But that's not really the issue, right? I mean you're REALLY asking "how can I be a more productive programmer?" Let's take a look at some of the factors:
<ol>
<li>How verbose the language... | You're never going to be able to solve new problems as fast as you can type. Just accept that. It might work for simple problems you've already done 1000 times.
But there is still value in typing skills. Muscle memory typing allows you to keep your mind in the problem, not on the keyboard. Your mind stays in the zone ... | https://softwareengineering.stackexchange.com |
2,950,011 | [
"https://math.stackexchange.com/questions/2950011",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/581242/"
] | The difference <span class="math-container">$$\log(2)-\sum_{n=1}^{100}\frac{1}{2^n n}$$</span> is
(1) less than <span class="math-container">$0$</span>
(2) greater than <span class="math-container">$1$</span>
(3) less than <span class="math-container">$\frac{1}{2^{100}101}$</span>
(4) greater than <span class="ma... | Use the fact that<span class="math-container">\begin{align}\log(2)&=-\log\left(\frac12\right)\\&=\frac12+\frac1{2\times2^2}+\frac1{3\times2^3}+\cdots\\&=\sum_{n=1}^\infty\frac1{n2^n}.\end{align}</span>
| You could also determine the value of the summa by using the polylogarithm functions:
<span class="math-container">$\sum\limits_{n=1}^{\infty}\frac{1}{2^n\,n}=\sum\limits_{n=1}^{\infty}\frac{{\big(\frac{1}{2}}\big)^n}{n}=Li_1(\frac{1}{2})=\ln2$</span>
| https://math.stackexchange.com |
83,432 | [
"https://physics.stackexchange.com/questions/83432",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/12995/"
] | From basic airfoil theory the following free body diagram can be determined for a two dimensional asymmetric airfoil:
<img src="https://i.stack.imgur.com/MlDJx.png" alt="enter image description here">
Here the direction of the resultant force is governed by the geometry of the airfoil section.
However, I'm unsure ... | The direction of the Resultant force $R$ is always dependent on the direction of the $V\infty$
But however, the direction/orientation of the Normal force $N$ is dependent on the orientation of the body itself ($N$ is perpendicular to the body and axial force $A$ is parallel to the body.)
In the above case, since ther... | That would sure make it easy to figure out the drag on the flat plate if you knew the lift: $$ D = R \sin(\alpha)$$ and $$ L = R\cos(\alpha)$$ so that $$D = L \tan(\alpha)$$ and the lift to drag ratio is simply $$\frac{L}{D}=\cot(\alpha)$$ Common sense should tell you that can't be right. Back to reality...
| https://physics.stackexchange.com |
11,600 | [
"https://physics.stackexchange.com/questions/11600",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/2146/"
] | For a system of $N$ particles with $k$ holonomic constraints, their Cartesian coordinates are expressed in terms of generalized coordinates as $$\mathbf{r}_1 = \mathbf{r}_1(q_1, q_2,..., q_{3N-k}, t)$$ $$...$$ $$\mathbf{r}_N = \mathbf{r}_N(q_1, q_2,..., q_{3N-k}, t)$$
Each particle in space can be uniquely identified ... | The generalized coordinates of a system of $N$ particles apply to the system as a whole, not the individual particles, and accordingly they can (and often do) combine the coordinates of multiple particles.
One common example is that of two-body orbital motion: one generalized coordinate is the position of the center o... | The $k$ holonomic constraints are used to eliminate $k$ $q$s, so reducing their number from $3N$ to $3N-k$. This then introduces the dependence of some of the transformation equations on t and other $q$s.
You have k holonomic constraints of the form $$\mathbf{f}_1(q_1, q_2,..., q_{3N},t) = 0$$ $$...$$ $$\mathbf{f}_k(q... | https://physics.stackexchange.com |
432,049 | [
"https://physics.stackexchange.com/questions/432049",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/208138/"
] | We know average velocity in its strictest sense, means total displacement over total time taken: <span class="math-container">$$\frac{X_f-X_i}{T_f-T_i}$$</span>
There's a special case, when a body is moving in a straight line with a constant acceleration. Of course since its acceleration is constant, it has to be a re... | You are mixing things. Those formulae are not the same; the problem is that you are using the same symbols, but the meaning is different.
