qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
9,541 | [
"https://mathoverflow.net/questions/9541",
"https://mathoverflow.net",
"https://mathoverflow.net/users/717/"
] | I'm pretty sure that the following (if true) is a standard result in linear algebra but unfortunately I could not find it anywhere and even worse I'm too dumb to prove it: Let $k$ be a field, let $V$ be a finite-dimensional $k$-vector space and let $S \subseteq \mathrm{End}_k(V)$ be a subset of pairwise commuting (i.e.... | All of these are true. First note that the space of endomorphisms of $V$ is finite-dimensional, so even an infinite $S$ can just be replaced by finitely many matrices that have the same span (it's really more elegant to think about the span of $S$ as a Lie algebra, rather than $S$ itself). You actually may want to lo... | And the answer to the additional question (which Ben skipped) is also positive.
Indeed, there are two parts here:
<ol>
<li>$\chi_i$ is a group morphism (this is obvious for any subgroup $G\subset GL(V)$</li>
<li>$\chi_i$ is algebraic (this is obvious because matrix elements of matrices in $GL(V)$
in any basis are alge... | https://mathoverflow.net |
220,181 | [
"https://dba.stackexchange.com/questions/220181",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/160329/"
] | I've newly taken over administration of a system with about 25 databases. Using Redgate Monitor to chart some metrics, I see that each day, one database shows values for log flushes / second that look like a "normal" chart - a zig-zag line throughout the day.
Redgate explains the metric: "A log flush occurs when a tr... | I don't know anything about the Redgate tool you're using, but it sounds like "transaction per second" would include read and write transactions together. So the likely explanation is that the one database with high log flushes per second is the only one with a significant <em>write</em> workload (thus generating log ... | Log flushes per second doesn't mean anything by itself. It goes up when there are many transactions happening - that's all.
Are users complaining that they are loosing their work after they hit submit button? Are users complaining that application is slow? If not, don't worry abt it. It could be a completely normal pa... | https://dba.stackexchange.com |
6,870 | [
"https://electronics.stackexchange.com/questions/6870",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/712/"
] | I'm working on debugging a boot problem with an Atmel AT91SAM9G20 board. Everything goes great for the first 700 ms or so. It seems that about 700 ms after reset, the processor freezes. What's curious is that the CPU drives the reset line after I release the reset button.
Here's a scope shot that shows what's going on... | Looking at the datasheet:
<blockquote>
14.3.4.5 Watchdog Reset The Watchdog Reset is entered when a watchdog fault
occurs. This state lasts 3 Slow Clock
cycles.
When in Watchdog Reset, assertion of
the reset signals depends on the
WDRPROC bit in WDT_MR: If WDRPROC is
0, the Processor Reset and the
P... | Are the JTAG lines af any device connected to things they shoudn't be ?
Like, say address bus lines ?
(It took months to debug that one time.)
| https://electronics.stackexchange.com |
146,772 | [
"https://dba.stackexchange.com/questions/146772",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/76362/"
] | I am designing a database which needs to store some fairly complex relationships among many different types of entities.
In the simplest example, let us say I have three types of entities - "Student", "Tutor", and "Course", each with their own tables (<code>student</code>, <code>tutor</code>, <code>course</code>). Fi... | The two examples are not equivalent and interchangable implementations; they embody different semantics.
In the first, the three-way table imposes no conditions on the participants. The example shows this. Alex is enrolled in Biology, Emma is assigned to Alex and Emma knows how to tutor Physics. The tutor's subject is... | I like option 1 better. My first thought is always maintaining data integrity so my question is, "Could it be possible to relate a student to a tutor for a course the tutor is not approved for?" With table <code>student_course_tutor</code>, the field <code>student_id</code> would, as you say the student needn't be atte... | https://dba.stackexchange.com |
162,426 | [
"https://stats.stackexchange.com/questions/162426",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/78726/"
] | I am trying to create a logistic regression model and a random forest model on the same data to predict probability of default. For the logistic regression model, I have created some dummy variables from categorical variables. Finally, for the input of logistic regression, I have 9 dummy variables and 2 numeric variabl... | <strong>Let's compare the two models.</strong>
The original one is clearly and well expressed in the question,
$$y = a + b_1x_1 + b_2 x_2 + b_{12}x_1x_2 + \epsilon.$$
Let's write the second model as
$$y = a^\prime + b^\prime_1 z_1 + b^\prime_2 z_2 + b^\prime_{12}z_1z_2 + \delta.$$
Because the values of the numbers... | The $p$-values did not change because of the rescaling, but because you added constants to the variable. The intercept is the expected value of <code>y</code> when all explanatory variables are 0. The $p$-value is the test of the hypothesis that that conditional mean is equal to 0. So if you add a constant to one or mo... | https://stats.stackexchange.com |
34,145 | [
"https://dba.stackexchange.com/questions/34145",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/9662/"
] | Let's say I have a single table
<pre><code>CREATE TABLE Ticket (
TicketId int NOT NULL,
InsertDateTime datetime NOT NULL,
SiteId int NOT NULL,
StatusId tinyint NOT NULL,
AssignedId int NULL,
ReportedById int NOT NULL,
CategoryId int NULL
);
</code></pre>
In this example <code>TicketId</cod... | If this particular work load is the majority of queries against the table you might consider:
<pre><code>ALTER TABLE Ticket ADD CONSTRAINT PK_Ticket PRIMARY KEY NONCLUSTERED (TicketId);
CREATE UNIQUE CLUSTERED INDEX IX_Ticket_Covering ON Ticket (
InsertDateTime ASC
);
</code></pre>
Considerations:
<ul>
<li>can ... | I've used this technique in the past. The table wasn't nearly as big but the search criteria was more complex.
This is the short version.
<pre><code>CREATE PROC usp_Search
(
@StartDate Date,
@EndDate Date,
@Sites Varchar(30) = NULL,
@Assigned Int = NULL, --Assuming only value possible
... | https://dba.stackexchange.com |
24,287 | [
"https://electronics.stackexchange.com/questions/24287",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | How fast can an LED achieve it's full brightness at it's rated voltage and current?
I need to do multiplexing of LEDs to make a matrix display and I've calculated that each LED can only stay on for 40µs. I don't know if that is enough time for the LED light to be seen however.
| (1) LED on times for phosphor LEDs are in the 100'2 of nanoseond range
(2) Turn on times for non-phosphor LEDs are typically in 10's of nanosecond range if driven correctly.
Average current = Peak_Current x time_on / ( time_on + time_off )<br>
Peak current is assumed to be "steady".
