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179,180 | [
"https://physics.stackexchange.com/questions/179180",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/9604/"
] | If I wanted to find the coefficients of a linear transformation between 2 vectors in the basis for 2 spin $1/2$ paticles (let's say for starters we are not even looking for a unitary transform):
\begin{equation}
Z=\{|++\rangle,|+-\rangle,|-+\rangle,|--\rangle\},
\end{equation}
should I look for 16 coefficients,
or... | First of all, the equation
$$ \begin{equation}A\otimes B=A\otimes \mathbb{1}+\mathbb{1}\otimes B,\end{equation} $$
is a claim about an identity, and this claim is incorrect. Note that for $1\times 1$ matrices, the matrices are numbers and the equation above reduces to
$$ a\cdot b = a\cdot 1 + 1 \cdot b$$
which is clear... | Adding to Lubos' answer, let me address this part more specificially:
<blockquote>
I am very confused about this - actually - I'm guessing that transformations that can be written $A⊗B$ are a subset of all possible transformations with all 16 coefficients free.
</blockquote>
This is correct. First some notation: Le... | https://physics.stackexchange.com |
343,820 | [
"https://softwareengineering.stackexchange.com/questions/343820",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/145002/"
] | So, I am trying to create an English language trie data structure implementation in C++. I have created a <code>Trie</code> and <code>TrieNode</code> class. The <code>TrieNode</code> class takes in its constructor a <code>vector<string></code> that is a list of words to construct the Trie from.
My solution to ge... | When seeing a class with a constructor signature like
<pre><code> EnglishWordsListGenerator(const std::string &wordFileName)
</code></pre>
I think it is pretty obvious that this constructor will read the given file (and so need some time), and it should not be to hard to understand that the caller has to care for... | If you are new to C++, it may be desirable to shy away from doing big work in a constructor. Constructors are wedded tightly to the way the language behaves, and you really don't want the constructor getting called unexpectedly (<code>explicit</code> is your friend!). Constructors are also rather unique in that they ... | https://softwareengineering.stackexchange.com |
317,220 | [
"https://physics.stackexchange.com/questions/317220",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/147876/"
] | If there is one coulomb of charge passing through the inductor, and one volt is supplied to that coulomb, what happens to the 1 joule of energy as it goes through the inductor?
| <blockquote>
one volt is supplied to that coulomb
</blockquote>
The implication here is that it requires the expenditure of 1 joule of energy to move 1 coulomb of charge through an inductor.<br>
If the inductor is ideal and the current is steady this is not true as it takes no work to move a charge though an ideal i... | It is stored in the magnetic field. When the voltage is taken away the current keeps flowing for some time untill the magnetic field is exhausted.
| https://physics.stackexchange.com |
58,095 | [
"https://chemistry.stackexchange.com/questions/58095",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/30246/"
] | While solving some questions on the stoichiometry on redox titrations, I come across this question:
<blockquote>
Calculate the volume of $0.05\ \mathrm{M} \ \ce{KMnO4}$ solution required to oxidize completely $2.70\ \mathrm{g}$ of oxalic acid in acidic medium.
</blockquote>
I know how to solve this question. The ... | Recall that molarity <span class="math-container">$c$</span> is
<span class="math-container">$$c=\frac{n_\text{solute}}{V_\text{solution}}$$</span>
whereas for molality <span class="math-container">$b$</span> is
<span class="math-container">$$b=\frac{n_\text{solute}}{m_\text{solvent}}$$</span>
While in the extreme ... | Example: 5 moles of solute in 1 liter of solution.
The Molarity at the beginning is (5moles ÷ 1Liter) = <strong>5 M</strong>.
When the solution is warmed up and expanded by 1% say, to 1.01L, the new Molarity = (5moles ÷ 1.01Liter) = <strong>4.95 M </strong>
P.S. Don't over think this question! The amount of content... | https://chemistry.stackexchange.com |
60,690 | [
"https://physics.stackexchange.com/questions/60690",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/11633/"
] | Whatever happens in there is not falsifiable nor provable to the outside. If for (amusing) example the interior consisted of 10^100 Beatles clones playing "Number Nine" backwards, do we know how to unscramble the Hawking radiation to divine this? The same question applies to this new firewall furor. So of what use is a... | Simply because our final goal is a set of laws of physics that describes <em>any</em> part of the universe equally well. Let's say a physicist jumped into a black hole and saw that the interior of the black hole was composed entirely of John Lennon clones. His last thoughts before getting spaghettified would be "why?".... | <em>Whatever happens in there is not falsifiable nor provable to the outside.</em>
General relativity predicts this, but a) no one has ever checked experimentally, and b) it seems to be incompatible with the rules of quantum physics. Every attempt at mixing quantum theory and GR has produced results like Hawking radi... | https://physics.stackexchange.com |
378,192 | [
"https://mathoverflow.net/questions/378192",
"https://mathoverflow.net",
"https://mathoverflow.net/users/169969/"
] | Problem setting :
<span class="math-container">$ \underset{x}{\text{min}} \|Ax-b\|$</span>, where <span class="math-container">$A \in \mathcal{R}^{m \times n}, m\gg n $</span>, full rank.
L1 loss is used for robust estimation using IRLS. The corresponding equation to solve turns out to be <span class="math-container">... | Partial answer: the minimal dimension is at least
<span class="math-container">${n-2 \choose 2} + 1$</span>, with equality if <span class="math-container">$n-1$</span> is a power of <span class="math-container">$2$</span>.
For example, if <span class="math-container">$n=5$</span> the minimum is <span class="math-contai... | One more exact answer: for <span class="math-container">$n=8$</span> the minimal dimension is <span class="math-container">$22$</span>,
again attaining the "easy" bound <span class="math-container">${n-1 \choose 2} + 1$</span>
and the same as the value for the next dimension <span class="math-container">$n=9$... | https://mathoverflow.net |
135,099 | [
"https://softwareengineering.stackexchange.com/questions/135099",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/44933/"
] | Take a User class and the idea that a User is to be profiled. I see four ways to handle this:
<ol>
<li>Write the code for the profile into the User class. I am dismissing this right away.</li>
<li>Create a Profile class and make it a property of the User class.</li>
<li>Write a User class (with the boiler-plate name, ... | <em>I'll assume that you are only storing profiles for users.</em>
This is an easy decision. The user has a "has a" relationship to the profile and thus the profile should be encapsulated in its own class and exposed as a component of the User class (e.g. a property). So your second approach is the cleanest one.
Opti... | <blockquote>
Write the code for the profile into the User class. I am dismissing this right away.
</blockquote>
Why? This is the simplest solution. I would do this until the pain appeared. That moment may come very soon. So what if it does? Just extract the profile data into a separate class.
| https://softwareengineering.stackexchange.com |
3,399,387 | [
"https://math.stackexchange.com/questions/3399387",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/239682/"
] | Let <span class="math-container">$A$</span> be a <span class="math-container">$k$</span>-algebra of finite dimension, where <span class="math-container">$k$</span> is a field, with <span class="math-container">$k$</span>-basis <span class="math-container">$e_1,\cdots,e_n$</span>. Let <span class="math-container">$K$</s... | I believe that Lord Shark's answer is the right way to approach the problem. I will try to explain their answer.
Suppose <span class="math-container">$\sum_{i=1}^ne_i\otimes_k\lambda_i=0$</span> for some <span class="math-container">$\lambda_1,\ldots,\lambda_n\in K$</span>. If we define a <span class="math-container">... | For each <span class="math-container">$i$</span>, there's a <span class="math-container">$k$</span>-bilinear map <span class="math-container">$\beta_i:A\otimes_k K\to K$</span>
defined by
<span class="math-container">$$\beta_i\left(\sum_{j=1}^n a_j e_j,b\right)=a_ib.$$</span>
This corresponds to a <span class="math-con... | https://math.stackexchange.com |
592,187 | [
"https://electronics.stackexchange.com/questions/592187",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/223151/"
] | I have a car inverter (DC 12 V to AC 240 V). Inverter's frequency is 60 Hz.
I want to connect the output (240 V) of the inverter to an transformer (AC 240 V to AC 16 V) which indicates input frequency 50 Hz.
Is it ok to connect them? Will the frequency difference damage the transformer?
| It's almost certainly okay with the same ratings, with 60Hz and the same voltage in.
Flux density is 20% lower decreasing core losses as transformers are usually optimized to run close to saturation, probably more than compensating for any small increase due to the frequency. Copper (<span class="math-container">\$I^2R... | It is sort of OK. You will not damage it, but the efficiency probably will be lower. It could be a problem for a motor, but a transformer will probably work.
Are you sure 12V isn't enough where you are going to use 16V? Perhaps you could skip the transformer.
| https://electronics.stackexchange.com |
302,834 | [
"https://softwareengineering.stackexchange.com/questions/302834",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/27072/"
] | I see the following design in the code which is part of the default web application project in visual studio:
A single data model class in constructed and decorated with various data validation annotations. For Example, there's a <code>RegisterViewModel</code> class that looks like this:
<pre><code>public class Regis... | If you're asking how to manage your own keys then there are 2 places to store them:
For dev/test - you might as well put them in the SCM repo. Unless your repo is publicly accessible.
For production, you want to store them with a single point of authority, either somebody (with a deputy) who keeps the originals on a ... | Secrets such as credentials to a database should be kept in a local configuration file, either of your own making, or securely transmitted to you.
| https://softwareengineering.stackexchange.com |
73,588 | [
"https://security.stackexchange.com/questions/73588",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/61366/"
] | Suppose we have passwords that are statistically 7-8 characters long. Is appending a 200 character long salt less secure than a 5 character salt, because of the similar hash function inputs?
I was wondering: what if someone tries to guess the salt by brute forcing the salt with for example the password "123456", or an... | As Mike and Gumbo have mentioned in comments, a salt isn't intended to add protection to bad passwords. It's meant to keep the attackers from breaking the whole database at once. The length of the salt isn't meant to add difficulty to breaking the stored passwords. It's meant to ensure that your salt is reasonably uniq... | A too long salt will not reduce security. A too short salt will reduce security.
As the salt gets longer security will improve. At some point you will cross a boundary, where you start getting diminishing returns on increasing salt length. And eventually you will cross another boundary, where a longer salt does not ad... | https://security.stackexchange.com |
1,859,211 | [
"https://math.stackexchange.com/questions/1859211",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/275806/"
] | Say you have the following function:
$$y=x^2+x$$
Then
$$\frac{dy}{dx}=2x+1$$
However, what if you wanted to find $dy/dy$? I differentiated both sides of the original equation with respect to $y$, getting
$$\frac{d}{dy}[y]=\frac{d}{dy}[x^2+x]$$
Now, I’ve always thought that $dy/dy=1$. After all, the derivative of a vari... | You have not applied differentiation to the right hand side in the correct manner.
When you take the derivative of $y$ with respect to $x$, you must think of $x$ as the independent variable and $y$ as the dependent variable.
On the other hand, when you reverse the roles and take the derivative of $x$ with respect to... | The mistake is simply in understanding the notation you are using, if $y = x^2 + x$ then $\frac{d}{dy} = \frac{d}{d(x^2 + x)}$, so the LHS is $\frac{dy}{dy} = 1$ and the right hand side is $\frac{d}{dy}(x^2 + x) = \frac{d}{d(x^2 + x)}(x^2 + x) = 1$ so both sides agree.
The point is that in ignoring the relationship be... | https://math.stackexchange.com |
342,655 | [
"https://math.stackexchange.com/questions/342655",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/49668/"
] | I've been trying to rack my brain for my high school maths to find the right calculation for this but I've come up blank.
I would like to know how many combinations there are of choosing 1-9 items from a set of 9 items.
i.e.
There are 9 ways of selecting 1 item.
There is 1 way of selecting 9 items.