For the rectilinear uniformly accelerated movement, you use
<span class="math-container">$$v_{average}=\dfrac{v_{initial}+v_{final}}{2}$$</span>
Whereas ni the other case, you use... | It's incorrect to use the word "only". (1) is always valid if acceleration is constant, but that doesn't exclude the other situation. It still can be valid in certain special situations.
| https://physics.stackexchange.com |
576,261 | [
"https://physics.stackexchange.com/questions/576261",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/270597/"
] | <blockquote>
Consider a circular loop kept in a time-changing magnetic field. We know, via Faraday Law, that EMF is induced across the loop and hence a current appears in the loop. Let there be some Resistance given in the wire. Then heat will appear in the circuit.
</blockquote>
How does heat energy appear in the circ... | The heat comes from current flowing through the wire, since we are told the wire has resistance. So it's just like your usual DC circuit with heat being dissipated in a resistor caused by charge carrier collisions with the molecules of the resistor.
The energy comes from whatever is causing the varying magnetic field. ... | Okay let's start with the changing magnetic field. We know that in the region of time varying magnetic field , electric field is induced and ( they have some energy released by the source and it depends on the process involved in bringing the change) and when a coil is placed in this region then the electrons experienc... | https://physics.stackexchange.com |
9,713 | [
"https://dba.stackexchange.com/questions/9713",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/5114/"
] | CUSTOMER:
<ul>
<li>CustomerID (PK)</li>
<li>Name</li>
<li>Email</li>
</ul>
PAYMENT:
<ul>
<li>PaymentID (PK)</li>
<li>Amount</li>
<li>Date</li>
</ul>
PRODUCT:
<ul>
<li>ProductID (PK)</li>
<li>Type</li>
<li>Name</li>
<li>Price</li>
</ul>
PURCHASE:
<ul>
<li>CustomerID (FK)</li>
<li>PaymentID (FK)</li>
<li>ProductI... | If it were me, I would make two changes:
1) Create a "PurchaseID" field on the "Purchase" table (which can double as an order number for your customers to reference).
2) Move "Quantity" to a new table called "Purchase_Line" for each line (item) on the order (purchase). Otherwise, you're going to repeat the CustomerI... | If you were to use the key as a verbal reference then yes, I agree with you. But I had assumed that it would just be a unique identifier for the data.
| https://dba.stackexchange.com |
1,023,099 | [
"https://math.stackexchange.com/questions/1023099",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/142293/"
] | I want to compute the variance of a random variable $X$ which has hypergeometric distribution $\mathrm{Hyp}(n,r,b)$, where $n$ is the total number of balls in the urn and $r$ and $b$ are the numbers of red/black balls, by using the representation
$$X= I_{A_1} + \cdots + I_{A_n}$$
($I_A$ is the indicator function of ... | $\newcommand{\var}{\operatorname{var}}\newcommand{\cov}{\operatorname{cov}}$
The variance of $I_{A_1}+\cdots+I_{A_n}$ is trivially $0$ since the sum is $r$ with probability $1$.
But suppose there had been more than $n$ balls in the urn, so that it would not be certain that every red ball had been drawn after $n$ tria... | <strong>Outline:</strong> I will change notation, to have fewer subscripts. Let $Y_i=1$ if the $i$-th ball is red, and let $Y_i=0$ otherwise.
We are picking $n$ balls. I will assume that (unlike in the problem as stated) $n$ is <strong>not necessarily</strong> the total number of balls, since that would make the probl... | https://math.stackexchange.com |
147,209 | [
"https://dba.stackexchange.com/questions/147209",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/16668/"
] | (I use sql server 2015)
In my Orders table Postal Code is a <code>varchar</code>.
I want to do a search like this:
<pre><code>SELECT distinct email
FROM [dbo].[tb_Order]
where postalCode in (20004,20528,20260,20529,22060,22181,20708)
</code></pre>
(with many more zip codes)
I do not want to have to convert the... | If you're actually using Sql Server 2016, you can probably use the new STRING_SPLIT command to create a 'table' to join against. Just put your comma delimited integers in the STRING_SPLIT command. Here is an example.