(3) Brightness when mutiplexed
... | It does not matter only how long you switch LED on but what is the duty cycle ie. how long it is switched on compared on how long it is switched off. Exact LED response time depends on LED type (color) but these are usually in tens or hundreds of nanoseconds. Your 40µs is more than enough to fully lit it but the averag... | https://electronics.stackexchange.com |
282,836 | [
"https://physics.stackexchange.com/questions/282836",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/62755/"
] | In "Introduction to Quantum Mechanics" by Griffiths, right at the beginning of section 9.1.1 (Time-Dependent Perturbation Theory, The Perturbed System), Griffiths states:
<blockquote>
Now suppose we turn on a time-dependent perturbation, $H'(t)$. Since $\psi_a$ and $\psi_b$ constitute a complete set [of the two-leve... | A basis is a set of wave functions such that a any wave function can be formed as a linear combination of basis wave functions. Often you choose them to be eigenfunctions of the Hamiltonian. But you don't have to.
If you change the Hamiltonian, you change the egienfunctions, so you change the most common choice for a... | That's why it's called perturbation. You use the Hamiltonian $H_0$ and you get a set of eigenfunctions. Then you add a perturbative Hamiltonian $H'$. Though you tweaked the Hamiltonian, the original eigenfunctions remains the same. You can always calculate the perturbative eigenfunctions using iteration method, but you... | https://physics.stackexchange.com |
1,344,727 | [
"https://math.stackexchange.com/questions/1344727",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/76778/"
] | Differentiate the Function $f(x)= \sqrt{x} \ln x$
<img src="https://i.stack.imgur.com/56q8w.jpg" alt="enter image description here">
| $f(x) = \sqrt{x} \ln x$. Using the product rule we have that $$f'(x) = \ln x \cdot \frac{\mathrm{d}}{\mathrm{d}x}\sqrt{x} + \sqrt{x}\cdot\frac{\mathrm{d}}{\mathrm{d}x} \ln x$$
Hence $$f'(x) = \frac{\ln x}{2\sqrt{x}} + \frac{\sqrt{x}}{x}.$$
Further simplification results in $$f'(x) = \frac{\ln x}{2\sqrt{x}} + \frac{2}... | Why did you not take the derivative of $\sqrt{x}$ in step 2? Also, verify what it means to take the log of both sides of an equation. If you want to simply fix your solution, those are my suggestions. <br>
Alternatively, I propose this could be solved with the chain rule.
\begin{equation}
f'(x)=\frac{1}{2\sqrt{x}}\ln(x... | https://math.stackexchange.com |
69 | [
"https://biology.stackexchange.com/questions/69",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/79/"
] | I understand that rooted and unrooted phylogenetic trees are similar in structure
But how can they be easily identified as one or the other?
Is it simply based on the presence or lack of a named root (the root is identified as a particular ancestor) or outgroup?
| In case of a drawn figure, either look for the a short stem to the left, or for an explicitly labelled outgroup. Trees derived from phylogenetic analyses are normally unrooted by default, you need to root them by either making an arbitrary (but hopefully informed) decision or by adding an outgroup.
| Trees can not be distinguished from each other because every unrooted tree can be made rooted by adding a root and vice versa by deletion.
If you mean dendrograms... the root is always the one node where the distance to each leaf is the same. But I don't know of an unrooted dendrogram.
| https://biology.stackexchange.com |
232,323 | [
"https://softwareengineering.stackexchange.com/questions/232323",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/76623/"
] | Using Visual Studio 2012 with C#, when I write multi-line comments, VS automatically begins each line with an asterisk, like this:
<pre><code>/*
*
*
*/
</code></pre>
I was just curious if this was the case in programming languages other than C#, or if there was a specific reason for this template.
| Some of the first comment syntax introduced into programming where statement comments. These kinds of comments required their own line.
Such as in basic
<pre><code>REM This is a comment.
</code></pre>
This created longer source code and used a keyword. Around the same time came <em>end-of-line</em> comments that req... | I've seen this pattern many times in various C-syntax languages such as C, C++, Java, C#, and even JavaScript. The extra asterisks at the beginning of each line have <em>no</em> syntactic significance. They are there purely to aid in readability by catching your eye and making obvious that you are looking at a multi-li... | https://softwareengineering.stackexchange.com |
428,303 | [
"https://physics.stackexchange.com/questions/428303",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/147188/"
] | Lets say I have a operator $\textbf{A}$ = $ \begin{bmatrix}
1 & 2 \\
3 & 4
\end{bmatrix} $ in a canonical basis {|a⟩ ,|b⟩}.
The operator can be re-written in Dirac notation as $\textbf{A}$= $|a⟩⟨a| + 2 |a⟩⟨b| + 3|b⟩⟨a| + 4 |b⟩⟨b| $, since any operator can be written as the sum of basis states $\sum_{i,j}... | Write
$$
\boldsymbol{A}=\sum_{ij} c_{ij}\vert i\rangle\langle j\vert\, .
$$
Then
\begin{align}
A_{11}&=1\, ,\\
&=\langle 1\vert A\vert 1 \rangle =\sum_{ij} c_{ij}
\langle 1\vert i\rangle\langle j\vert 1\rangle\, ,
&=c_{11}\, , \\
A_{12}&=2\, ,\\
&=\langle 1\vert A\vert 2 \rangle =\sum_{ij} c_{ij}... | This formula derivates from how you write the representation of Operators, so, you begin to the operator equation
$$\hat{A} \vert \psi \rangle = \vert \phi \rangle $$
$ \vert \psi \rangle$ is a complete set of orthogonal basis, thus, they are expanded
$$\vert \phi \rangle = \hat{A} \vert \psi \rangle = \hat{A}\s... | https://physics.stackexchange.com |
178,046 | [
"https://softwareengineering.stackexchange.com/questions/178046",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/66605/"
] | I'm reading "Effective Java" by Josh Bloch and in there is Item 16 where he tells how to use inheritance in a correct way and by inheritance he means only class inheritance, not implementing interfaces or extend interfaces by other interfaces. I didn't find any mention of interface inheritance in the entire book.
Doe... | Generally, yes. However, you must be aware of surprises, some of which I mention next.
Disclaimer: none of these lists is exhaustive.
Badly designed interfaces:
<ol>
<li>with lots of methods;</li>
<li>with methods that don't throw sensible exception types, or methods that don't throw at all (a problem in checked exc... | <blockquote>
<blockquote>
Does this mean that interface inheritance is always safe? Or there are guidlines for interface inheritance?
</blockquote>
</blockquote>
No; you should always be careful of how you design the interface and what contracts does it enforce on the implementing classes. In Java you are obli... | https://softwareengineering.stackexchange.com |
163,727 | [
"https://electronics.stackexchange.com/questions/163727",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/50374/"
] | I have a 2V regulator circuit which is used to drive a microcontroller (EFM32G222F128). On the output of this regulator I have a delay switch type circuit (see image below) which is used in order to allow the reservoir capacitor to charge enough in order to deal with the initial start up current of the \$\mu\$C.