For 2 items you c... | Line up the items in front of you, in order. To any of them you can say YES or NO. There are $2^9$ ways to do this. This is the same as the number of bit strings of length $9$.
But you didn't want to allow the all NO's possibility (the empty subset). Thus there are $2^9-1$ ways to choose $1$ to $9$ of the objects.
<... | 9 ways of selecting 1item
36 ways of selecting 2 items
84 ways of selecting 3 items
126 ways of selecting 4 items
126 ways of selecting 5 items
84 ways of selecting 6 items
36 ways of selecting 7 items
9 ways of selecting 8. items
1 ways of selecting 9 items
Total ways are 511
| https://math.stackexchange.com |
178,923 | [
"https://physics.stackexchange.com/questions/178923",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/73149/"
] | How can you see the difference between a melamine plate and a plate with a melamine coating?
| The work done on a body of mass $m$ by a constant force $F$ across a distance $s$ is $Fs$ and that must equal the change in the kinetic energy of the body. Since the body started from rest, the change in its kinetic energy is $mv^2/2$ where $v$ is the body's speed at the end of the track of length $s$. So,
$Fs = \frac... | Simple example: the force, F, on a body on a frictionless surface, starting from rest, over a distance d where d and F are in the same direction the work done is W=F*d. if F= 2 Newtons and d= 8 meters the work done is 16 Joules. Assuming no potential energy containing elements then all the work goes into increasing th... | https://physics.stackexchange.com |
22,967 | [
"https://dba.stackexchange.com/questions/22967",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/8365/"
] | I have the following trigger in my database:
<pre><code>CREATE TRIGGER dbo.triggerGeocodedAddressUpdate ON dbo.Party AFTER UPDATE AS
IF UPDATE(Latitude)
UPDATE pt
SET pt.GeocodedAddress = geography::Point(i.Latitude, i.Longitude, 4326)
FROM dbo.Party AS pt INNER JOIN inserted AS i ON i.Part... | It turned out to be that I needed to convert to the geography type differently. Building off of @Mr.Brownstone's answer (which was helpful since it simplified the trigger):
<pre><code>CREATE TRIGGER dbo.triggerGeocodedAddressUpdate ON dbo.Party AFTER UPDATE AS
IF UPDATE(Latitude) OR UPDATE(Longitude)
UPDATE pt
... | Try this one. I have moved the conditional update into a single statement because the action you were taking was the same for both conditions. Also I have altered the way that you join to the INSERTED table so that it performs the filter pre-join:
<pre><code>CREATE TRIGGER dbo.triggerGeocodedAddressUpdate ON dbo.Party... | https://dba.stackexchange.com |
107,717 | [
"https://datascience.stackexchange.com/questions/107717",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/64876/"
] | I recently built a logistic regression for binary classification
While I understand that logistic regression is inherentlt interpretable, I am trying to use explainable AI solutions to understand the predictions. For that, I am trying to make a list of all XAI solutions and compare the results against each other.
As of... | If you perform the encoding before the split, it will lead to <strong>data leakage</strong> (train-test contamination) In the sense, you will introduce new data (integers of Label Encoders) and use it for your models thus it will affect the end predictions results (good validation scores but poor in deployment).
After ... | If you train the encoder model on the whole dataset before you split it into train/validation/test sets you will introduce bias into the training. The introduction of bias happens because the encoded categories will now contain information about the samples that will be in your validation and/or test sets.
This is comm... | https://datascience.stackexchange.com |
97,530 | [
"https://dba.stackexchange.com/questions/97530",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/62266/"
] | I have an SSIS package stored in the Integration Services catalogs on a SQL server instance.
This package is used as a step in a SQL Server agent job.
The package has 4 required parameters.
Using SSMS on my local machine if I edit the package I can add all of these parameters and the job runs fine.
However editing ... | Allowing even trusted users to login to what appears to be a production database is in my mind a big no-no. The solutions you mention above may provide you with a sense of security/relief but they their own have side effects.
I would be particularly worried about your statement
<blockquote>
Manual updating and in... | Use read-only copies of subsets of the data to service users. Combine with views/stored procedures and you have solid control over who can how much data and through what means.
Refresh the data periodically to suite the needs of the users.
| https://dba.stackexchange.com |
122,773 | [
"https://dba.stackexchange.com/questions/122773",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/5391/"
] | I use SQL Server 2008 R2 and ASP.NET 4.5.
Sometimes, I get this error when I executed a complex procedure:
<blockquote>
System.Data.SqlClient.SqlException
Timeout expired. The timeout period elapsed prior to completion of the operation or the server is not responding
</blockquote>
Any suggestions for troubleshooting o... | I don't like the <code>USING</code> syntax. The MySQL documentation shows the following as a way to declare which tables to delete from a join, which is almost identical to the <code>SELECT</code> syntax. You can use aliases of course:
<pre><code>DELETE t, p -- delete from both tables
... | Please be careful. If you want to delete from only one table, don't include all alias in the first line. Deletions will occur only on the table where its alias is included right after the <code>DELETE</code> keyword.
This will delete rows on both <code>topics</code> (<code>t</code>) and <code>posts</code> (<code>p</co... | https://dba.stackexchange.com |
51,873 | [
"https://softwareengineering.stackexchange.com/questions/51873",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/7083/"
] | I have always had this question in my mind and I would really be happy to get an explanation for this.
Is it only me or do you also feel the same way that it's hard to find anything on MS site.
For example, every time I need to download .NET framework I have to Google it. You never know what you can download, no catego... | I think you have Microsoft confused with a corporation that cares about the free downloads. Don't get me wrong, I have met and talked to several people from Microsoft and they are smart, intelligent, and nice people. However, Microsoft is more like Oracle in the sense that they know how to make money. If you make it... | Not really. It's pretty much their own fault and they should definitely consider implementing basic things like Categories and so on. I'm not an Apple Person, but if you look at their download section one can easily find System Updates, Third Party Programs and Drivers.
| https://softwareengineering.stackexchange.com |
153,159 | [
"https://dba.stackexchange.com/questions/153159",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/108816/"
] | I am dealing with performance issues with a Windows app that uses SQL Server Express (2014) on the back-end.
I have managed to get this running a lot better primarily by reviewing the indexing SQL Server side but there is one particular report that is still running quite slowly.
Looking into what it is doing, it appe... | The queries being identical is not the problem, and in some ways helps since the Execution Plan is cached and the data pages needed for the query should still be cached. The issue would then tend to be the per-connection overhead of authentication and initializing the session.
The first thing to look into is: is "conn... | If you can't change the queries you can't optimize this. From the numbers you posted almost all time is spent <em>not</em> in query execution.
<blockquote>
Now each query above runs very very fast, we are talking about a few tens of micro seconds in each case. In fact if you add up all 1,031 queries used to make thi... | https://dba.stackexchange.com |
119,270 | [
"https://physics.stackexchange.com/questions/119270",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/1186/"
] | Can any gas be liquidified by lowering the temperature? What happens with gases at absolute zero? Are there gases that remain gases at absolute zero? Do their molecules move at these temperatures? Does the gas acquire a crystallic structure at these temperatures while still remaining gaseous?
| The answer is, yes,sort of. What you're missing is that once light leaves a point (pixel) on the monitor's surface, it radiates in all directions, which is why you can see the image wherever you're sitting. The blocks of plastic you envision will not change this, so you'll find yourself just looking through them at ... | You can also Google "edgeless computer monitor". Three new monitors is likely to be cheaper than a fiber bundle!
| https://physics.stackexchange.com |
25,306 | [
"https://stats.stackexchange.com/questions/25306",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/7795/"
] | I have the following Y outcomes distribution with the normal density function represented by the superimposed red line:
<img src="https://i.stack.imgur.com/HFElK.png" alt="enter image description here">
I need to develop a regression methodology to predict $Y$ given a number of predictors $X_n$. OLS doesn't seem to f... | <strong>Which distribution of the dependent variable is relevant?</strong>
First, there is no reason to think that OLS will do badly on this data. At least none from looking at your dependent variable. However...
Second, Looking at the distribution of your dependent variable is not so helpful. Even regression mode... | This is an old thread but I just came across it. Just one quick comment - when your range is so large, 0.5 increments are fairly minute. That means it approaches being a continuous variable, and linear regression would be far easier to interpret than an ordered logit. Ordered logit coefficients are easy to look at, but... | https://stats.stackexchange.com |
164,867 | [
"https://stats.stackexchange.com/questions/164867",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/82197/"
] | In the OLS setting, the mean shifted outlier model connects two behaviors:
<ol>
<li>delete the $i^{th}$ observation</li>
<li>adding a variable</li>
</ol>
In other words, assume the original model, $\omega$ ,is:
$$ Y = X\beta + \epsilon$$
with $\epsilon$ ~ $N_n(0,{\sigma}^2 I$). Next, we add a variable to the model ... | Essentially, I agree with @IrishStat, but I would like to "rephrase" the answer a little.
If you assume that $Y_t$ follows an MA(2) process, then you have
$$Y_t = \varepsilon_t + \theta_1 \varepsilon_{t-1} + \theta_2 \varepsilon_{t-2}$$
(I assume no intercept for simplicity.) Note that this is <em>not</em> what you... | The current error $e_t$ is never known until after the $Y_t$ is observed thus it is set to 0.0 . The MA(2) process is $Y_t= + .5 * e_{t-1}+ .5* e_{t-2} + e_t$ where $e_t= 0.0$. No forecast is possible until period 3.
| https://stats.stackexchange.com |
220,312 | [
"https://dba.stackexchange.com/questions/220312",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/-1/"
] | What is the general difference between OLTP and Inmon-style Datawarehouse? It seems like they are the same. OLTP just copies all the tables into a Read-Only Datawarehouse DB.
I know what a Kimball datawarehouse is (denormalized, wide with surrogate identifier).
Inmon is more normalized.
| The difference is more to the subject of the database than anything else. By the way, Inmon approach focus on normalizing as much as possible to make the ETL process easier and less error-prone; but non-normalized data are acceptable on data marts, even to Inmon.
<strong>OLTP</strong>: it is a full normalized database... | Welcome to DBA Stackexchange !
<blockquote>
OLTP is Online Transaction Processing.
Any system that helps to do transactions or record data changes over online is called OLTP. I believe it is not necessary to compare it with the Data warehouse where the data is stored over long time for the purpose of doing analysi... | https://dba.stackexchange.com |
41,569 | [
"https://mathoverflow.net/questions/41569",
"https://mathoverflow.net",
"https://mathoverflow.net/users/8141/"
] | A neutral Tannakian category over a field $k$ is a rigid $k$-linear abelian tensor category
$\mathcal{C}$ whose unit $1$ satisfies $\mathrm{End}(1) \simeq k$, and is
moreover equipped with an exact faithful tensor functor $\omega : \mathcal{C} \rightarrow
\mathrm{Vect}_k$ into the category of finite dimensional $k$-ve... | If you say the other axioms correctly, then the condition on $\operatorname{End}(1)$ is redundant. Indeed, the word "tensor functor" implies that $\omega: 1 \mapsto k$, and the word "faithful" implies that $\operatorname{End}(1) \hookrightarrow \operatorname{End}(\omega(1))$. What you should include that you don't on... | Assuming you have such an equivalence of categories, the object $1$ is sent to the trivial representation of your affine $k$-group $G$. This is the representation that factors through the canonical homomorphism from $G$ to the trivial group, and its endomorphisms are the endomorphisms of the one dimensional $k$ vector... | https://mathoverflow.net |
1,174,494 | [
"https://math.stackexchange.com/questions/1174494",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/177498/"
] | Assume that there is a parametrized smooth curve $c$ on the manifold $M$, mapping from $[a,b]$ to $M$. Also assume that there is a tangent vector on $M$ in the form $(p,v)$. Tu's text states that it is assumed that the curve $c$ is starting at $p$ if $c(0)=p$. Is there a way to show that $c(0)=p$ in any way? Any help w... | If $M$ is a manifold, then there is some coordinate chart $\phi:\mathbb{R}^n\rightarrow M$ that is a smooth homeomorphism onto its image such that $\phi(0)=p$. Restrict $\phi$ to a small portion of the $x$-axis that includes $0$. This will be a smooth curve such that $c(0)=p$. Further, if you want $c'(0)=v$, you kno... | If there is a tangent vector $v$ at $p$, then $v \in T_p(M)$. Since $M$ is a manifold, there exists a parametrization $\phi: U \rightarrow V$ on a neighborhood $p \in V$ such that $\phi(0) = p$, and $d\phi_0(u) = v$ for some $u \in U$. Consider the line given by $L = \{ x\cdot u|x\in\mathbb{R}\}$ and consider $L \cap U... | https://math.stackexchange.com |
500,505 | [
"https://physics.stackexchange.com/questions/500505",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/208833/"
] | I recently learned about an example where an operator <span class="math-container">$O$</span> (not Hermitian) acted on a wavefunction <span class="math-container">$|\psi \rangle$</span> and carried the wavefunction out of Hilbert space, i.e. <span class="math-container">$O|\psi \rangle$</span> is not in Hilbert space.