<pre><code>declare @tb_Order table (col1 int, postalcode varchar(5))
insert into @tb_Order values(1,... | For most Microsoft SQL versions (tested on 2005+) this will work (using Microsoft's demo "AdventureWorks" DB as a lab source):
<pre><code>SELECT DISTINCT [PostalCode]
FROM [Person].[Address]
WHERE
isnumeric([PostalCode]) = 1
AND [PostalCode] IN (61953, 29910, 78100);
</code></pre>
The main issue is that we need to ex... | https://dba.stackexchange.com |
35,249 | [
"https://mechanics.stackexchange.com/questions/35249",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/19901/"
] | For very large bolts (example: axle nut) I often see mechanics just use an impact wrench, typically they let it "rattle" a certain time and then they consider the bolt tightened. Is this also common/considered acceptable practice in other shops/locations? For smaller bolts or applications like head bolts, alloy rims an... | Neither.
Just get a 1m long bar (by extending a breaker or similar), stick it on the nut so that it is <strong>horizontal</strong> and simply hang 250N of mass at the end of it: (*)
250N = 56.2 lbs = 25.5 Kg
250N * 1m = 250Nm
Rinse and repeat until it hangs and doesn't tighten the nut anymore. The trick is to keep ... | To answer your question directly, this is a "standard practice" but a <strong><em>VERY</em></strong> poor one. Getting the correct torque is by far more important than getting it done quickly.
With the axle nut it is imperative you tighten it to the correct spec. If you tighten it too tight, the wheel bearing will se... | https://mechanics.stackexchange.com |
143,160 | [
"https://dba.stackexchange.com/questions/143160",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/48659/"
] | We have an ERP system that is a little less than modern, the backend is currently sitting on a SQL Server 2008 R2 installation. We have through mandate of management (isn't that always the case) the completely impractical practice of allowing many users to extract data from this system at will for the purposes of manip... | Unfortunately, we've dealt with too may issues with this where I work. In cases where this has been a problem, people who don't know databases, literally open a SQL table "live" in MS Access. At first things can appear transient because they may open and close Access quickly. But then there are those moments where they... | I have same environmental vulnerability, albeit at smaller scale: Many users connect with their preferred front-end such as MS Access via ODBC, inadvertently locking SQL tables and views even when user has SELECT ONLY.
Happily much avoidance of blocks seems feasible following a mandate that these users also install... | https://dba.stackexchange.com |
79,684 | [
"https://security.stackexchange.com/questions/79684",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/58446/"
] | So, I understand DoSing to an HTTP Server. I understand Layer 7 DoS attacks and how to even make these work.
But what for an normal IP that isn't HTTP and is connected to the internet. Is the only way to attack them is by a bandwidth DDoS, which can be only done by more than 1 computer?
Pretend, I had my next door ne... | To use the kernel's crypto module to initialize the partition/disk do this:
<pre><code>cryptsetup create --key-file=/dev/urandom eraseme /dev/sde
dd if=/dev/zero bs=1M of=/dev/mapper/eraseme
cryptsetup remove eraseme
</code></pre>
This initializes a crypto mapping named <em>eraseme</em> spanning the partition/disk us... | <code>/dev/urandom</code> is basically just a stream cipher, only with periodic reseeding from its entropy sources to protect against its state or entropy sources becoming compromised.
Given that it's extremely unlikely the state of your cipher will become compromised while you initialize the disk, that if this happen... | https://security.stackexchange.com |
95,032 | [
"https://security.stackexchange.com/questions/95032",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/81904/"
] | Let say my local system's shell prompt is in this format: <code>myname@mysurname:~$</code>
Is it logged in some server when I login there via SSH/FTP? Or is it completely private information?
| No, not by default. When setting up a connection no local username will be send over to the server, only the username / password needed to connect to that server.
They can try to find this out by using something like <code>finger</code> once you have connected, but since you would have to have <code>fingerd</code> run... | If it's SSH, then normally your connection is encrypted end-to-end. With FTP it would depend on if it's plain ftp (unencryped), SFTP (FTP using SSH, which is encryped) or FTPS (FTP using SSL/TLS, which is also encrypted).
In case of plain FTP, it would definitely leak your username, password and any other information... | https://security.stackexchange.com |
47,671 | [
"https://physics.stackexchange.com/questions/47671",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/17201/"
] | I'm a pure mathematician by trade, and have been trying to teach myself A-level mechanics. (This <em>is not</em> homework, it is purely self-study.)
I've been working through the exercises and have come up against a stubborn problem. Here it is:
<strong>Question</strong>
A train of mass 150 tonnes is moving up a str... | You're very nearly there.