<img ... | In many cases this is a side effect of a converter that uses a variable frequency that shifts down when under light load. Unfortunately, it comes down low enough to be heard. Under normal conditions, the switching frequency should be much higher. This type of converter uses something similar to pulse density modulation... | Most small offline SMPS use Flyback Fixed frequency peak Current mode. This approach gives a simple cheap circuit that is reliable considering the price. The switching frequencies are well above audio but there are ways that you can still get audible noise. Sub harmonic oscillations can and do occur in these types of s... | https://electronics.stackexchange.com |
89,812 | [
"https://security.stackexchange.com/questions/89812",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/77030/"
] | I know that a filtered response on NMap means that the firewall dropped the packets or that NMap just didn't receive a response, but is there any way to circumvent this?
Is it possible that the firewall is just dropping NMap's type of ping packets but would respond to a normal connection in telnet or a web browser?
I... | Seeing a 'filtered' state for a port has nothing to do with a "ping" or an exploitation attempt. Nmap's traffic is generally not exploitative. An adaptive firewall <em>could</em> detect the default (with privileges) half-open SYN scan after it has detected an open port, or it could detect any of it scan types based on ... | The standard scan method (<code>TCP SYN</code>) used by <code>nmap</code> for TCP scans is to start opening a connection, then abandon it halfway through. Individually, these connections are indistinguishable from an ordinary connection. Collectively, they can be identified because of how many of them there are, but ... | https://security.stackexchange.com |
312,687 | [
"https://softwareengineering.stackexchange.com/questions/312687",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/220412/"
] | Today I had a task to "write a health check" for a long running service that is an orchestration system to deploy a web-app.
I am trying to determine what the scope for such a health check would be, and came up with these questions related to the scope of the health check :
<ol>
<li>Is it good enough to consider th... | <blockquote>
This is hard to implement because of the definition of what is healthy
</blockquote>
You answered your own question here. The definition of a health check is going to vary, because what is healthy varies. It also depends on what is issuing the healthcheck.
A good question to ask yourself is, "from the ... | Generally a health-check just means "is it alive and is it responding". Further checks than that are highly specialised and depend entirely on the use of the system. Whether you go the extra mile to check that a system is processing requests correctly is up to you, but you should do the basics first - check it's there,... | https://softwareengineering.stackexchange.com |
304,599 | [
"https://softwareengineering.stackexchange.com/questions/304599",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/206937/"
] | I was wondering if somebody has done this, and to what success compared to the classic method of getting them to solve a problem as you watch on?
Any pointers on how to carry this out in an interview situation?
I was thinking about doing this for mid/senior candidates which should definitely have the technical knowle... | When I was 6 and my brother was 11, he made me eat a ball of feathers. It wasn't easy. I choked it down with a lot of dry gagging and a little wet vomit. Partially I did it because I was afraid of my brother. But mostly I did it because it proved I was harder than him. He was this vicious, brilliant, beautiful boy. I w... | I'd say no to this. Reviewing anything but a trivial pull request (spelling fixes) requires an understanding of the code base. If you do not know the codebase, you may not be aware that a certain (obviously good) change might have some major effects somewhere else. Even veterans to a codebase can miss the repercussions... | https://softwareengineering.stackexchange.com |
97,933 | [
"https://security.stackexchange.com/questions/97933",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/55307/"
] | I'm looking for ensure the integrity of uploaded files and demonstrate this integrity to a user.
In my current scenario, a user sends multiple files in several different formats, these files are transported to a storage device or location.
I need to create a report provider a container with these files(eg. Zip), bu... | You already have your answer on methods to demonstrate integrity.
Any of those techniques are as "trustable" as the entity implementing them is.
Perhaps what you meant to say was "most appropriate"?
Assuming this is your homework question:
A user transfers several files to a destination, and wants to prove that t... | It depends on what whether you really mean the "most trustworthy". As with many aspects of digital security, there is a sliding scale of strength / reliability vs usability / feasibility. I think some important questions to consider are:
<ul>
<li>Who are your users? To what extent do they care about proof of file inte... | https://security.stackexchange.com |
277,767 | [
"https://electronics.stackexchange.com/questions/277767",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/128030/"
] | I'm developing a code with Nuc240(ARM Cortex M0) Microcontroller.
Where I need to store the value in some of the variables to the Internal Data Flash.
I use ISP procedure for this, but i have seen the following statement in the datasheet of the Microcontroller ,about the Data Flash.
<blockquote>
'The size of each er... | Well, if you want to preserve data in erase block you should first read that block, store it in ram, do whatever changes you need to do, erase flash block, write block from ram. Simple enough.
| You need to do a read-modify-write (RMW) operation, in which you read out the entire 512-byte page to RAM, change the value(s) that need to be updated, then erase and rewrite the flash page.
There is a concern that power could fail while this procedure is executing, so more elaborate schemes that "bounce" the data bet... | https://electronics.stackexchange.com |
714,853 | [
"https://physics.stackexchange.com/questions/714853",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/299064/"
] | I'm reading Susskind's Classical Mechanics: The Theroretical Minimum and I also like to restrict my question to classical mechanics:
In chapter 4, momentum conservation is shown for a set of particles. In chapter 5 energy conservation is shown for a body in free fall towards Earth (potential energy decreases, kinetic e... | <blockquote>
what the preconditions for applying momentum and energy conservation in mechanics are?
</blockquote>
We write the laws of physics that describe a system in the system’s Lagrangian. If the Lagrangian is not an explicit function of time then energy is conserved. If the Lagrangian is not an explicit function ... | Momentum is conserved in a system if there are no external forces on the system.
Likewise, angular momentum is conserved in a system if there are no external torques on the system.
Energy is conserved in a system if there is no work being done on the system and no heat conducted into the system, or more generally, if t... | https://physics.stackexchange.com |
47,101 | [
"https://stats.stackexchange.com/questions/47101",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/16837/"
] | Can ordinary least squares estimation be considered an optimization technique? If so, how can I explain this?