... | Formally self-adjoint, but unbounded, operators can easily take a normalizable state (i.e a state in the Hilbert space) and make it unnormalizable and therefore no longer in the space. This can lead to all sorts of aparent paradoxes. For example consider the operator <span class="math-container">$p^4= \partial_x^4$</s... | The answer is negative from scratch. An operator <span class="math-container">$A:D(A) \to H$</span> with <span class="math-container">$D(A)$</span> a linear subspace of <span class="math-container">$H$</span> is said <strong>Hermitian</strong> when <span class="math-container">$\langle Ax|y\rangle= \langle x| Ay\rangle... | https://physics.stackexchange.com |
26,372 | [
"https://physics.stackexchange.com/questions/26372",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/993/"
] | Black holes were first predicted by astrophysics, then observed. Was the existence of galaxies first predicted by astrophysics, or first observed by astronomers?
| The idea of the existence of galaxies is certainly not new, and quite a bit older than the field of modern astrophysics.
In 1750, Thomas Wright, an English astronomer correctly speculated that the Milky Way was a flattened disk of stars and that some of the nebulae astronomers viewed in their telescopes were separate ... | Some galaxies are observable with the naked eye, so people have "observed" them (though not always knowing their true nature) as long as there has been humans. As mentioned in @ghoppe's answer, the idea that they were actually large formations of stars like the Milky Way formed gradually through the age of Enlightenmen... | https://physics.stackexchange.com |
165,894 | [
"https://electronics.stackexchange.com/questions/165894",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/72427/"
] | I wrote a code
<pre><code>int main(void) {
uart2();
NVIC_EnableIRQ(UART2_IRQn);
while(1);
}
void receive(void) {
SMR_485RECEIVE;
receive_byte = LPC_UART2->RBR;
}
void send(void) {
SMR_485TRANSMIT;
LPC_UART2->THR = receive_byte;
}
void UART2_IRQHandler(void) {
B... | Are you sure there isn't a global interrupt that requires clearing? I would say that most systems have a clearable flag somewhere.
Also, is your interrupt handler routine only triggered by the UART or is that where all interrupts will land?
On PIC micro and Atmel architectures (thus I assume ARM too, otherwise my ans... | Finally it works, here is code, thank you all for helping me.
<pre><code>int main(void) {
uart2();
NVIC_EnableIRQ(UART2_IRQn);
while(1);
}
void receive(void) {
SMR_485RECEIVE;
receive_byte = LPC_UART2->RBR;
}
void send(void) {
if(receive_byte != '\0'){ //ADDED THIS IF
SMR_4... | https://electronics.stackexchange.com |
58,006 | [
"https://mechanics.stackexchange.com/questions/58006",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/40870/"
] | I am looking at buying a second hand 2-stroke engine. I have seen a lot online about checking compression before buying used engines. I don't have a compression tester, but will buy one if necessary.
My question is, <strong>if the engine starts and runs fine, does that automatically mean the compression is okay, or sh... | You cannot assume just because it starts it has <em>good</em> compression. It can have minimal compression and still start and run just fine. That minimal compression is going to be different for every engine, so you'd have to look up the specifications for the exact engine you're looking at. The deal with it is, the m... | Engines can run with compression below the intended spec. But the compression amount alone is not the whole story.
On multi cylinder engines <em>differences</em> between cylinders can be an indicator of wear or damage.
Damage could mean worn or broken piston rings, damaged pistons or cylinder surface, burnt valves ... | https://mechanics.stackexchange.com |
309,123 | [
"https://softwareengineering.stackexchange.com/questions/309123",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/69801/"
] | I've recently had an argument with a colleague about using getters (without setters) in a view-model classes used by XAML.
Example:
<pre><code>public string FullName
{
get
{
return $"{FirstName} {LastName}";
}
}
//call OnPropertyChanged("FullName") when setting FirstName or LastName
</code></pre>
His ... | Your coworker is incorrect.
When working with UI logic in MVVM, it's common to have properties for binding that are derived from other data.
In these cases, you don't want to create another private member - that just adds a point of failure with no benefit.
Side note:
If you're using C# 6 then instead of hardcode... | Getters like your colleague expects, are a code smell. They're only there for language niggles anyway. What they're doing is exposing a private variable. To be honest, you might as well just access the private variable directly if that's all you're using getters for and cut out a layer of middleman.
Originally OO lang... | https://softwareengineering.stackexchange.com |
222,954 | [
"https://math.stackexchange.com/questions/222954",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/44374/"
] | I'd would like to know that, because I don't want to prove a function is onto if I don't have to. If the answer is no, is there any particular case where it is true?
| The function $f:\Bbb N\to\Bbb N:n\mapsto 2n$ is one-to-one but not onto, and there are many other easy examples. An even simpler one is $g:\Bbb N\to\Bbb N:n\mapsto n+1$.
About the only simple situation in which a one-to-one function $f:A\to B$ is necessarily onto is when $A$ and $B$ are finite sets of the same cardina... | The answer is no in general, although it does depend on the specific situation. The exponential function is one-to-one but it is not onto if we consider the co-domain to be $\mathbb{R}$. It is onto if we further restrict the co-domain to $\mathbb{R}^+$.
One prominent case in which one-to-one implies onto (and vice ve... | https://math.stackexchange.com |
33,185 | [
"https://stats.stackexchange.com/questions/33185",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/7918/"
] | I've dealt with <strong>Naive Bayes</strong> classifier before. I've been reading about <strong>Multinomial Naive Bayes</strong> lately.
Also <strong>Posterior Probability = (Prior * Likelihood)/(Evidence)</strong>.
The only prime difference (while programming these classifiers) I found between Naive Bayes & Multin... | The general term <strong>Naive Bayes</strong> refers the the strong independence assumptions in the model, rather than the particular distribution of each feature. A Naive Bayes model assumes that each of the features it uses are conditionally independent of one another given some class. More formally, if I want to cal... | In general, to train Naive Bayes for n-dimensional data, and k classes you need to estimate $P(x_i | c_j)$ for each $1 \leq i \leq n$, $1 \leq j \leq k$ . You can assume any probability distribution for any pair $(i,j)$ (although it's better to not assume discrete distribution for $P(x_i|c_{j_1})$ and continuous for $P... | https://stats.stackexchange.com |
214,783 | [
"https://security.stackexchange.com/questions/214783",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/191117/"
] | Is is safe to backup programming projects (for example websites that where made using HTML/CSS/JS with the help of some frameworks and libraries (Bootstrap, jQuery, etc.), C# projects made with the .NET framework or websites with backend made with PHP) from a possibly infected computer? What messures can I take to back... | If you're concerned enough about it to wipe the machine, and you don't already have an online repository for your code somewhere like Github, then I'd suggest getting a live boot CD/USB for a Linux distribution of your choice and use that to copy the files off to external storage or cloud storage. I don't know of any w... | Protocol conversion
<ol>
<li>Upload the files to pastebin, let pastebin convert to plain text</li>
<li>Open the pastebin file from your clean machine Copy from the
browser, paste to a new file </li>
<li>Repeat</li>
</ol>
Google AV
<ol>
<li>Use your non-personal Gmail, share a folder such that anyone can edit</li>
<l... | https://security.stackexchange.com |
27,264 | [
"https://softwareengineering.stackexchange.com/questions/27264",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/8849/"
] | I've been using underscore_case for about 2 years and I recently switched to camelCase because of the new job (been using the later one for about 2 months and I still think underscore_case is better suited for large projects where there are alot of programmers involved, mainly because the code is easier to read).
Now ... | I agree that it depends on the language you're using to some extent; code tends to look neater when your symbol names follow the same formatting regimen as the language's built-ins and stock libraries.
But where there's a choice, I prefer underscores to camel case, for one simple reason: I find that style easier to re... | I think you should use naming convention adopted by your platform. underscore_case will look weird in C# code, as camelCase in Ruby =)
| https://softwareengineering.stackexchange.com |
20,063 | [
"https://cs.stackexchange.com/questions/20063",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/11539/"
] | I come from an electronics background. I know that there are three types of implementations of multithreading (see <em>Computer Architecture: A Quantitative Approach, 5th Edition</em>):
<ol>
<li><strong>Fine-grain multithreading</strong> issues instructions for different threads after every cycle.</li>
<li><strong>Coa... | Hennessy and Patterson (Computer Architecture: A Quantitative Approach) use the term "multithreading" to refer to running more than one thread on a single core.
Their distinction between "fine-grain", "coarse-grain" and "simultaneous" involves different approaches for how the threads share the issue logic (the logic t... | Fine-grain multithreading and coarse-grain multithreading are two approaches that can be implemented even on single-core processors. The idea is that you "time-share" the different threads on the single core. Fine-grain multithreading switches between the threads every so often, while coarse-grain multithreading transf... | https://cs.stackexchange.com |
215,693 | [
"https://electronics.stackexchange.com/questions/215693",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/99426/"
] | I want to add a piece of code for watchdog timer within my source code so that the board resets automatically when programs hangs. I am using Mediatek Linkit One board.
| You can create a function that "Feeds the dog" in an appropriate place in your program. When the dog isn't fed, the watchdog timer will elapse and reset the program. Look at the microcontroller documentation to see how this is implemented. Generally the Watch Dog timer will need to be configured correctly (with appropr... | I have no idea what a Mediatek Linkit One board is (and you didn't provide a link), but, in general, you can't. If your program hangs how will the watchdog code be executed?
Watchdogs usually have to be implemented in hardware - either internally by a section of the CPU that runs independently of the user program or, ... | https://electronics.stackexchange.com |
115 | [
"https://mathoverflow.net/questions/115",
"https://mathoverflow.net",
"https://mathoverflow.net/users/65/"
] | I think there was a theorem, like
<ul>
<li>every cubic hypersurface in $\mathbb P^3$ has 27 lines on it. </li>
</ul>
What is the exact statement and details?
| The exact statement is that every smooth cubic surface in $\mathbb P^3$ (over an algebraically closed field) has exactly $27$ lines on it. Many books on algebraic geometry include a proof of this famous fact. The proof that I first learned comes from chapter V of Hartshorne, where cubic surfaces arise as the blowup of ... | There is a completely elementary (i.e. no surface theory or Chern classes needed) way to carry out this computation. I give you a brief sketch omitting the details. First use an incidence correspondence to prove that every cubic (smooth or not) contains at least one line.