You're correct to say that $Power = Fv$, and that the velocity at the moment the train reaches the top of the slope is given by $v_\text{top} = 350/(6 + 150g\sin2)$ so the force at the top of the slope is $F_\text{top} = 1000(6 + 150g\sin2)$.
But the acceleration is the <em>net</em> force di... | For simplicity imagine you're in the frame where the train is moving at 0 velocity.
When track changes to horizontal, you can picture this as the gravitational force disappearing -- or an additional force acting on the train with magnitude $F_g\sin(\theta)$.
At this instant, this is the net force on the train.
| https://physics.stackexchange.com |
4,698 | [
"https://stats.stackexchange.com/questions/4698",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/2052/"
] | I have two models $M_1$ and $M_2$ that I am using to try and compare to observed data $D$. $M_1$ is an $n_1$-dimensional model, and $M_2$ is an $n_2$-dimensional problem. The Bayes factor $K$ to compare the models can be calculated using:
$K = P(D|M_1)/P(D|M_2) $
assuming no prior preference for either model. The nu... | Yes, you can do that. However, your I'd like to play with your formulas a little bit.
If the model is determined by the parameters, than $P(D|M_i)=\int P(D|w,M_i)P(M_i|w)*P(w)dw$ should be more appropriate. Since I guess the model is determined by the parameters in a deterministic (instead of stochastic) way, the form... | Model evidence $P(D|M_i)$ can be viewed as an expectation of $P(D|w, M_i)$ with respect to distribution $P(w|M_i)$. You can then use Monte-Carlo methods to estimate it with required precision.
Other suitable options include using Laplace Approximation and then finding closed-form solution for evidence (as they do in R... | https://stats.stackexchange.com |
2,753,052 | [
"https://math.stackexchange.com/questions/2753052",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/415693/"
] | <blockquote>
Consider a function $f(t)=\exp\left(-\dfrac{1}{t}\right)$, $t>0$. For each positive integer $n$, let $P_n$ be the polynomial such that$$
\frac{\mathrm{d}^n}{\mathrm{d}t^n}f(t)=P_n\left(\frac{1}{t}\right)\exp\left(-\frac{1}{t}\right). \quad \forall t>0
$$
</blockquote>
Well to start with this is a ... | If you are looking for an explicit formula note that
$$P_n(x)=\sum_{k=1}^{n}\binom{n}{k}\frac{(n-1)!}{(k-1)!}(-x)^{n+k}.$$
The above formula verifies the given recurrence
$$\begin{align}x^2\left(P_n(x)-\frac{\mathrm{d}}{\mathrm{d}x}P_n(x)\right)&=
\sum_{k=1}^{n}\binom{n}{k}\frac{(n-1)!}{(k-1)!}(-x)^{n+k+2}+\sum_{k=... | <strong>Solution:</strong>
$\dfrac{d}{dt}\cdot (\dfrac{d^n}{dt^n}f(t))=\dfrac{d}{dt} (P_n(\dfrac{1}{t})e^{-\dfrac{1}{t}})=e^{-\dfrac{1}{t}}\dfrac{d}{dt}P_n(\dfrac{1}{t})+P_n(\dfrac{1}{t})\cdot \dfrac{e^{-\dfrac{1}{t}}}{t^2} $
$\implies \dfrac{d^{n+1}}{dt^{n+1}}f(t)=e^{-\dfrac{1}{t}}\dfrac{d}{dt}P_n(\dfrac{1}{t})+P_n... | https://math.stackexchange.com |
457,800 | [
"https://stats.stackexchange.com/questions/457800",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/257939/"
] | Let <span class="math-container">$X_1,\cdots,X_n \sim f(x|\theta)=\frac{\theta}{x^2}, x> \theta$</span> be a random sample where <span class="math-container">$\theta>0$</span> is unknown. I want to use <span class="math-container">$\frac{\theta}{X_{(1)}}$</span> as a pivotal quantity. How can I use this pivotal q... | Find the distribution function of <span class="math-container">$\theta/X_{(1)}$</span>. For <span class="math-container">$t\in(0,1)$</span>, one should end up with
<span class="math-container">\begin{align}
P\left[\frac{\theta}{X_{(1)}}\le t\right]&=P\left[X_{(1)}\ge \frac{\theta}{t}\right]
\\&=\left\{P\left[X... | To find the distribution of <span class="math-container">$Z=\frac{\theta}{Y}$</span> you can do the following:
<span class="math-container">$F_Z(z) = P(Z\leq z) = P(\frac{\theta}{Y}\leq z) = P(\frac{\theta}{z} \leq Y)$</span> because <span class="math-container">$Y=X_{(1)}>0$</span>, so
<span class="math-containe... | https://stats.stackexchange.com |
22,919 | [
"https://cs.stackexchange.com/questions/22919",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/947/"
] | I have read that linear bounded automaton is a Non deterministic Turing machine. Why is it so?