Note:
From an AI perspective, supervised learning involves finding a hypothesis function $h_\vec{w}(\vec{x})$ that approximates the true nature between predictor variables and the predicted variable. Let some... | Yes, it is. In OLS, you are looking for the linear model that provides the "best" fit to the data. Implementation requires specifying some notion of what you mean by "best". OLS works by defining the "best" model as the one that minimizes a certain measure of model error -- in this case, the sum of the squares of the m... | I would have said that OLS is an optimization problem rather than an optimisation technique, as there are many optimization techniques/algorithms that can be used to solve OLS problems (e.g. analytical solutions for [ridge] regression, IRWLS for logistic regression, scaled conjugate gradients for neural nets, etc.). T... | https://stats.stackexchange.com |
127,165 | [
"https://chemistry.stackexchange.com/questions/127165",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/65872/"
] | I noticed that the temperature of water decreases noticeably when I mix an energy drink (Glucon-D) in it. The ingredients mentioned on the pack are majorly glucose (52%) and sucrose (45%). I believe that this is due to the inversion of sucrose being an endothermic reaction
<span class="math-container">$$\ce{C12H22O11 +... | Polar/hydrophilic soluble substances get dissolved, like table salt or sugar.
Polar/hydrophilic insoluble substances get wet, as they attract water, like sand, or limestone.
Nonpolar/hydrophobic insoluble substances do not get wet, as they repulse water, like wax, teflon or silanized glass.
| The water molecules undergo a sort of attraction between them. This attraction is due to <span class="math-container">$\ce{H}$</span> atoms being attracted by the oxygen atoms of neighboring water molecules. At the surface of the water this attraction produces a sort of "skin" due to the attraction of the molecules bet... | https://chemistry.stackexchange.com |
3,274,785 | [
"https://math.stackexchange.com/questions/3274785",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/116321/"
] | <blockquote>
Let <span class="math-container">$A=\begin{bmatrix}
1 & 2\\
3& 4
\end{bmatrix}$</span> then det<span class="math-container">$(A^3-6A^2+5A+3I)=3$</span>
</blockquote>
det<span class="math-container">$(A^3-6A^2+5A+3I)=$</span>det<span class="math-container">$((A^2-5A-2I)(A-I)+2A+I)= $</span>det<... | Yes, this looks fine. Since <span class="math-container">$A$</span> satisfies its own characteristic polynomial, you have:
<span class="math-container">$$\color{blue}{A^2-5A-2I=O}$$</span> and so, as you wrote:
<span class="math-container">$$A^3-6A^2+5A+3I=\underbrace{\left(\color{blue}{A^2-5A-2I}\right)}_{\color{blue}... | Here is another method. Assume that <span class="math-container">$\lambda_i\in\mathbb{C}$</span>, <span class="math-container">$i=1,2$</span> are the two igenvalues of <span class="math-container">$A$</span>. Let <span class="math-container">$f(x)\in \mathbb{C}[x]$</span> be the characteristic polynomial of <span class... | https://math.stackexchange.com |
53,228 | [
"https://dsp.stackexchange.com/questions/53228",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/38776/"
] | I am new to dsp, and I'd really appricate it if someone please help me with this problem. I guess it's a basic simple question, but I cannot get it write. Here is the question:
The variance of a random signal generated using MATLAB command randn is approximately 1. We need a random signal with variance 0.01. With whic... | In a practical setting to adjust the variance (thereof the power) of a random process, you could use the following to get what you want.
Let the variance of a given RV <span class="math-container">$X$</span> be <span class="math-container">$$\text{Var}\{X\} = \sigma_X^2 $$</span>
Then the following transform <span c... | standardizing a Normal random variable <span class="math-container">$x$</span>
<span class="math-container">$$
\frac{x -m}{\sigma} \sim \mathcal{N}(0,1)
$$</span>
so if <span class="math-container">$y$</span> is a random variable that is Normal with mean zero, with standard deviation <span class="math-container">$1$</... | https://dsp.stackexchange.com |
21,303 | [
"https://cogsci.stackexchange.com/questions/21303",
"https://cogsci.stackexchange.com",
"https://cogsci.stackexchange.com/users/21047/"
] | I've noticed that several psychological studies purport to measure one thing, but once participants enroll, they end up measuring something completely different.
For example, I recently came across a study where participants were told that the study was meant to help create personalized nutrition and exercise programs... | The whole point of these lies is to prevent participants from changing their answers because they want to please the researchers or convey their personal beliefs about a topic.
It is typical to inform participants about the true purpose at the end of the study if this is possible. Other times, studies use purposefully... | In addition to the previous answer, there's also a document called The Belmont Report which describes the ethical principles and guidelines for conducting research involving human subjects.
Oftentimes, it is listed out in the informed consent form that deception will be used in the study, and it is also required to gi... | https://cogsci.stackexchange.com |
80,233 | [
"https://security.stackexchange.com/questions/80233",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/67160/"
] | We have a web form that can be filled out with text fields and then they get emailed to us at work. Today we got some SQL commands it looks like in a bunch of emails. I just would like to have a bit general knowledge of what they were trying to do. I copied every command they sent through and have it below:
All I am a... | They were hoping the textbox submitted data to a sql server and that the data was not filtered/sanitized. <code>1=1'</code> is a common method for testing for sql injection. The <code>x || ping -n 3 127.0.0.1 &</code> request is used for testing for shellshock vulnerability.
Answer to comment below:
By filtered/s... | It's possibly an automated scanner. If you google 0x7b5d, there are lots of results to suggest this, so to me it looks like an unskilled attacker trying some script or other.
They are hoping that your site will spit out an error message that they can then use to glean further information.
| https://security.stackexchange.com |
160,200 | [
"https://softwareengineering.stackexchange.com/questions/160200",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/10869/"
] | We currently work with a company that has a fairly simplistic web system for processing warranty information. The only way to get data out of it is through excel exporting. Compilation of this data and correlation with our systems has to be manual and makes us be reactive in our response.
The ideal situation would be ... | I've worked on this exact problem with several B2B clients and it what it always comes down to is having a conversation with the team on their end where you clearly discuss the pros and cons of your proposal and work to mitigate any concerns they raise.
Before you do this you need to understand where your client is c... | A lot of organizations are hesitant to have an external source pull data from them. Perhaps a compromise would be to setup an endpoint on your end that will allow them to periodically push data. This way they know exactly what data you are processing and they control the frequency of data updates.
Education on your de... | https://softwareengineering.stackexchange.com |
55,934 | [
"https://math.stackexchange.com/questions/55934",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/7546/"
] | In the case of vectors in euclidean space, for instance, we can express one in terms of the other--i.e. length is distance from zero, distance is the length of the vector difference. Does this break down somewhere?
| It is equivalent to ask that maps from finite products of unit intervals into the base space lift. That is, you only need to lift maps $f:I^n\rightarrow B$ ($n$ is a non zero integer, $I=[0,1]$). This is no problem for the 2 first examples since they are covering spaces, and the total space is simply connected.