Once you have a line l consider planes $H$ con... | https://mathoverflow.net |
38,670 | [
"https://mathoverflow.net/questions/38670",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9220/"
] | Let <span class="math-container">$X$</span> be a quasi-projective variety, <span class="math-container">$Y$</span> a projective variety, and <span class="math-container">$f:X \rightarrow Y$</span> an open immersion. If <span class="math-container">$\mathcal{F}$</span> is a locally free coherent sheaf, what can be said... | About your new question:<br />
Let <span class="math-container">$Y$</span> be a projective variety and let <span class="math-container">$X\subset Y$</span> be an open subset with complement the closed subset <span class="math-container">$S:=Y\setminus X$</span>. Call <span class="math-container">$f:X\hookrightarrow Y$<... | Dear Yemon,
a)The sheaf $f_\ast \mathcal{F}$ is not coherent in general since its stalk will not be finitely generated over the local ring of a point of $Y\setminus X$. For example take $P$ a point of $\mathbb P^1=Y$ and $X= \mathbb P^1 \setminus P=\mathbb A^1$. Then for $\mathcal F =\mathcal O_X$, you get $(f_\ast ... | https://mathoverflow.net |
162,108 | [
"https://physics.stackexchange.com/questions/162108",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/64080/"
] | Supposed body A slides on a surface. The will be a kinetic friction that acts on body A and opposite its relative motion.
However, is there a kinetic friction that acts on the surface too i.e. the direction is opposite to the kinetic friction that acts on body A?
| Just to take the first one as an example. Assume that the square position corresponds to coordinates, so that first square is at x = 1, etc. The center of mass is given by
$$ CM = \frac{\Sigma_i (m_i*x_i)}{\Sigma_i m_i} $$
For the first one this equation gives
$$CM=\frac{1*1+1*2+5*3+1*4}{1+1+5+1} = 22/8 =3.75 $$
| Assume the four squares are at locations 0, 1, 2, and 3. Assume the mass of each square is $M_1$, $M_2$, $M_3$, and $M_4$. If $x$ is the center of mass, then you can write the following equation:
$$(x-0)\times M_1 + (x-1) \times M_2 + (x-2) \times M_3 + (x-3) \times M_4 = 0$$
This is basically saying that if $x$ is t... | https://physics.stackexchange.com |
660,790 | [
"https://physics.stackexchange.com/questions/660790",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/310823/"
] | The fact that light could theoretically create a black hole, which would be known as a kugelblitz, means that photons must curve spacetime. And since light can exist in an orbit (admittedly an unstable one) around a black hole, could two photons exist in an unstable orbit around each other?
| There is a class of solutions of general relativity called “geons”. These could be described as “clumps” of radiation (either electromagnetic or gravitational waves) held together by their own gravitational fields. Electromagnetic geon is not quite a kugelblitz, meaning that this amount of radiation has enough gravity ... | What happens if two Planck energy photons with opposite momenta occupy one Planck volume? That should be a blackhole.
| https://physics.stackexchange.com |
15,673 | [
"https://softwareengineering.stackexchange.com/questions/15673",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/2572/"
] | What's so unique about it? Heard great things about it, used it, found that beside the Google Apps Integration there's nothing really special about it. Maybe I just don't get it?
So, what's your reason to use basecamp?
| To me, the biggest draw has been the simplicity, which leads to flexibility. The concepts that Basecamp helps to manage are easily understandable, and there's very little configuration to worry about. (Have you ever tried to use a tool like JIRA? Even its configuration has configuration.)
The simplicity starts to pay ... | It's a great way to centralize information on projects and to have a solid record of communication between users. It's also great if you are working with a distributed team.
| https://softwareengineering.stackexchange.com |
618,860 | [
"https://physics.stackexchange.com/questions/618860",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/291075/"
] | I recently learned about gravitational force and found out the equation for gravitational force on a object by an object according to Newton's law of universal gravitation.
<span class="math-container">$$ F = \frac{Gm_1m_2}{r^2}. $$</span>
<span class="math-container">$r^2$</span> denotes the square of separation betwe... | The <span class="math-container">$r$</span> value in this equation represents the separation of the two bodies' centers of mass.
So, when you're standing on the surface of the earth, then the value of <span class="math-container">$r$</span> is equal to <span class="math-container">$r_E$</span>, the radius of the earth,... | There are various issues with this thinking, I will ignore the issue of the radius not being 0 on the surface, as you covered this already.
1: While space is continuous over R, physics as a whole tends to break apart and collapse at a non-infinitesimal size, that being the Planck Length, which is around 1.6 x 10<sup>-3... | https://physics.stackexchange.com |
29,717 | [
"https://dsp.stackexchange.com/questions/29717",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/19844/"
] | If P is a projection operator, show that I-P is a projection operator. Determine the range and nullspace of I-P.
How can I solve this? What should be my approach?
| Actually, you can't say how many non-zero values $a[n]$ is going to have because, depending on the values that $b[n]$ and $c[n]$ take, $a[n]$ may equal 0 for some values of $n$ or not.
Nevertheless, I think that you want to know the length of the sequence $a[n]$. As a general rule, for two sequences of length $P$ and ... | No, you aren't correct. Convolution is equivalent to multiplying polynomials, with a sequence of length $n$ corresponding to the coefficients of a polynomial (let's say for a variable called $x$) of degree $n-1$. So convolving sequences with length $n$ and $m$ is equivalent to getting a polynomial of degree $n-1+m-1$... | https://dsp.stackexchange.com |
595,163 | [
"https://physics.stackexchange.com/questions/595163",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/247020/"
] | Question is essentially: How can the states on a quantum dot be bound when we can tunnel onto them? If plane wave states can tunnel onto them, these plane waves states and the 'bound' states will have the same energy. Thus we could find a state containing plane waves on either side of the dot and the 'bound' state. So ... | The second law leads to (or can be stated)
<span class="math-container">$$
\Delta S_{\rm tot} \ge 0
$$</span>
not <span class="math-container">$\Delta S_{\rm tot} > 0$</span> (where 'tot' refers to everything that undergoes some change during the given process). The result is zero for reversible processes, and great... | The first term of your first equation only applies to the system for a reversible heat transfer process and the inequality only applies to an irreversible process.
For the second equation the entropy of the surroundings can only change if there is heat transfer to or from the surroundings. Since there is no heat trans... | https://physics.stackexchange.com |
304,828 | [
"https://math.stackexchange.com/questions/304828",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/62416/"
] | If a, b, p, and q are positive with $a<b$ find the x-coordinate of the stationary point of the curve $y=(x-a)^p(x-b)^q$ in the domain $a<x<b$.
This is what I tried using the product rule:
$\dfrac{dy}{dx}=(x-a)^pq(x-b)^{q-1}+(x-b)^qp(x-a)^{p-1}$
I am stuck here and I don't know if I even differentiated corre... | If your first formula is correct, your second can't be. Taking $N=\pi$ you don't have normed vectors. After scaling them the proof should be the same with a little substituion in the Integrals.
Edit: you corrected the formel, now just using the subsitution rules for Integrals will bring you the result.
| In general, for a proposed family $\{e_n(x)\}$, to determine if it is <em>orthonormal</em>, just check whether $$\langle e_n(x),e_m(x)\rangle=\begin{cases}1, &n=m,\\ 0, &n\not=m,\end{cases}$$ where here the inner product is $$\langle u,v\rangle=\int_a^b u(x)\overline{v(x)}\,dx.$$
To show that an orthonormal fa... | https://math.stackexchange.com |
82,286 | [
"https://mathoverflow.net/questions/82286",
"https://mathoverflow.net",
"https://mathoverflow.net/users/19642/"
] | Can anyone give a reference, a proof, or a reference that explains why Maple can evaluate this identity mathematically correctly:
$$n-i-1=(d-1)\sum_{l=1}^{n-i-1}\frac{\binom{n-i-1}{l}}{\binom{n-i+d-3}{l}}$$
| The canonical reference for this sort of thing is Petkovsek and Zeilberger's book "A=B". Maple (almost certainly) uses the Zeilberger-Wilf algorithm for hypergeometric summation (which really goes back to Bill Gosper). You can also read the Wilf-Zeilberger paper (Inventiones, around 1990).
| As Gerhard Paseman suggested, it look better to replace $m=n-i-1$ and also $x=d-2$. With this the question takes the form $S:=\sum_{\ell=1}^m\binom{m}{\ell}\binom{m+x}{\ell}^{-1}\frac{x+1}m$ and we show $S\equiv1$. Let
$$F(m,\ell):=\binom{m}{\ell}\binom{m+x}{\ell}^{-1}\frac{x+1}m \qquad \text{and}
\qquad
G(m,\ell):=-\b... | https://mathoverflow.net |
63,589 | [
"https://mechanics.stackexchange.com/questions/63589",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/40441/"
] | I mostly want to focus on the practical / mechanical perspective of this question.
I have thought already many times on buying a small electric motorcycle for daily commute etc but i wouldn't min to have small excursion/trip on it (even on these reduced speeds).
What blocks me though is that it has such a limited ran... | One of the biggest problems to solve in electric vehicles at the moment is battery - if the battery can be made more efficient, lighter the cumulative increases in efficiency makes the vehicle much more desirable to customers.
Sharing a standard battery is a good idea eventually but currently there are two forces aga... | I'm not entirely sure that this question fits the primary purpose of this group BUT I have to say that I've long wondered why electric car manufacturers don't standardise on a battery format and devise some sort of unattended method of battery replacement.
I thought something that you drive the car onto and then the b... | https://mechanics.stackexchange.com |
272,692 | [
"https://mathoverflow.net/questions/272692",
"https://mathoverflow.net",
"https://mathoverflow.net/users/24494/"
] | Consider a collection of unit vectors $v_1, \ldots, v_n$ in $\mathbb{R}^d$ (we think of $n$ being much larger than $d$). I would like to minimize the sum:
$$\sum_{i\neq j}|\langle v_i,v_j\rangle|.$$
Clearly, if $n=d$, the minimum is attained by taking $v_i=e_i$. Could it be that for $n>d$ in order to minimize the ... | It is quite likely. At least, the proof for the case $d\mid n$ is easy. First of all, the restriction $i\ne j$ does not matter: adding $n$ ones changes nothing in the problem. Now notice that $|\langle v_i,v_j\rangle|\ge \langle v_i,v_j\rangle^2=\langle V_i,V_j\rangle$ where $V_i=v_i\otimes v_i$. Now, $\langle V_i,I\ra... | In addition to fedja's clever argument for the case $d|n$, let me prove this for $d=2$ (and $n$ of arbitrary parity).
We have $|\cos x|\geqslant 1-\frac2\pi x$ for $x\in [0,\pi/2]$ by concavity of cosine. So, it suffices to prove that the sum of angles between lines $\ell_1,\dots,\ell_n$ (which are parallel to vectors... | https://mathoverflow.net |
46,454 | [
"https://biology.stackexchange.com/questions/46454",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/24083/"
] | In a book about community ecology, I learned about Lotka-Volterra models and dynamic food web models (I am not an ecologist in the first place).
In one of the chapters, a Jacobian matrix of partial derivatives of the Lotka-Volterra model at equilibrium densities is given:
\begin{bmatrix}-&-&0&0\\+&0&... | The Jacobian tells how the system changes along different state variables (which can be, for instance, the concentrations of the predator and the prey).
The Jacobian matrix by itself doesn't give you a lot of intuitive information. However, the eigenvalues of the Jacobian matrix at the equilibrium point tell you the n... | The matrix above depicts the signs of the partial change of a function with respect to each species. Because there are 4 rows and columns, this means there are 4 species. Each row represents a partial change in each of the 4 differential equations representing the rates of change for each species with respect to each s... | https://biology.stackexchange.com |
82,885 | [
"https://security.stackexchange.com/questions/82885",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/29728/"
] | Suppose I have the public key of a recipient I'd like to send an email to, and I've never sent this person an email before. Does it make sense to encrypt my first email to this recipient and also attach my public key? Can they decrypt my email?
(This is somewhat an "etiquette" sort of question.)
thanks
| They don't need your public key at all to decrypt.