| The definition of LBA (for example given in Wikipedia) is a non-deterministic Turing machine which uses linear space. So an LBA is a (space-restricted) non-deterministic Turing machine by definition. There could be other, equivalent definitions.
| If we are saying non deterministic Turing machine and LBA are same then its wrong.
If we say non deterministic Turing machine with limited space then we can call it as LBA.
LBA has space boundaries where as Turing machine don't have.
| https://cs.stackexchange.com |
721,064 | [
"https://physics.stackexchange.com/questions/721064",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/326259/"
] | From what I've learned so far, I look at yield strength as the beginning of plastic deformation in an object.
If ceramics don't (well usually don't) undergo plastic deformation, how can it be said that ceramics have a higher yield strength then metals?
| You can also think of yield strength as the end of the elastic region. For ceramics this is convenient because they do indeed have an elastic region. Alternatively, instead of saying they have "no" plastic region, say that ceramics have zero plastic region, which fits with the fact that the breaking point i... | <h1>In General</h1>
There is a big ol' IN GENERAL appended to everything we say about material classes. There will be overlap, exceptions, and special cases. The stuff here is simply in general: you would not be crazy for expecting this kind of performance.
<h1>Why Are Ceramics so ... Not Plastic?</h1>
Ceramics general... | https://physics.stackexchange.com |
3,642,373 | [
"https://math.stackexchange.com/questions/3642373",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/778570/"
] | I've recently started getting in touch with complex numbers and I found it is quite easier to operate with them (multiplication, division, powers) in polar form rather than algebraically developing the whole thing. Would it be recommended? The main problem I'm having is that as I'm computing the angles with the calcula... | Yes: <em>don't</em> compute the angles with a calculator. Why would you want to do that? For instance, if you want to compute<span class="math-container">$$\left(4\left(\cos\left(\frac34\right)+\sin\left(\frac34\right)i\right)\right)\times\left(3\left(\cos\left(\frac23\right)+\sin\left(\frac23\right)i\right)\right),$$<... | Well you could write, for instance, <span class="math-container">$\cos1$</span> instead of the approximation. Or <span class="math-container">$re^{i\theta}=r\cos\theta+ir\sin\theta$</span>, using Euler's formula, in general.
| https://math.stackexchange.com |
454,831 | [
"https://physics.stackexchange.com/questions/454831",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/173206/"
] | If <span class="math-container">$\Bigl( \Psi(x,t),\Psi(x,t) \Bigr) =1$</span>, I want to find out if <span class="math-container">$\Bigl( \Psi(x-ct,t),\Psi(x-ct,t) \Bigr) =1$</span>.
My attempt was
<span class="math-container">$\Bigl( \Psi(x-ct,t),\Psi(x-ct,t) \Bigr) = \int_{-\infty}^\infty |\Psi(x-ct,t)|^2dx$</span>... | The scalar product means integration over <span class="math-container">$x$</span>. The normalization at the time <span class="math-container">$t$</span>
<span class="math-container">$$
\int_{-\infty}^{+\infty}\left| \Psi(x,t) \right|^2 dx =1
$$</span>
Notice that the integral is over <span class="math-container">$x$</s... | This is not a complete answer as I am not sure your substitution step is justified, since you are leaving the second argument <span class="math-container">$t$</span> unaffected...