Indeed... | It is also worth noting that any map can be replaced by a fibration. Replaced in the sense that the maps are homotopic, the domain is also changed but its homotopy type is not changed. Since you don't change the homotopy type the homotopy groups and induced maps in homotopy are not changed. You can do this in general w... | https://math.stackexchange.com |
410,786 | [
"https://electronics.stackexchange.com/questions/410786",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/206535/"
] | New to using PIDs. When normalizing a range, we would need to know the maximum and minimum of that range. Since a PID is summing the error in the I portion wouldn't the range be potentially infinite? How would we limit the output to the expected range, (-1 to 1 in my case). Would we also need to normalize the error tha... | In the textbook PID controller, the output is not limited. In a real PID controller the output has saturation limits. Normally you should at least stop integrating when the output is saturated, otherwise the integral term will "wind up" and cause a large amount of overshoot.
I write "at least" because there are other... | After more research, I believe to clip the output to the maximum and minimum values and further research "integral windup" to combat the issues that will cause.
| https://electronics.stackexchange.com |
10,208 | [
"https://physics.stackexchange.com/questions/10208",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/955/"
] | <strong>Question</strong>: are they mathematically possible at all? physically?
with finite mass systems, usually the binding energy contributes to the rest-mass of the system. It would seem that even if you could bind two massless fields/particles, the coupled system would still have a finite rest mass because of the... | Dear lurscher, a good question. But a bound state is something that has a negative binding energy - otherwise it wouldn't be bound. If the rest mass of a bound state AB of massless objects A,B is positive, it can clearly decay to A,B with some energy without violating any conservation law. So AB surely can't be quite s... | If a bound system is complicated, it may have "massless" excitations. They are quasi-particles. I think all that we observe are quasi-particles rather than free particles in an empty space.
Solitons may be considered as bound states of different "massless" harmonics in a non-linear dispersive medium.
| https://physics.stackexchange.com |
29,682 | [
"https://stats.stackexchange.com/questions/29682",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/8402/"
] | The likelihood could be defined by several ways, for instance :
<ul>
<li>the function $L$ from $\Theta\times{\cal X}$ which maps $(\theta,x)$ to $L(\theta \mid x)$ i.e. $L:\Theta\times{\cal X} \rightarrow \mathbb{R} $.</li>
<li>the random function $L(\cdot \mid X)$</li>
<li>we could also consider that the likelihood i... | Your third item is the one I have seen the most often used as rigorous definition.
The others are interesting too (+1). In particular the first is appealing, with the difficulty that the sample size not being (yet) defined, it is harder to define the "from" set.
To me, the fundamental intuition of the likelihood is ... | I think I would call it something different. Likelihood is the probability density for the observed x given the value of the parameter $θ$ expressed as a function of $θ$ for the given $x$. I don't share the view about the proportionality constant. I think that only comes into play because maximizing any monotonic fu... | https://stats.stackexchange.com |
263,076 | [
"https://mathoverflow.net/questions/263076",
"https://mathoverflow.net",
"https://mathoverflow.net/users/100552/"
] | It seems that there are different conventions in the literature as to what is a locally compact space (when the space is not supposed Hausdorff).
The two main non equivalent definitions I've seen are :
<ul>
<li>(LC1) every point has a compact neighborhood</li>
<li>(LC2) every neighborhood of any point contains a co... | To me, the second definition of local compactness is much to be preferred for the simple reason that such locally compact spaces $X$ are exponentiable in $Top$, meaning that $X \times -: Top \to Top$ has a right adjoint $(-)^X: Top \to Top$ (even without the Hausdorff condition), and all this implies (such as $X \times... | The notion LCn1 just boils down to "the connectedness components of the space are clopen". If this property does indeed show up somewhere, I would expect that the latter is a more convenient way of expressing it.
LC1 on the other hand does indeed seem to capture some intuition about "this space has some properties of ... | https://mathoverflow.net |
4,596 | [
"https://mathoverflow.net/questions/4596",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1593/"
] | It is well-known that
A: The series of the reciprocals of the primes diverges
My question is whether property A is in some sense a truth strongly tied to the nature of the prime numbers.
Property A tells us that the primes are a rather <em>fat</em> subset of $\mathbb{N}$. Is there a way to define a topology on $\mat... | Yes, it's possible. Define the closed sets to be the sets the sum of whose reciprocals converges, together with $\mathbb{N}$. This collection of subsets is closed under arbitrary intersection and finite union, so it does form the closed sets of a topology.
A subset of $\mathbb{N}$ is dense in this topology if its ... | By Fubini's theorem, the sum of the reciprocals of the primes is equal to $\int_1^\infty \frac{\pi(x)}{x^2}\ dx$, where $\pi(x)$ is the number of primes less than x. The prime number theorem tells us that $\pi(x) \sim x/\log x$ for large x, which implies the divergence of this integral. (One does not need the full st... | https://mathoverflow.net |
9,443 | [
"https://quantumcomputing.stackexchange.com/questions/9443",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/5008/"
] | I know the definition of projective measurement, generalized measurement, POVM.
I understand the usage of generalized measurement for the reason that it can model experiments "easier" (for example measurement of a photon that will be destructive so that measuring again the state just after the first measurement will g... | For me, generalised measurements cover everything (obviously, that's why they're generalised), with projective measurements being a simple case that covers what we usually want to be doing.
So, yes, why introduce POVMs which are basically the generalised measurements but without the output state? Because they describe... | If you want to prove a no-go theorem in quantum mechanics, such as the impossibility of distinguishing two non-orthogonal states given a single unknown state, you want to prove that even if you add ancillae, apply unitaries, do projective measurements in weird bases, apply unitaries conditional on previous measurements... | https://quantumcomputing.stackexchange.com |
188,224 | [
"https://electronics.stackexchange.com/questions/188224",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/55008/"
] | Freshmen EE circuit. Resistance, inductivity, capacitance are given and effective value of voltage. No phase angles are given.
When calculating complex power, may I assume the phase angle of the voltage source? Current should adjust accordingly and give me the same power no matter which angle I assume.
Am I right? (... | Yes, it's typical to assume a phase angle of zero for the source, but it really doesn't matter- you should get the same results if the math is done right.
| No. The phase angle between voltage and current has a great deal to do with the power. This is the difference between VA (Volt-Amps) and Watts, and is what power factor is all about.
When the voltage and current are in phase, then power is simply the volts times the amps. When they are 90° out of phase, then no... | https://electronics.stackexchange.com |
474,882 | [
"https://stats.stackexchange.com/questions/474882",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/264040/"
] | I need to construct two <span class="math-container">$10$</span> X <span class="math-container">$1$</span> vectors <span class="math-container">$\overrightarrow{x}, \overrightarrow{y}$</span>, such that Kendall´s <span class="math-container">$\tau $</span> is zero but there exists a function <span class="math-container... | Your example is correct. In fact any symmetric function applied to the vector you defined would work.
| The easiest way to prove it is just by calculation. Work out <span class="math-container">$\tau$</span>. It is zero.