You need <em>their</em> public key to encrypt the message, which they decrypt with their <em>private</em> key. The only thing they need <em>your</em> public key for is to verify that the message comes from you. In that sense it doesn't make sense to attach your public... | In the asymmetric encryption scheme you can achieve two things:
<ul>
<li>message confidentiality : this is done by using someone's public key to encrypt a message. Only the owner of the private key can decrypt the message</li>
<li>message authentication : this is done by using your own private key to sign a message. A... | https://security.stackexchange.com |
66,689 | [
"https://quant.stackexchange.com/questions/66689",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/6686/"
] | This is going to be a embarrassingly basic question. But the answer seems to be hard to find.
What does, say, selling, <span class="math-container">$d$</span> delta of calls mean? How is the "delta" defined? I am not asking about Greek as in <span class="math-container">$\frac{\partial V}{\partial S}$</span> ... | You'll find the same issue with all of the greeks.
I would say that the standard rule for delta is the following:
If you're talking about a single option/strategy, then people will talk about delta percentage*.
If you're talking about a single option/strategy, and you don't plan to hedge the delta when it tades (i.e. y... | If you want to split hairs, as I like to do, there are 2 ways to express Delta.
"Pure Delta" is a fraction, i.e. a number between 0 and 1 (for a Call). In terms of units, it is a pure number.
"Position Delta" is equal to Delta times the size of your Call position. If you have Calls on 100 shares and... | https://quant.stackexchange.com |
210,318 | [
"https://mathoverflow.net/questions/210318",
"https://mathoverflow.net",
"https://mathoverflow.net/users/24494/"
] | Consider a probability distribution on $\mathbb{R}^k$, say $\mu$. Then there is a sequence of probability measures $\mu_n$ that converge weakly to $\mu$ so that each of them is discrete (takes finitely values).
Question: Assume we replace $\mathbb{R}^k$ by any any locally compact Hausdorf group $G$. Is the previous st... | Since the answer above addresses the problem for signed measures rather than probabilities let me add to it by noting that both versions are true and are direct consequences of versions of the Hahn-Banach theorem (bipolar theorem). The appropriate duality is that between the space of bounded, continuous functions on a... | I guess the prime reference for questions like this is Bogachev's "Measure Theory I & II". Theorem 8.9.4 ii) states that the space of Baire measures is separable if $X$ is separable and the proof uses discrete measures for a dense set in $X$.
| https://mathoverflow.net |
182,158 | [
"https://mathoverflow.net/questions/182158",
"https://mathoverflow.net",
"https://mathoverflow.net/users/41032/"
] | Let $E$ be an elliptic curve over rational field. Let $P=(a/d^2,b/d^3)\in E(\mathbb{Q})$ and
$$G=\{P,2P,3P,4P,\cdots\}.$$
Is there an integral point $Q\in G?$
| I presume that (1) $E$ is meant to be in minimal form with integer coefficients,
else you can change coordinates to put $P$ and $nP$ anywhere, and that
(2) $P$ is not itself integral (i.e. $d>1$), else $Q=P$ works.
Then the answer is No, because $d^2$ and $d^3$ divide the denominators
of $x(nP)$ and $y(nP)$ for all... | You probably meant to specify that the coordinates of $P$ are in lowest terms, and that $d\ge2$. Then, as Noam indicates, the answer is no. And it doesn't matter if the equation is minimal, as long as it has integer coefficients and as long as you start with a point $P$ having non-integer coordinates.
A good way to s... | https://mathoverflow.net |
158,211 | [
"https://electronics.stackexchange.com/questions/158211",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/68951/"
] | This question is actually from one of my previous discussions, which I still don't understand how to implement. The goal is to use abstraction to design a circuit, which converts two-digit ASCII decimal numbers into 2’s complement representation.
"Recall that characters in ASCII are represented with seven bits and th... | The steps I usually follow to find the solution are explained here. (Disclaimer:I am not an expert here.)
<h3>1. Derive the input-out relationship</h3>
The first step is to understand and express the input-output relationship in some form. You can express this relation in a convenient form. Some of the standard forms a... | Nidhin used multiplication, I'm going to use just the opposite (division) but it will really be just a bunch of subtractions, easy to do with an adder.
First, I'm going to assume all of the ASCII digits have been converted to BCD (binary coded decimal) by anding off the 0x30 (making each of the digits 4 bits instead o... | https://electronics.stackexchange.com |
600,851 | [
"https://stats.stackexchange.com/questions/600851",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/372662/"
] | The solution to the minimizing problem: <span class="math-container">$$RSS(f, \lambda) = \sum_{i=1}^n (y_i - f(x_i))^2 + \lambda \int (f''(t))^2 dt$$</span> is written in matrix form as <span class="math-container">$f = N\theta = \sum_{j = 1}^n N_j(x_i) \theta_j$</span> where the <span class="math-container">$N_j(x)$</... | <strong>A spline is a method of fitting a function to a set of points <span class="math-container">$(x_1,y_1),$</span> <span class="math-container">$(x_2,y_2),$</span> <span class="math-container">$\ldots, (x_n,y_n).$</span></strong> The answer to the question is <em><strong>because natural cubic splines exist.</strong... | <strong>This is a partial answer to be completed, I posted it just for clarification and drawing more attention.</strong>
I have consulted the ESL section. Let me first clarify the notations. The problem is 1D function estimation so the training data is <span class="math-container">$(x_i, y_i): i = 1, \ldots, n$</spa... | https://stats.stackexchange.com |
247,305 | [
"https://softwareengineering.stackexchange.com/questions/247305",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/27333/"
] | Consider these polygons:
<img src="https://i.stack.imgur.com/jSeLV.png" alt="Consider these polygons">
For reasons of simplicity I only consider triangles or polygons with 4 vertices.
These shapes are specified by the vertices, the output of the program should be modified vertices.
I am trying to find an algorithm t... | Basically you just have to think about sliding edges inward and imagine where they intersect to form an interior polygon. Picture that and you'll be set.
| What determines the size of the space?
I think you're focusing on the vertices when you should be focusing on the lines.
Since you've changed the shape as well as the size, it would seem to be pretty easy. Given a gap width W, slice W/2 each side of all internal lines and W away from all borders. Then revise the ver... | https://softwareengineering.stackexchange.com |
511,050 | [
"https://electronics.stackexchange.com/questions/511050",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/257924/"
] | I want to design a bias-T for satellite application where L band RF (950-2150 MHz),10 MHz, and DC will be multiplexed.
I need help in finalizing/selecting the inductor(choke) through which DC (13V/18V,2 amperes) will be passed.
Also what I understood is the inductor must block both L band RF and 10 MHz signal.
Exactly ... | It has a designator of C38 which means it is a high voltage capacitor with a spark gap.
Typically the coaxial cable interface is isolated from the PC chassis ground, with the exception that the cable shield is connected to PC chassis via a 1 Mohm resistor in parallel with a 10nF high voltagre capacitor. The capacitor v... | it's a spark gap. I'm sure this has been answered before.
| https://electronics.stackexchange.com |
404,636 | [
"https://physics.stackexchange.com/questions/404636",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/194370/"
] | Electrons and holes behave differently in a silicon semiconductor (e.g. mobility of holes is one order of magnitude smaller than that of electrons, the collection time of holes at the same electric field is larger than for electrons... ). I was wondering, if holes are simply "a lack of electrons", they should behave in... | One qualitative way to understand this concept is by thinking about the orbital origins of the conduction band and valence band.
For example, let's assume the conduction band is primarily coming from hybridized <span class="math-container">$s$</span>-orbitals, while the valence band comes from hybridized <span class="m... | Check that electrons move in the conduction band, whereas holes "move" in the valence band. They have different energies, but they are also at a different border.
So the difference arises that the mass of electrons depends on the second derivative of the energy with respect to <span class="math-container">$k$</span>.... | https://physics.stackexchange.com |
3,396,414 | [
"https://math.stackexchange.com/questions/3396414",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/640983/"
] | I'm working on a problem but I need additional feedback to see if its correct. I'm trying to figure out if....
<span class="math-container">$$P(A \cup B) ⊆ P(A) \cup P(B) \cup P(A \cap B)$$</span>
Where power set is denoted by P.
I used A = {1,2,3} and B = {2,4}. I did all the power sets for each of the following... | While the statement is indeed false, your counterexample is incorrect: the set <span class="math-container">$\{2, 4\}$</span> is an element of <span class="math-container">$\mathcal P(B)$</span> and therefore also of <span class="math-container">$\mathcal P(A) \cup \mathcal P(B) \cup \mathcal P(A \cap B)$</span>.
Try... | Yes, you are correct.
An even simpler example to see why you are correct is <span class="math-container">$A=\{1\}$</span> and <span class="math-container">$B=\{2\}$</span>.
| https://math.stackexchange.com |
520,291 | [
"https://physics.stackexchange.com/questions/520291",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/248514/"
] | When we let the electron move freely in an electric field, the electric potential of electron must decrease but the electron moves opposite to the field so do we say that it's electric potential is increasing? Also what happens to its electric potential energy?
| Assuming an adiabatic expansion, there can be no change in internal energy. In order for the gas molecules at the interface between the evacuated and gas occupied chambers to accelerate into the vacuum, other parts of the gas behind the interface must do work to "push" the gas molecules into the evacuated space. That w... | As long as your system is thermally isolated from the environment so that the expansion is adiabatic, the internal energy must stay constant during the expansion. This follows directly from the first law of thermodynamics.
<blockquote>
But thinking in terms of the gas particles accelerating into the vacuum due to th... | https://physics.stackexchange.com |
52,241 | [
"https://mathoverflow.net/questions/52241",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3503/"
] | Let E be an elliptic curve, let $L(s) = \sum a_n n^{-s}$
denote its L-function, and set
$$ f(x) = \sum a_n \frac{x^n}{n}. $$
Then Honda has observed that
$$ F(X,Y) = f^{-1}(f(X) + f(Y)) $$
defines a formal group law.
The formal group law of an elliptic curve has applications to
the theory of torsion points, appa... | Okay, here's a few words about the relation between the $L$-series and the formal group. In general, if $F(X,Y)$ is the formal group law for $\hat G$, then there is an associated formal invariant differential $\omega(T)=P(T)dT$ given by $P(T)=F_X(0,T)^{-1}$. Formally integrating the power series $\omega(T)$ gives the f... | The usual(?), or at least more prosaic, way to define the formal group law on an elliptic curve $E$ is to take a Weierstrass equation and expand the addition law in terms of the formal parameter $z = -x/y$, which is a uniformizer at the identity element of $E$. Then one studies formal groups abstractly, proves various ... | https://mathoverflow.net |
400,309 | [
"https://stats.stackexchange.com/questions/400309",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/97856/"
] | I'm trying to <em>prove</em> the efficiency of OLS over GLS when the covariance matrix of the error <span class="math-container">$\varepsilon$</span> is mistakenly assumed to be <span class="math-container">$\sigma^2\Sigma$</span> instead of <span class="math-container">$\sigma^2 I$</span>. After deriving the variances... | This is what I ended up doing:
<span class="math-container">$$Var(\beta^{gls}) = Var[(X'\Sigma^{-1}X)^{-1} X'\Sigma^{-1}\varepsilon]\\
=(X'\Sigma^{-1}X)^{-1} X'\Sigma^{-1} Var(\varepsilon) \Sigma^{-1} X(X'\Sigma^{-1}X)^{-1}\\
= \sigma^2 (X'\Sigma^{-1}X)^{-1} X'\Sigma^{-1} \Sigma^{-1} X(X'\Sigma^{-1}X)^{-1}\\
$$</span>
... | It is known that <span class="math-container">$V(\beta^{gls}-\beta^{ols}|X)$</span> is positive semidefinite. Here it turns out that <span class="math-container">$$V(\beta^{gls}-\beta^{ols}|X)=V(\beta^{gls}|X)-V(\beta^{ols}|X),$$</span> hence the conclusion that <span class="math-container">$\beta^{ols}$</span> is rela... | https://stats.stackexchange.com |
67,784 | [
"https://dsp.stackexchange.com/questions/67784",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/50600/"
] | I have a sequence of (real) numbers that represent the magnitude of a certain natural event. I know that the samples are equispaced in time, but not the exact value of the spacings. So does that mean I do not know the sampling rate? And, how should I proceed on to doing a DFT on this dataset?