... but any wavefunction in quantum mechanics<span class="math-container">$^*$</span> obeys the Schrödinger equation, which results in <em>... | https://physics.stackexchange.com |
51,423 | [
"https://astronomy.stackexchange.com/questions/51423",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/22022/"
] | I've heard of black holes forming in particle accelerators. This was a huge topic of discussion back in the early '00 with the grand experiment in CERN to prove the Higgs boson. Many people started expressing concerns about the formation of black holes. Of course scientists weren't concerned due to their very short exi... | The requirement to produce a "black hole" (at least of the simplest kind - a non-spinning, uncharged black hole) is just get a mass <span class="math-container">$M$</span> inside a radius <span class="math-container">$2GM/c^2$</span>. If <span class="math-container">$M$</span> is in kg and we use SI units, th... | Yes a threshold of concentrated mass/energy has to be exceeded. (by E=mc², Energy is Mass). How you achieve this is up to you!
The only proven way to concentrate enough mass into a sufficiently small volume is to collapse a large stellar core. The gravity of a core that is more than about 3 solar masses would compress ... | https://astronomy.stackexchange.com |
262,661 | [
"https://softwareengineering.stackexchange.com/questions/262661",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/156025/"
] | I'm building an application where there are different "Locations". There are Stores, Bars, Schools, and Churches (and so on) all of which are geocoded and defined by existing data sets. While not exactly alike, these entities can probably all fit into a "Locations" table. This will be helpful because users will const... | I had a similar problem with my code with global state via singelton.
As @Thomas-Junk-s and @SHODAN-s comment suggested i refactored my code to make the static global state non-static through constructor Dependency injection.
Example
original code
<pre><code>public static class Global {
public static int getSom... | Yes, it's better not to share <em>state</em> between unit-tests, and have them independent from each other. But it doesn't mean that you can't share <em>code</em> between unit-tests.
For example(using NUnit + FluentAssertions + FakeItEasy):
<pre><code> [TestFixture]
[Category("Unit")]
public class when_rol... | https://softwareengineering.stackexchange.com |
22,167 | [
"https://cs.stackexchange.com/questions/22167",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/1342/"
] | How will you find a random collection of $n$ points in the plane, all with integer coordinates in a specified range (e.g. -1000 to 1000), such that no 3 of them are on the same line?
The following algorithm eventually works, but seems highly inefficient:
<ol>
<li>Select $n$ points at random.</li>
<li>Check all $O(n^3... | Here's an approach that I think achieves $O(n^2)$ running time, as long as the points are not too dense (as long as $n$ is not too large compared to the size of the region).
Store the set of all slopes of lines between any pair of points. There are $O(n^2)$ pairs of points, and each pair of points determines line; ad... | You can improve on your algorithm while keeping the general idea:
<ol>
<li>Draw 2 points at random and add them to the (previously empty) set of selected points.</li>
<li>Draw a new point at random. Check all triples involving two of the previously selected points and the new point. If one of them fails, dicard the ne... | https://cs.stackexchange.com |
72,308 | [
"https://mathoverflow.net/questions/72308",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1465/"
] | Consider a $(p,q)$ torus knot $K$ in 3-dimensional Euclidean space $\mathbb R^3$ where $p,q \geq 2$ and $\operatorname{GCD}(p,q)=1$.
Let $\operatorname{Isom}(\mathbb R^3,K)$ be the isometries of $\mathbb R^3$ that preserve $K$.
It's a fairly standard argument using theorems about uniqueness of Seifert fiberings to ... | The answer no. Neither quantum invariants nor the Alexander polynomial sees the difference between a knot in the three sphere and a knot in Euclidian three space. In the case of the Alexander polynomial the missing point does not interfere with the first homology of the infinite cyclic cover. In the case of quantum ... | It seems to me that the isometry group of a $(2,q)$ torus knot can be a dihedral group, thus containing both $\mathbb{Z}_2$ and $\mathbb{Z}_q$. The standard realization (on a torus of revolution, take the curve having the right homotopy class and whose latitude and longitude move at constant speed) should do the trick... | https://mathoverflow.net |
347,199 | [
"https://softwareengineering.stackexchange.com/questions/347199",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/248946/"
] | I have a very simple question that has been haunting me for a while when my code starts growing.
<strong>Should parameters be replaced by global variables when they go through long routes of nested function calls?</strong>
I understand that global environment can make the state of a program unpredictable because man... | Don't use global variables.
Also, don't pass parameters down chains of functions!
Its difficult because you don't use an actual example. But normally there will be a better approach.
Lets say we have a password variable which we need to use to call apis which inturn are used by various low level functions.
Global a... | Avoid globals like the plague.