More generally than the <span class="math-container">$10\times 1$</span> case, consider the transformation <span class="math-container">$X\to -X$</span>.
This switches a positive association to a negativ... | https://stats.stackexchange.com |
161,012 | [
"https://electronics.stackexchange.com/questions/161012",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16744/"
] | I am currently working with a project where i am creating a small embedded board consisting of a 9DoF IMU which is transmitting its data with RF (BLE or normal RF). Furthermore there will be a battery attached extremely close to the unit.
I have few questions for this application:
<ol>
<li>Can i have a RF antenna clo... | We sell a product that is very similar to what you propose.
<ul>
<li>RF should not affect it. We have a Bluetooth daughterboard to provide wireless comms and it does not affect the compass.</li>
<li>Temperature will affect the readings.</li>
<li>Metal parts such as USB connectors and SD card sockets will cause a magne... | <blockquote>
Can i have a RF antenna close to the IMU and how will it impact the electronic compass?
</blockquote>
The RF should have no significant effect on either the MEMS inertial sensors or the magnetometers.
<blockquote>
Can i have a battery on the back or top of the board very close to it, and how will it ... | https://electronics.stackexchange.com |
33,389 | [
"https://mathoverflow.net/questions/33389",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1291/"
] | Consider Schrödinger's <em>time-independent</em> equation
$$
-\frac{\hbar^2}{2m}\nabla^2\psi+V\psi=E\psi.
$$
In typical examples, the potential $V(x)$ has discontinuities, called <em>potential jumps</em>.
Outside these discontinuities of the potential, the wave function is required to be twice differentiable in order ... | To answer your first question:
Actually the assumption is <em>not</em> that the wave function and its derivative are continuous. That follows from the Schrödinger equation once you make the assumption that the probability amplitude $\langle \psi|\psi\rangle$ remains finite. That is the physical assumption. This is ... | Since you talk about 'jump' discontinuities, I guess you are interested in a one dimensional Schroedinger equation, i.e., $x\in\mathbb{R}$. In this situation a nice theory can be developed under the sole assumption that $V\in L^1(\mathbb{R})$ (and real valued of course). By a nice theory I mean that the operator $-d^2/... | https://mathoverflow.net |
90,699 | [
"https://security.stackexchange.com/questions/90699",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/69169/"
] | While browsing this community I notice that some people say that the main advantage of usernames accompanied by passwords is as they take more tries to be brute forced, however I don't think that is the case, for example:
<pre><code>#Easy password just for example
Username: admin
Password: c1235
</code></pre>
Is jus... | In most systems, username is required to be unique but password is not.
If password was used as a login credential without a username, then password would have to be unique. In that case the same attacks against username would work for password, such as trying to sign up with a dictionary-word password and looking fo... | Before the password can be validated, the user's record must be looked up in the database so that you know what salt to use when hashing the password. If you didn't have a username you'd have to extract the salt from each stored hashed password, salt and hash the inputted password, and compare the result to the stored ... | https://security.stackexchange.com |
340,956 | [
"https://electronics.stackexchange.com/questions/340956",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/131243/"
] | Is there any difference between relative stability and absolute stability?
Do all the control system analysis techniques (Root locus, Routh-Hurwitz, Nyquist, Bode plot) are able to find both stabilities?
| Relative stability and absolute stability are not two different "kinds" of stability. Absolute stability is a binary thing, is the system stable or not?
Relative stability will tell you, if your system is stable, by how much can you increase the gain of the system or the phase lag of the system before it becomes unsta... | (RELATIVE STABILITY)it is measure of how fast the transient dies out in the system .relative stability is related to settling time. a system having poles away from the left half of imaginary axis is considered to be relatively more stable compared to a system having poles closed to imaginary axis.
(ABSOLUTE STABILITY... | https://electronics.stackexchange.com |
21,643 | [
"https://physics.stackexchange.com/questions/21643",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/6336/"
] | Let us assume there is a closed room with two people in it and only one of them is smoking a cigarette.
Which equation describes the behavior of the smoke from the cigarette spreading? Is it “diffusion”? If so, what are the parameters?
Is there a technique or device that I can use or build that allows me to control t... | This is covered in the standard convection-diffusion type of equation:
$$ \frac{\partial C}{\partial t} + \vec{u} \cdot \nabla C= D \nabla^2 C$$
Where $C$ is the smoke concentration, and $D$ is the diffusion coefficient of smoke.
While the air may be stagnant initially, it will come to move due to buoyancy effects, ... | Very incomplete answer. Opening a window does little with a major smoking indoors situation. Here's why:
Lower floor rooms in a house or apartment tenants smoke and their rooms filling them with smoke. They turn up the heat in winter and heat from outside rises through their open windows.
Smoke tends to rise up through... | https://physics.stackexchange.com |
176,839 | [
"https://mathoverflow.net/questions/176839",
"https://mathoverflow.net",
"https://mathoverflow.net/users/29961/"
] | What is the cardinality of the continuous dual of $C([0,1])$ (the set of continuous functions from $[0,1]\to \mathbb{R}$)?
| The polynomial space $P([0,1])$ is dense in $C([0,1])$ by the Stone-Weierstrass theorem. Therefore $P$ and $C$ have the same (continuous) dual space. But since $P$ has a countable Hamel basis, its <em>algebraic</em> dual has the same cardinality as $\mathbb R^{\mathbb N}$. Thus $|C^*|\leq|\mathbb R^{\mathbb N}|$. The e... | <em>Update: just realized that there is a very simple argument. $C([0,1])$ is separable, i.e. has a dense countable set (choose your favourite, for example polynomials as in the answer of Joonas) and every continuous functional is determined by its values on this set. Hence $|C^*([0,1])|=\mathbb{R}$.</em>
The previous... | https://mathoverflow.net |
238,907 | [
"https://softwareengineering.stackexchange.com/questions/238907",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/93050/"
] | I am working on a project where there will be plenty of static options being stored in the database. I looked at using Enums for this, but do not see how they could be useful.
They do not create any kind of look-up table, just reference a number in the table which can be used in code as an enum option. The number is m... | Using a number to represent an enum value is slightly more efficient in terms of database lookup. The downside is of course that it is ghastly difficult to understand what anything is.