P.s. Let's say the datase... | Continuing from my comments.
The units equation in the comments usually has these variables:
<span class="math-container">$$ f_{Hz} = k \cdot \frac{F_s}{N} $$</span>
Where <span class="math-container">$k$</span> is the bin index. This can be rearranged a little bit to:
<span class="math-container">$$ f_{Hz} = \fr... | If you don’t know the sample spacing, you don’t know the sample rate.
If you know that samples are uniformly spaced, you can do a DFT and get relative frequencies. You won’t be able to map one dft bin to a specific frequency (in Hertz) unless there is some additional side info (perhaps a known reference hidden within ... | https://dsp.stackexchange.com |
894,724 | [
"https://math.stackexchange.com/questions/894724",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/80452/"
] | So I'm reading through Lang's <em>Algebra</em>, and he keeps saying something along the following lines:
"Let $K$ be a finite extension of a field $k$ and let $\sigma_1,\ldots,\sigma_r$ be the distinct embeddings of $K$ in an algebraic closure $k^\text{a}$ of $k$."
But the thing is that it doesn't seem clear to me th... | The key is that if you have a finite extension $K/F$, adding elements to $F$ will always raise the degree of the extension by some factor, so you get a tower of simple extensions $F \subseteq F(\alpha_1) \subseteq F(\alpha_1)(\alpha_2) \subseteq \cdots$. By finiteness of $K/F$, this process has to stop. Then you should... | If $K = k(a_1,\dots,a_n)$ is a finite field extension, then an embedding $\sigma: K \rightarrow k^{a}$ must send each $a_i$ to another root of its minimal polynomial over $k$. (Indeed, if $p(a_i)=0$ for $p \in k[x]$, then $p(\sigma(a_i))=0$. ) This shows there are only finitely many possibilities for the image of each ... | https://math.stackexchange.com |
342,498 | [
"https://electronics.stackexchange.com/questions/342498",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/168193/"
] | I've been trying to find information about the formula \$ v = L \cdot \frac{di}{dt} \$, it seem to have something to do with voltage drop, and I know voltage drop is caused by resistance, so would a material with zero resistance still have weaker levels of induction with higher frequencies of changing current?
| Yes, it does. Actually, for an inductor,
\$ v = L \frac{di}{dt} + Ri \$
R is the resistance of the wire in your inductor. If you use a superconductor, it would be zero. The first part of this equation models a theoretically perfect inductor (ie, superconducting, like all inductors in spice simulation unless you speci... | Your formula is the basic law on how inductors behave in electric circuits. Actually it's derived from a relation between magnetic and electric field, more specificly from the one that states how strong electric field is caused if magnetic field changes. That law is as valid in all materials and in the empty space.
Co... | https://electronics.stackexchange.com |
390,810 | [
"https://softwareengineering.stackexchange.com/questions/390810",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/334511/"
] | My team has a problem with making code review.
Everyone is constantly busy with their tasks and only few of developers do review on a daily basis. As every merge request needs 2 approvals, some of them stay in review for days if not for weeks (!), which slows down the project.
Everyone understands the importance of... | It seems like the problems begin with planning. When you determine the capacity of the team to take on a given body of work, you should consider the time that it will take to peer review the work done (in addition to everything else that is needed to complete the work). The idea that people are simply too busy to perfo... | Ah the fallacy of "I'm too busy developing to code review."
Well code reviews <em>are</em> development - just because it's inherently not your feature doesn't affect that.
Ultimately everyone suffers. It's not straightforward at all to get a culture of prioritising code reviews first but it is necessary.
Hence code ... | https://softwareengineering.stackexchange.com |
83,028 | [
"https://security.stackexchange.com/questions/83028",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/69612/"
] | My goal is to sniff the HTTPS traffic of some digital devices (AppleTV, game consoles, etc.), and decrypt the HTTPS packets in my local network.
I cannot figure out a way by using some HTTPS debugging proxy tools like Charles or Fiddler, because they need to have a certificate installed on the device. I don't have ac... | The entire point of SSL is its resistance to eavesdropping by man-in-the-middle attacks like the one you're proposing. If you cannot make the client device trust your self-signed certificate, then your only options are:
<ul>
<li>Intercept an initial HTTP request and never let the communication be upgraded to HTTPS (bu... | <blockquote>
Any suggestions? Is is doable?
</blockquote>
You need to own a certificate trusted by the device to intercept the traffic. How this can be achieved depends on how proper and open the certificate validation on the device is.
<ul>
<li>The device might have a buggy or non-existing validation of certificat... | https://security.stackexchange.com |
106,000 | [
"https://mathoverflow.net/questions/106000",
"https://mathoverflow.net",
"https://mathoverflow.net/users/25634/"
] | Hi, I am really struggling with this question.
The question is :
Let $f:R^3\to R$ and $f\in L^2(R^3)$. $f$ is supported on a ball of radius 1/2 centred at origin. Let $u$ be the solution to $\Delta u=f$ , where $ u $ is given by $u(x)= \frac{1}{4\pi}\int_{R^3}\frac{1}{|x-y|}f(y)\,dy$.
<ol>
<li>Show that $L^2$ norm... | The Grothendieck group of a semiring is a ring. So you are just asking what will happen if you take the multiplicative Grothendieck group of a ring.
Well, it depends on whether you include $0$ in the multiplicative structure! If you include $0$, then $a/b=0a/0b=0/0$ so you get the trivial group. Similarly, inverting z... | <ol>
<li>The Grothendieck group of a commutative group is group itself, hence applying the construction twice doesn't change the result. The semiring case is a special case of this.</li>
<li>What do you mean by "order of application". There is no order if you apply the same thing twice. G(G(M)) is the same as G(G(M)) .... | https://mathoverflow.net |
132,991 | [
"https://softwareengineering.stackexchange.com/questions/132991",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/39810/"
] | Where I currently work the general approach is -
<strong>avoid documentation as much as possible</strong>
<strong>Only document if a different team will need it</strong>
just for clarification, I don't mean code-documentation - this we do, I mean all the documentation surrounding the design process - if it's UML or... | I've found ANY documentation is better than NO documentation. The appropriate amount is usually determined by the amount of time we have to do it, or by how much we hate support phone calls and emails.
It appears that your current team members have some unrealistic expectations of their memories, or they are ashamed ... | You cannot escape allocating time to write proper documentation. Balance it however you wish depending on how much work you are given, but leave a good 15-20% of your time to document what you have done. Everyone on the team has to be on board with this, including your manager, otherwise you will only be documenting fo... | https://softwareengineering.stackexchange.com |
3,797 | [
"https://mechanics.stackexchange.com/questions/3797",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1918/"
] | What can be the cause of a vibrating steering wheel when driving faster than a specific velocity (let's said 60 mph). How to discriminate one cause from on other ?
| Vibration felt in the steering wheel is usually caused by the front tires out of balance. That's the first place to look, other possibilities include: broken belt in the tire, out of round tire, a bent rim, a bent or out of round hub, wheel bearings.
One of the things you can do to help narrow it down would be to rot... | I had a bad vibration when cruising on highway, I did an alignment and changed my wheels bearing. The vibration was mostly gone but I got a "death wobble", which is a loud noise coming from the front at high speed. I changed my tie rod ends and steering damper, redone an alignment and now everything is fine.
I'll do ... | https://mechanics.stackexchange.com |
128,888 | [
"https://mathoverflow.net/questions/128888",
"https://mathoverflow.net",
"https://mathoverflow.net/users/19409/"
] | Consider the action of $\mathbb{Z}/p^\times$ the units of $\mathbb{Z}/p$ on the classifying space $B\mathbb{Z}/p$ by left multiplication on the $n$-simplices
$$
\alpha\cdot (g_1,...,g_n)=(\alpha g_1,...,\alpha g_n).
$$
Here $B\mathbb{Z}/p$ denotes the usual model as the realization of the simplicial set whose $n$-sim... | $\newcommand{\Ext}{\operatorname{Ext}}$$\newcommand{\To}{\longrightarrow}$$\newcommand{\dash}{\text{-}}$$\newcommand{\sSet}{\mathrm{sSet}}$$\newcommand{\ZZ}{\mathbb{Z}}$For convenience, I will denote by $G$ the group $(\ZZ/p)^\times$, and by $X$ the simplicial set $B(\ZZ/p)$ for $p$ a prime. I will prove later in this ... | <em>See the comments: the action is not properly discontinuous so the spectral sequence converges to the Borel construction rather than to the quotient, so this does not really compute what is wanted.</em>
Let $\ell$ be a prime number.
Let $G=(\mathbb Z/\ell)^\times$ and $C_p=\mathbb Z/\ell$, and suppose $G$ acts on ... | https://mathoverflow.net |
116,989 | [
"https://stats.stackexchange.com/questions/116989",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/56539/"
] | I'm having a problem with my dissertation.
My research is "level of satisfaction in relation to customer service: comparative study between 2 fast foods
my questionnaire consists of 19 questions. I'm using SERVERF, the 5 dimensions. 8 questions for Tangibility, 3 for Reliability, Responsiveness, Assurance and 2 quest... | First, make sure you have clearly defined your problem of interest, and correctly formulated your null hypothesis. Given that you research is "level of satisfaction in relation to customer service: comparative study between 2 fast foods", the null hypothesis would be "there is no different in terms of satisfaction betw... | First, this
<blockquote>
my null hypothesis is to know if there's a significant difference
between the 2 fasfoods in terms of gender, age, year level and school.
</blockquote>
is not a null hypothesis. The null hypothesis would be something like "There is no difference between preference for fast food based on ge... | https://stats.stackexchange.com |
1,977,776 | [
"https://math.stackexchange.com/questions/1977776",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/376253/"
] | Why is it that when we are finding the limit as x tends to infinity of a function, we disregard all variables on the numerator and denominator, except for the ones with the highest degree?
| If $B$ is nonempty then $A$ must be closed, because if $b \in B$ then $A$ is the inverse image of $A \times B$ by the map $\mathbb{R} \to \mathbb{R}^2, x \mapsto (x,b)$. But if $B$ is empty then $A$ can be arbitrary (because $A \times B$ is empty), and may not be closed.
| Suppose $A,B$ are non-empty subsets of $R$. Note for any sequence $\{(a_n,b_n)\}_1^\infty; x_n \in A, y_n \in B$ for all $n$, the sequence converges (in $R^2$) if and only if it converges coordinate-wise. Suppose it converges to $(x,y) \in R^2$, then $(x,y) \in A \times B$ by assumption, and hence $x \in A$.
Now fix ... | https://math.stackexchange.com |
129,148 | [
"https://mathoverflow.net/questions/129148",
"https://mathoverflow.net",
"https://mathoverflow.net/users/30342/"
] | Let M be your favorite moduli stack over the field of complex numbers.
Is it reasonable to expect M to be a Deligne-Mumford stack?
I know this is true for the moduli space of curves of genus g, ppav's and K3 surfaces. I'm just wondering what I should expect when considering other moduli stacks.
| If the objects under consideration all have finite automorphism groups, you should expect your stack to be Deligne-Mumford. Otherwise, it isn't Deligne-Mumford; but that is no cause for alarm.
| No (per the many examples in the comments).
| https://mathoverflow.net |
141,466 | [
"https://electronics.stackexchange.com/questions/141466",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/31102/"
] | As I understand, all MOSFETs have body diode. But I see some symbols have body diode shown while some not. Is there a difference in such MOSFETs?
| No, there is no difference. There is no "official" MOSFET symbol, just variations on a theme. The diode will always be there regardless.