Any code can modify a global. So if you had a chain A(x) -> B(x) -> C(x) -> ... -> Z(x), and you store x into a global X and now you have a chain A->B->C->...->Z, then at every single step of that long chain, or in completely independent code, someone could change X. And the value that Z... | https://softwareengineering.stackexchange.com |
140,936 | [
"https://stats.stackexchange.com/questions/140936",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/20093/"
] | I have a variable <code>young</code> that is equal to <code>1</code> if a participant is less than 25 years old. I then have a list of of each participant's favorite ice cream flavor (everyone has to choose among 25 flavors and can only make one choice). I would like to test if the distribution of tastes differs by age... | You would normally test for homogeneity of proportions, generally via a chi-square test, though other tests could be applied.
This would in your case result in conducting a chi-square test on a 2x25 table.
| You may use a goodness of fit test, i.e. chi-square test. However, you should first make sure your sample meets the following requirements:
<ol>
<li>there should be at least 5 observation in each of the 25 ice-cream group (in both young and old subgroup).</li>
<li>the number of observations in each subgroup should be ... | https://stats.stackexchange.com |
620,436 | [
"https://physics.stackexchange.com/questions/620436",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/254930/"
] | To calculate the evolution of a wave function under Schrodinger equation, we need to set an initial condition. In this context, can we associate a unique wave function to a given physical (observable) intial condition? The modulus-squared value of the wave function corresponds to the probability amplitude. So, it seems... | Consider the following two states describing a free particle in 1 dimension
<span class="math-container">\begin{eqnarray}
\psi_1(x,t) &=& \frac{1}{\sqrt{2\pi}} \exp\left[i \left(k x - \frac{\hbar k^2}{2m}t\right)\right] \\
\psi_2(x,t) &=& \frac{1}{\sqrt{2\pi}} \exp\left[i \left((k+\Delta k) x - \frac{\h... | The initial wave functions with different phases at different points will in general be associated with different physical states, and thus can lead to different measurement outcomes. The key here is that only the <em>global phase</em> of a statevector doesn't modify the physical state itself, but a <em>local phase</em... | https://physics.stackexchange.com |
79,799 | [
"https://mathoverflow.net/questions/79799",
"https://mathoverflow.net",
"https://mathoverflow.net/users/18954/"
] | The following assertion appears in a paper I am reading, and I can't seem to verify it.
Let $\text{Gr}_{n,m}$ denote the set of pairs $(V,W)$ where $V$ and $W$ are as follows.
<ol>
<li>$V$ is an $n$-dimensional subspace of $\mathbb{C}^{\infty}$.</li>
<li>$W$ is an $m$-dimensional subspace of $\mathbb{C}^{\infty}$.</l... | The forgetful map $Gr_{n,m} \to Gr_n$ that drops $W$ is a fiber bundle (exercise), and the map $Gr_{n,m} \to Gr_n \times Gr_m$ is a map of fiber bundles. It's an equivalence on the (connected) base space, so it suffices to check that the map of fibers is an equivalence.
The fibers over $V$ are, respectively: $m$-dime... | Look at the canonical principal $U(n)\times U(m)$ bundle over $Gr_{n,m}$ given by pairs of orthonormal frames $(v_1,\ldots, v_n), (w_1,\ldots w_m)$. Its total space is the set of all orthonormal $n+m$-frames in $\mathbb C^\infty$. It's contractible (that's well-known) and hence $Gr_{n,m}$ is a homotopy $B_{U(n)\times ... | https://mathoverflow.net |
10,815 | [
"https://quant.stackexchange.com/questions/10815",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/7712/"
] | I am looking for efficient numerical approaches for pricing American options when two or more sources of noise are involved (the simplest case coming to mind would be the Heston Model)
Eventhough I am familiar with lattice methods I don't see how this could work in a "poly-noise" setting. A solution might present itse... | Generally speaking, if you have two or three sources of noise, you are still going to be <em>much</em> better off pricing American options on a lattice than via LSMC. Too often, LSMC becomes the refuge of academics lacking patience to learn proper lattice techniques.
Now, you can frequently reduce the difficulty of... | Regarding your second question: one possible approach is to reduce the instrument you are trying to value to something simpler, for which an analytical solution are an alternative methodology does exist. You can then vary parameters and check that the valuation is behaving as expected.
If you are using simulations be... | https://quant.stackexchange.com |
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