This is a matter of opinion, however I believe emphasis should be placed on readability, also in the database. As such, I would pr... | For reporting scenarios, the database will not be able to report any meaningful information about the enum. This makes Entity Framework enums much less useful unless you use the enum to supply the name or text value, and graft that onto a class that represents the lookup table (which is not an EF enum, I realize).
| https://softwareengineering.stackexchange.com |
1,120 | [
"https://astronomy.stackexchange.com/questions/1120",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/-1/"
] | I've visited several "how sundials work" sites and can't seem to get a
clear answer to this: is "sundial time" just a linear function of
solar azimuth? More specifically:
<ul>
<li>When the sun is due south (northern hemisphere), it is sundial
noon. All sites I've visited agree on this. </li>
<li>When the sun is du... | Any sundial that gives the same result as this is correct and any other is wrong (but sometimes close enough):
<pre><code> _ /############
/| /#############
skewer / /##############
(central) v / /###############
| north /#########... | The sundial translates the position of the sun to the time of day, so it depends on the path the sun takes across the sky, this is called the ecliptic.
Because the earth's rotation is tilted with respect to its orbit around the sun, the ecliptic shifts across the sky during the year, which is also the cause of seasona... | https://astronomy.stackexchange.com |
2,970,061 | [
"https://math.stackexchange.com/questions/2970061",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/607861/"
] | Which grows at a faster rate <span class="math-container">$\sqrt {n!}$</span> vs <span class="math-container">$(\sqrt {n})!$</span> ? How to solve such type of questions considering <span class="math-container">$n \rightarrow \infty$</span>?
| Assume <span class="math-container">$n=k^2$</span> is a square. <span class="math-container">$\sqrt{n!}$</span> is the square root of a product of <span class="math-container">$n$</span> integers. So you can see it as a product of <span class="math-container">$n$</span> square roots of integers: <span class="math-conta... | As alluded to in the comments, <span class="math-container">$(\sqrt{n})!$</span> doesn't make sense, so I'm going to compare the growth of <span class="math-container">$n!$</span> to the growth of <span class="math-container">$\sqrt{(n^2)!}$</span>. Or, equivalently, compare <span class="math-container">$(n!)^2$</span>... | https://math.stackexchange.com |
14,869 | [
"https://cs.stackexchange.com/questions/14869",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/10398/"
] | I am trying to work out the recurrence relation for Ternary Search. This is what I came up with:
<pre><code>C(n) = C(n/3) + 2
</code></pre>
However, I talked to my professor and he said it's not correct. He says that we need to take all of their cases into account. This part confuses me a little bit, can you please c... | Hint: Recall what you are actually doing in ternary search - you basically partition the list into 2 parts, on of roughly $n/3$ elements, and the other of $2n/3$ elements.
So, on a bad day (worst case) you do $2n/3$ recursive calls.
Then the recurrence relation is $$T(n) = T(2n/3) + c $$
I'll cheat a bit here and ... | Ternary search (a)-> If you divide the array into 3 subsets of equal size and consider 3 cases key lies in left,middle, right tree, Then the recurrence :
T(n)=T(n/3)+O(1) must be correct,
because you are searching in an array of size(n/3).
Ternary search (b)-> If partitioned in size (n/3) and (2n/3) 2 partitions then ... | https://cs.stackexchange.com |
194,279 | [
"https://mathoverflow.net/questions/194279",
"https://mathoverflow.net",
"https://mathoverflow.net/users/62367/"
] | I am looking for a explicit isomorphism between $Cl(8)$ (Clifford algebra over $\mathbb{R}^8$ with standard Euclidean metric) and $\mathbb{R}(16)$ (algebra of $16\times 16$ matrices over $\mathbb{R}$). More concretely, it would be very useful to know:
<ul>
<li>The image of the basis elements $e_k$</li>
<li>The image o... | Here's a standard explicit formula: Let $\mathbb{O}\simeq\mathbb{R}^8$ denote the algebra of octonions, and for $x\in\mathbb{O}$, let $L_x$ (respectively $R_x)$ denote the linear map from $\mathbb{O}$ to itself generated by left (respectively, right) multiplication by $x$ and let $C:\mathbb{O}\to\mathbb{O}$ be conjuga... | In order to establish isomorphism of Clifford $C_8$ with $M_{16}\mathbb R$ it is enough to define 8 letters generators which square to $-1$ and anticommute. Define
$e_k$=$$\begin{pmatrix} L_k & \\
& R_k \end{pmatrix}
$$
where $L_k$ and $R_k$ are left and right multiplication by imaginary base octonions, $k$=1..... | https://mathoverflow.net |
164,183 | [
"https://physics.stackexchange.com/questions/164183",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21542/"
] | Can you also explain the two in plain words ?
| The two are confusingly similar. Heat transfer coefficient is given by:
$$
h = \frac{q}{\Delta T}
$$
where $q$ is heat flux. This corresponds to the ratio of heat flux to the temperature difference between two points.
Thermal conductivity is <em>often</em> given by:
$$
k = -\left|\frac{\mathbf{q}}{\nabla T}\right|
$$
i... | the heat transfer coefficient (<em>h</em>) is equal to the thermal conductivity (<em>k</em>) divided by the thickness of the object.
$$
h=\frac{k}{l}
$$
the units for <em>h</em> are $[W/m^2 K]$
the units for <em>k</em> are $[W/mK]$
| https://physics.stackexchange.com |
464,594 | [
"https://physics.stackexchange.com/questions/464594",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/223420/"
] | According to my knowledge of physics, torque can only exist on a rigid body and an electric dipole is defined as a "system of charges" (equal in magnitude, opposite in sign) separated by an infinitesimal distance.
clearly, we can't call a dipole as a "rigid body", since it's just a system of particles, so how does tor... | Electric dipoles are charges separated from one another, but they can reside on a molecule that maintains the separation. An example is a water molecule. The arrangement of the Oxygen and two Hydrogen atoms is such that the molecule is more positive in one area and negative in another area, that is, the charge distribu... | <blockquote>
shouldn't the individual charges just start separating away from each other?
</blockquote>
If the field is strong enough, certainly. But keep in mind that there is an attraction between the oppositely charged particles. Just imagine two balls connected by a somewhat elastic string that will break if the... | https://physics.stackexchange.com |
8,563 | [
"https://mechanics.stackexchange.com/questions/8563",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4345/"
] | What items are in the cooling system loop?
I know there's the Radiator, and the Block, but what else?
| You'll also have the:
<ul>
<li>Cylinder head(s)</li>
<li>Water pump</li>
<li>Thermostat</li>
<li>Heater core</li>
</ul>
Some cars also have water pipes in the inlet manifold, and some have water-cooled transmission oil coolers.
You've also usually got an expansion tank, but that's not part of the loop itself.
| <ol>
<li>Radiator </li>
<li>Thermostat</li>
<li>Engine Block</li>
<li>Heater Core</li>
<li>Water Pump</li>
</ol>
| https://mechanics.stackexchange.com |
3,081,237 | [
"https://math.stackexchange.com/questions/3081237",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/587635/"
] | I am working in wireless communication.