The symbols with a diode explicitly shown are very useful when the diode itself is an important part of the circuit, to serve as a reminder as to which way the diode is biased.
| There is not. It is accepted that the body diode is reverse biased in diagrams where it is not explicitly shown.
| https://electronics.stackexchange.com |
1,934,174 | [
"https://math.stackexchange.com/questions/1934174",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/227967/"
] | <blockquote>
Question:
Given metric space $\left ( X,d \right )$ and $\left ( Y,e, \right )$,
define the product metric on $X \times Y$ by $f\left ( \left ( x_{1},y_{1} \right ), \left ( x_{2},y_{2} \right )\right ):=\max\left \{ d\left ( x_{1},x_{2} \right ),e\left ( y_{1},y_{2} \right ) \right \}$
Show ... | You can understand this in a few steps.
First, prove that there is a basis for the product topology on $X \times Y$ consisting of all subsets of $X \times Y$ of the form $B_d(x,r) \times B_e(y,s)$, for $x \in X$, $y \in Y$, $r,s > 0$ (notice that the two radii $r,s$ are allowed to vary independently). This is a gen... | A useful criterion is as follows: (Munkres, Lemma 2.2) Let $B,B'$ be bases for the topologies $T,T'$ on $X$. Then the following are equivalent:
<ul>
<li>$T'$ is finer than $T$</li>
<li>For each $x \in X$ and each basis element $b \in B$ containing $x$, there is a basis element $b' \in B'$ such that $x \in b' \subset b... | https://math.stackexchange.com |
98,327 | [
"https://electronics.stackexchange.com/questions/98327",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/36437/"
] | I need to communicate with a piece of hardware on an elevator car. I have a few twisted copper pairs available, but it's not CAT5, so Ethernet is out. Instead I'd like to use RS485.
I've been reading and ground level difference can really mess up 485, I'm also passing power along with the RS485. ( So 6 conductors: A,... | If you can guaranteed the grounds are going to be close (within +/-7V peak) under all possible conditions, then no isolation is required.
Personally, I would go for isolation <strong>without question</strong>. What happens when lightning strikes nearby? I foresee a bunch of RS-485 transceivers getting replaced and an... | I'd consider using radio transmitters. I've used 433MHz off-the-shelf cheap radios for sending data down 200 feet of tunnels and along about the same distance in railway carriages and they worked fine with less than 1mW output power.
Your data rate isn't very great (you said) so sending data half-duplex shouldn't real... | https://electronics.stackexchange.com |
159,957 | [
"https://softwareengineering.stackexchange.com/questions/159957",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/61302/"
] | Suppose I have a method
<pre><code>public List<User> GetBatchOfUsers(IEnumerable<int> userIDs)
{
List<User> users = new List<User>();
// some database stuff
return users;
}
</code></pre>
I have read that it would be better to return an interface (either <code>IList</code> or <cod... | Generally speaking, you may start with interfaces, and only move to put the concrete type as the return type if you find that you use the extra methods more frequently than expected.
Well, if you return an interface, you retain more flexibility. You can change the implementation later to return a different concrete ty... | If You need your collection to have a <code>Count</code> you can use <code>ICollection<T></code>, which is general enough.
| https://softwareengineering.stackexchange.com |
53,486 | [
"https://cs.stackexchange.com/questions/53486",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/46793/"
] | Problem:
<blockquote>
We'll define a binary tree as a tree where the degree of every internal node is exactly 3. Show that the set of all binary trees is countable.
</blockquote>
My attempt:
A set is countable if it is finite or there is a one-to-one correspondence with the natural numbers. So we need to show tha... | As concluded via non-direct means in discussion interpreting a polytime program cannot be done in polynomial time in general. The following example shows this directly.
The trick is that for the interpreter to run in polynomial time there must be an polynomial that bounds the running time for <em>every</em> input. Thi... | <blockquote>
If a language can interpret itself then it is not total
</blockquote>
I take this to mean that if there is a universal machine for a class in the class itself, the class can not be total (i.e. there have to be non-total functions in the class). What you probably have in mind is that the class can not be... | https://cs.stackexchange.com |
406,094 | [
"https://electronics.stackexchange.com/questions/406094",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | I'm controlling a Permanent Magnet DC motor with PWM for a treadmill. I'm using a reflective sensor with 6 pulses per rev to get a speed feedback. So I'm actually doing "speed control" directly, but not "torque control". So I have two specific questions:
1- Do I need direct torque control for this application by measu... | 1-No not necessarily. You need to control the torque, since in a treadmill you want at a specific setting a constant speed no matter how much the load varies, and the speed loop will make sure that happens. however adding internal torque loop ( cascade PID ) could help with improving response and better disturbance re... | Strictly, you don't need torque control. You could simply wire a fixed value resistor to the generator.
The downside is the current in the resistor is speed dependent, which gives you a quadratic speed-power relation. This doesn't feel like natural running, more like running in molasses.
| https://electronics.stackexchange.com |
512,691 | [
"https://physics.stackexchange.com/questions/512691",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/222367/"
] | I am confused as to how fermi level is defined within a crystal/ solid
It is normally situated midway between valence band and conduction band, is this how it is defined or is there other reasons this is so?
In different fields, the fermi level has different definitions (e.g. the energy needed to add one electron to a ... | <blockquote>
It is normally situated midway between valence band and conduction band, is this how it is defined or is there other reasons this is so?
</blockquote>
Not necessarily. You're right - if the definition of <span class="math-container">$\mu$</span> was simply that all states with energy <span class="math-... | This is rather the definition of the valence and conduction bands, rather than of the Fermi level. Given a solid, all the states below the Fermi energy are occupied, hence this is the valence band, and all the levels above the Fermi energy are unoccupied, and can be used for conduction (assuming they are not localized)... | https://physics.stackexchange.com |
333,877 | [
"https://mathoverflow.net/questions/333877",
"https://mathoverflow.net",
"https://mathoverflow.net/users/94097/"
] | Consinder a smooth manifold <span class="math-container">$M$</span> and <span class="math-container">$\omega$</span> a smooth <span class="math-container">$1$</span>-form on <span class="math-container">$M$</span>. Assume that there is an open set <span class="math-container">$U\subset M$</span> such that <span class="... | Even allowing <span class="math-container">$A$</span> and <span class="math-container">$B$</span> to be <em>real</em> numbers, the vectors <span class="math-container">$A a + B b$</span> will all lie in some fixed plane <span class="math-container">$P$</span>. But then, if <span class="math-container">$n \ge 3$</span>,... | For <span class="math-container">$n=1$</span> the probability that such <span class="math-container">$A$</span>, <span class="math-container">$B$</span> exist is at least
<span class="math-container">$$\frac6{\pi^2}\left(1+\frac18\right)=68\%$$</span>
since it can happen at least in the following two disjoint ways:
<u... | https://mathoverflow.net |
107,031 | [
"https://physics.stackexchange.com/questions/107031",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5729/"
] | Are there any QM effects that have been/could be measured from interactions involving non-charged particles?
Elementary QM is all about the electron energy levels in the atom, photon - atom interactions, etc.
When one looks at the nucleus, its all about quark interactions - which are also charged particles.
I can... | Every particle that interacts with something is charged -- in some sense. We say that particles are charged under a certain interaction if they are affected by that interaction, and their charge measures how strongly they interact.
But what you seem to be asking about is <em>electric</em> charge. Then one idea of an o... | Am I missing something here? Photons and the double-slit experiments do the trick. Likewise, you can entangle the polarisation degrees of freedom of photons. This is inherently quantum and photons aren't charged. True, they are the excitations of electromagnetic fields, but they are not charged.
Anyway, I guess the pr... | https://physics.stackexchange.com |
142,143 | [
"https://dba.stackexchange.com/questions/142143",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/95730/"
] | 1.
<pre><code>SELECT COUNT( * )
FROM tbl_shipment
WHERE `awdno` != '' AND `prtner_name` != ''
GROUP BY prtner_name
</code></pre>
2.
<pre><code>SELECT SUM( inscan )
FROM tbl_shipment
WHERE `awdno` != '' AND `prtner_name` != ''
GROUP BY prtner_name
</code></pre>
3.
<pre><code>SELECT SUM( is_deliver )
FROM... | Since the <code>FROM</code>, <code>WHERE</code> and <code>GROUP BY</code> clause are identical, combine them as follows:
<pre><code>SELECT
prtner_name,
COUNT(*) shipment_count,
SUM(inscan) inscan_count,
SUM(is_deliver) is_deliver_count,
SUM(is_rto) is_rto_count
FROM tbl_shipment
WHE... | Hi all query will be merge like this
<pre><code>SELECT prtner_name,
count(id) AS cnt,
SUM(inscan) AS inscan,
SUM(is_deliver) AS deliver ,
SUM(is_rto) AS rto
FROM `tbl_shipment`
WHERE `awdno` != ''
AND `prtner_name` != ''
GROUP BY `prtner_na... | https://dba.stackexchange.com |
35,156 | [
"https://physics.stackexchange.com/questions/35156",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/5050/"
] | We know that space cannot spread a sound wave as there is no "air" or a medium that would support the spread of a sound wave. However if we put ourselves in the vicinity of an exploding star, would it be possible to hear something?
The question arises from the idea that within the explosion of a star (first few second... | If you were close enough to be hit by a significant amount of something (material or just radiation) being ejected from the star, then you would probably hear it hitting the walls of whatever is keeping air around you (spaceship, space-suit, whatever).
This would not last very long though, since the noise would be th... | Sound is a longitudinal compression/rarification wave; these things can't really be said to exist unless the wavelength is much longer than the mean free path in the medium. In space the mean free path is going to be very, very long even is a dense nebula.
So the first, reasonable answer is very, <em>very</em> low pit... | https://physics.stackexchange.com |
167,031 | [
"https://dba.stackexchange.com/questions/167031",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/78725/"
] | Title says it all. Strangely can't find a result on this.
| Yes, it does. How come ? Run this query in the RDS Instance:
<pre><code>mysql> select * from information_schema.engines where engine='MEMORY'\G
*************************** 1. row ***************************
ENGINE: MEMORY
SUPPORT: YES
COMMENT: Hash based, stored in memory, useful for temporary table... | This answer applies to AWS Aurora not straight MySQL RDS.
Just because <code>SHOW ENGINES</code> says the database has the <code>MEMORY</code> storage engine doesn't mean you can actually use it. We have found that in AWS Aurora the <code>SHOW ENGINES;</code> call will tell you that the <code>MEMORY</code> engine is s... | https://dba.stackexchange.com |
278,571 | [
"https://softwareengineering.stackexchange.com/questions/278571",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/61302/"
] | Currently I have 3 service classes, they all have a similar pattern, and I need to make a 4th service class which amalgamates the functionality of the other three.
<strong>Current three classes</strong>
<pre><code>public class PersonService : IPersonService
{
public PersonServiceResult CreatePerson(CreatePersonPa... | I would start with eliminating the duplicated code first by building a generic creation service, something along the lines of
<pre><code> class GenericCreatorService<T>
{
UnitOfWorkFactory _unitOfWorkFactory;
// ...
public T Create(Func<T,UnitOfWork> func)
{
... | Inject the three Creator-classes and test the calls to them by unittesting the QuickOrderService. This keeps the tests on the relevant classes.
Also, you might not need to haul the unitOfWork around. The implementation of Create could be changed to simply create a new transaction if none exists and otherwise return th... | https://softwareengineering.stackexchange.com |
680,825 | [
"https://physics.stackexchange.com/questions/680825",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/321100/"
] | If I had a 1000km long steel rod and I pushed one end of it, when would someone standing at the other end observe movement? Would it travel exactly the speed of sound in that material, or is the speed of sound variable depending on the amplitude of the impulse (ie would it travel quicker)?
| You are completely right: the stone, due to its higher inertia (because of its higher mass), accelerates less but is still moving. That’s the essence of <span class="math-container">$F=ma$</span>. So the example in your book is indeed not accurate.
An accurate experiment would take place in more controlled context, e.g... | If you had taken a 1000 kg football then if you kicked it, would it move? The answer is I don't know until you tell me how much force you had done on that object.. Assume there's no friction (which we usually assume always in Newtonian mechanics, we rarely work with friction in newtonian mechanics but I will show what ... | https://physics.stackexchange.com |
6,370 | [
"https://physics.stackexchange.com/questions/6370",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/2383/"
] | How do I find the distance traveled of an object if the speed is not constant?
| If the speed is a function of time, than the total distance is just the integral with respect to time. For example, the distance traveled $D$ for an object moving at a velocity $v(t)$ over a time interval $t_0$ to $t_f$ is
$D=\int_{t_0}^{t_f}v(t)dt$
This is elementary calculus. If you didn't know this already, then y... | Well, you could always lay down a measuring tape between the final position and the initial position and see what it reads ;-)
But seriously though: I'm guessing that all you know is the velocity as a function of time, right? In that case, you'll have to do an integral. Velocity is defined as the time derivative of po... | https://physics.stackexchange.com |
132,310 | [
"https://dba.stackexchange.com/questions/132310",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/89718/"
] | I have multiple tables (12 for each month) that have 3 columns each ("code", "test_name", "value")
Example:
<hr>
<pre><code>January
code | test_name | value
0001 name1 17
0002 name2 45
0005 name5 12
</code></pre>
<hr>
<pre><code>February
code | test_name | value
0001 name1 3
0002 ... | The ampersand character (<code>&</code>) prompts for values before execution time by default. That is not how you display values of variables. Try the below instead.
<pre><code>set serveroutput on
SPOOL logs\MVP_MEC_UPDATED.log APPEND
DECLARE
precount NUMBER;
nowcount NUMBER;
BEGIN
SELECT COUNT(*) I... | Are you prompted for &&CLIENTID &&precount and &&nowcount?
I believe that's where your problem comes from.
If you want to display the results for precount and nowcount, can you try:
set serveroutput on
<pre><code>DECLARE
precount NUMBER;
nowcount NUMBER;
BEGIN
SELECT COUNT(*) I... | https://dba.stackexchange.com |
30,210 | [
"https://softwareengineering.stackexchange.com/questions/30210",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/231/"
] | I heard a while back that there used to be a compiler that attempted to fix syntax errors by analyzing context and inferring what was intended.
Does such a compiler really exist? Obviously it has little practical value, but would be very interesting to play with and learn from.
| In some sense, the act of compiling <em>is</em> inferring what certain syntax is meant to do, and hence a syntax error is when the compiler isn't able to figure it out. You can add more "guessing" to have the compiler infer further things and be more flexible with the syntax, but it must do this inferring by a specific... | Sounds really dangerous. If a compiler tries to infer your intent, infers it wrong, fixes the code, and then doesn't tell you (or tells you in some warning that you, like everyone, ignore), then you're about to run code that may seriously do some damage.
A compiler like this is probably something that has very intent... | https://softwareengineering.stackexchange.com |
68,944 | [
"https://math.stackexchange.com/questions/68944",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/16961/"
] | Given the following quadratic equations:
<ul>
<li>$4n^2 + 128n - 131$</li>
<li>$4n^2 + 16n - 11$</li>
<li>$4n^2 + 24n - 3$</li>
</ul>
Is it possible to determine how many values of n will generate a perfect square? Or better yet, is it possible to determine which values of n will generate a perfect square?
| You can complete the square. For the third example, $4n^2+24n-3=(2n+6)^2-39.$ As $(n+1)^2-n^2=2n+1$, this cannot be a perfect square for any $2n+6$ greater than $20$, leaving only $7$ possibilities.
We can do better. You want $(2n+6)^2-39=p^2.$ This means $39=(2n+6-p)(2n+6+p)$. There will be one solution for each... | <strong>HINT:</strong> Let's rearrange the first equation:
$4n^2-4n+132n+1-132=(2n-1)^2+132(n-1)=m^2$ now we can easily see that $n-1$ has to be $0$ so $n=1$
For the second equation we may write:
$4n^2+4n+12n+1-12=(2n+1)^2+12(n-1)=m^2 \Rightarrow n=1$
For the third equation:
$4n^2+20n+4n+25-28=(2n+5)^2+4(n-7)=m^2 ... | https://math.stackexchange.com |
675,579 | [
"https://physics.stackexchange.com/questions/675579",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/318499/"
] | Do air parcels not push against other air and do work on them? When air molecules within an air parcel bump into air molecules outside the air parcel do they not transfer energy to them?
| I think it's easiest to do this in Cartesian coordinates, then convert back to cylindrical at the end. The potential at position <span class="math-container">$\mathbf{r}$</span> is
<span class="math-container">$$V(\mathbf{r}) = \frac{1}{4\pi\epsilon_0}\int_{-a}^{a}{\left[\iint_{\mathcal{R}}{\frac{k\delta(x')\delta(y')}... | Defining the charge density with a delta function in cylindrical coordinates just means that when we integrate over all space, we'd better recover the total charge.
In Cartesian coordinates:
<span class="math-container">$$\int_{-\infty}^\infty\int_{-\infty}^\infty\int_{-\infty}^\infty k\delta(x)\delta(y)\theta(a-|z|)dx... | https://physics.stackexchange.com |
74,009 | [
"https://mathoverflow.net/questions/74009",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9947/"
] | I have a very simple question, because I basically just need to know if a certain train of thought I've had is correct. My reference is Liu's book "Algebraic Geometry and Arithmetic Curves", in particular Proposition 8.1.15, and of course Hartshorne. Consider the following situation:
Let $f:W\to X$ be a morphism of lo... | Suppose $f={\rm Id}_X$, $X={\bf A}^3_{\bf C}$ (affine space of dimension $3$ over the complex numbers). Suppose that $\cal I$ is the sheaf of ideals of a smooth curve going through $0$ and that $\cal K$ is the sheaf of ideals of the point $0$ in ${\bf A}^3_{\bf C}$. Then the
pull-back of ${\cal J}={\cal I}$ to $\wide... | I wonder if the statement (about the existence of $\tilde f$) is correct. Consider the case when $W=X=\mathbb{C}^3$, $f=id_X$, $\mathcal{I}$ is the ideal sheaf of a line $L$, and $\mathcal{K}$ is the ideal sheaf of a point $x\in L$. We obtain two blow-ups $\tilde W=\widehat{\mathbb{C}^3_x}$,
$\tilde X=\widehat{\mathbb{... | https://mathoverflow.net |
4,951 | [
"https://electronics.stackexchange.com/questions/4951",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1235/"
] | Say I have a 1F capacitor that is charged up to 5V. Then say I connect the cap to a circuit that draws 10 mA of current when operating between 3 and 5 V. What equation would I use to calculate the voltage across the capacitor, with respect to time, as it is discharging and powering the circuit?
| charge on a cap is a linear product of capacitance and voltage, Q=CV. If you plan to drop from 5V to 3V, the charge you remove is 5V*1F - 3V*1F = 2V*1F = 2 Coulombs of charge. One Amp is one Coulomb per second, so 2C can provide 0.01A for 2C / (0.01 C/sec) or 200 seconds. If you actually withdraw charge from the cap at... | The general equation for the voltage across the capacitor is
<blockquote>
\$ V = V_0+\dfrac{1}{C} \int {i dt}\$
</blockquote>
In the special case where \$I\$ is constant this translates to
<blockquote>
\$ V = V_0 + \dfrac{I \times t}{C} \$
</blockquote>
We want to find \$t\$, so rearranging gives us
<... | https://electronics.stackexchange.com |
350,420 | [
"https://stats.stackexchange.com/questions/350420",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/210999/"
] | Assume I have data where multiple attributes are measured for countries and the attributes can be divided into dimensions. For example one dimension can be 'Education' and have 5 attributes associated to it, and another dimension can be 'Income' and have 4 attributes associated to it.
How can I find a scalar value tha... | Consider variable clustering using hierarchical clustering on a similar measure which is the squared Spearman correlation, as implemented in the R <code>Hmisc</code> package <code>varclus</code> function. Though this will not keep the variables within a group together, it will provide a free-floating depiction of how ... | I would choose Spearman's correlation coefficient. It's non-parametric and can be used for ordinal variables which I believe is your case (the attributes of education and income can be ordered).
I'm not sure which software you are using but it's very straight forward to calculate the Spearman correlations in any softw... | https://stats.stackexchange.com |
48,965 | [
"https://electronics.stackexchange.com/questions/48965",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16129/"
] | For obvious safety reasons my residential PV system disconnects from the grid if it notes the grid is down. The thing is it also shuts itself off so that during a grid blackout rather than providing me power but detaching from the grid the inverter disconnects itself from both the grid and the panels leaving me without... | All grid tie inverters MUST disconnect the A/C supply when the grid is lost. This is a safety measure to prevent injuring hydro employees when they isolate systems to work on them. It should be noted that standard procedures require the linesmen to ground the secondary of transformers they have isolated so your inver... | If your inverter shuts down completely when there is no line power, it is probably not capable of putting out AC without AC present. Some inverters assume the power line is essentially a 0 Ω source. They look at the voltage and decide what current to dump onto it. These types of inverters don't actually synthe... | https://electronics.stackexchange.com |
79,309 | [
"https://electronics.stackexchange.com/questions/79309",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/11077/"
] | I'm working on an open source filter design where the PCB can be reused for many future designs. It is based around a Sallen-key filter since a few changes to the capacitors and resistors can change it from a low-pass to a band-pass or a high-pass. When looking at layout, I've realized it would be very beneficial to ma... | <strong>Assumption 01:</strong> the board is intended for hand assembly, tabletop experiments and hacking.
<strong>Assumption 02:</strong> the frequencies are low (say, under 1MHz)
In that case, I would make the passive pads 3216 (tantalum size A) or 3528 (tantalum size B). If you are planning to have pads for a larg... | If somebody might want to assemble this board with automated equipment (pick and place), you don't want to do this. When you place a small part on pads that are too big for it, the excess solder will move the part around and cause defects, such as "tombstones".
If your circuits will only be assembled by hand-soldering... | https://electronics.stackexchange.com |
244,486 | [
"https://mathoverflow.net/questions/244486",
"https://mathoverflow.net",
"https://mathoverflow.net/users/38620/"
] | Following problem though not a research problem
if $x,y,z,w$ are postive integers,and such
$$xyzw=504(x^2+y^2+z^2+w^2)$$
such example $(x,y,z,w)=(21,63,84,84)$ hold,
Now My problem there exist distinct postive integer solution? or find this equation all solution?
| The basic idea for Markoff-Hurwitz type equations
$$ x_1^2+\cdots+x_n^2=Ax_1x_2\cdots x_n $$
with $A\in\mathbb Z$ is that if you have a solution $(x_1,\ldots,x_n)$ in integers, then by fixing $n-1$ of the variables to be the given values, you get a monic quadratic equation for the last variable, so since there is one i... | Try $(x=28, y=42, z=84, w=98)$ and $(x=13, y=84, z=204, w=221)$.
EDIT: It was a coincidence.
The following are some more solutions that have no $84$:
$$\matrix{ \left\{ 15,78,3570,6246 \right\} ,& \left\{ 21,60,453,900
\right\} ,& \left\{ 21,60,900,1797 \right\} ,\cr \left\{ 29,35,11670,
13128 \right\} ,&... | https://mathoverflow.net |
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