When I cheek the books about MFG I found the MGF of random variable <span class="math-container">$X$</span> is given by the following formula
<span class="math-container">$$
M_X(s)=E\{e^{sx}\}
$$</span>
However when I read papers, I found the following definition
<span clas... | Your <span class="math-container">$M_1$</span> is the correct matrix if you have a polynomial expressed in terms of the <span class="math-container">$v$</span>s and you want it expressed in terms of the <span class="math-container">$p$</span>s and if your polynomials are column vectors. If I have a polynomial <span cl... | The matrix <span class="math-container">$M_1$</span> is the transition from <span class="math-container">$V$</span> to <span class="math-container">$P$</span>. You take the vectors in <span class="math-container">$V$</span>, you apply the transformation <span class="math-container">$M_1$</span> and you get the vectors ... | https://math.stackexchange.com |
66,631 | [
"https://dba.stackexchange.com/questions/66631",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/39559/"
] | My requirements are,
I want to create a ddl script which will check if a stored procedure exists on DB, if yes then drop it and recreate it.
What I tried is,
<pre><code>IF EXISTS (select procname into Migration_procname from sysibm.sysprocedures where procname like 'GIAM_PRIVILEGE_MIGRATION') THEN
DROP PROCEDU... | The sequences are designed like that, the are not supposed to produce contiguous numbers.
However, you can reset them before (re)trying the <code>COPY</code> with
<pre><code>SELECT setval('sequence_name', (SELECT max(id) FROM your_table));
</code></pre>
| Don't use a sequence if you want contiguous numbers that roll back with an aborted transaction.
Write a pl/pgsql procedure implementing a <code>nextval_gapless</code> that increments a counter in a table. This counter will get rolled back if the transaction aborts.
Of course, you also get the downsides of this approa... | https://dba.stackexchange.com |
719,912 | [
"https://physics.stackexchange.com/questions/719912",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/319991/"
] | I am currently learning quantum mechanics and I am trying to understand the connection between the wave function and the state vector.
Is it correct to say that the components of the state vector of a quantum system are all possible wavefunctions in that state?
| A state vector is just a wavefunction where the domain doesn't need to be <span class="math-container">$\mathbb{R}^d$</span>. Similarly, you can call wavefunctions vectors because the functions used in quantum mechanics (square integrable ones) are elements of a space which is closed under addition and scalar multiplic... | The relationship between wave functions and state vectors is the <em>exact</em> same relationship as between vector components and vectors in Euclidean vector space.
When you have an "ordinary" vector in 3D Euclidean space, given in terms of components, such as
<span class="math-container">$$\mathbf{v} = \lan... | https://physics.stackexchange.com |
71,535 | [
"https://softwareengineering.stackexchange.com/questions/71535",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/13805/"
] | For custom software, when you are giving your customer an estimate, how much detail do you tend to include?
Do you:
<ul>
<li>break it down into small tasks that can be done in a few hours and give them the full list?</li>
<li>give them one big number and work towards that? And if so does that come from a more deta... | You don't want to be too detailed or too vague - both will give you problems.
Too vague and you won't have a clear idea of what's involved yourself either and that will cause problems when something unforeseen crops up.
Too detailed and you run the very real risk of information overload. You might also get someone qu... | I'll usually break it into two sections:
<ul>
<li>Overview</li>
<li>Detailed</li>
</ul>
I generally make sure that the overview is a kind of executive summary (brief and understandable by all). The detailed section will then break down atomic tasks with estimates.
Even though I don't know a ton about vehicles, I wou... | https://softwareengineering.stackexchange.com |
1,460 | [
"https://electronics.stackexchange.com/questions/1460",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1199/"
] | My college undergraduate electronics classes covered some analog design, and I'd like to further my knowledge and experience. What would be a good project that would require significant effort as far as research and learning new material? Ideally, the project, when finished, would also serve as evidence that I have ana... | Music ...
An analog synthesizer has a number of functional blocks --
voltage controlled oscillator, voltage controlled amplifier, mixer, envelope generator,
filter with voltage control over the cutoff frequency, noise generator,
analog multiplication
Power Electronics ... DC to DC converter, DC to AC conver... | <ul>
<li>a log-amplifier (output voltage increases by V0 volts every time input voltage doubles)</li>
<li>an optical interrupter (put two LEDs on either end of a tube with a slot cut through it; put current into the transmit LED, amplify the current produced by the receive LED)</li>
<li>a thermocouple temperature reade... | https://electronics.stackexchange.com |
40,111 | [
"https://security.stackexchange.com/questions/40111",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/29137/"
] | I recall reading once online about a website that had a name that sounded Japanese (Matsz... something) with security problems for programmers to do and learn about different security issues. Does anyone know what I'm talking about? I can't for the life of me remember the name, nor find if on google.
| You seem to be mixing two security objectives: protection of the code against reverse engineering, and protection of the application against attacks. These objectives are often contradictory: protections against reverse engineering increase the complexity of the code and therefore make it more likely that the code is v... | In many programming languages, initialization of local variables is forced, or the engine will flatly refuse to read uninitialized data. Even in languages where you <em>can</em> read uninitialized variables and thus get a copy of what remained in RAM at that emplacement, you cannot count on it to be "random"; it will h... | https://security.stackexchange.com |
126,525 | [
"https://electronics.stackexchange.com/questions/126525",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/31102/"
] | When I place a pad, there is an option <em>Plated</em>. Here is the picture:
<img src="https://i.stack.imgur.com/Wtnro.png" alt="enter image description here" />
What is the difference between plated and unplated pad without hole?
| There is no difference. The setting applies to plating of the hole, where there is one.
| A plated hole is lined with copper; an unplated hole is not. For example, clearance holes for mounting screws or standoffs might be specified as unplated, whereas holes for through-hole components are always plated. Plating the walls of the hole ensures electrical contact with inner layer traces that must connect to t... | https://electronics.stackexchange.com |
214,786 | [
"https://physics.stackexchange.com/questions/214786",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/59714/"
] | I'll start with a few definitions:
$$\beta \equiv \frac{1}{k_bT}$$
Where T is the temperature of a system.
And the partition function:
$$Z \equiv \sum_{j}e^{-\beta \epsilon_j}=\int D(\epsilon)d\epsilon e^{-\beta\epsilon}$$
Where s is an index over all distinguishable microstates of the system (in the case of discre... | In some cases we can approximate the sum by an integral appropriate:
$$\sum_j e^{-\beta\epsilon_j} =\int e^{-\beta E}D(\epsilon)d\epsilon=\int e^{-\beta E(\omega)}D(\omega)d\omega$$
In fact that is how we determine the density function. And I think there is no reason we can write $\sum_i Z_{\omega_i}=\int Z_\omega D(... | Your answer works for 1D case. In 1D k-space, any "sn", or equivalently "frequency" has only one corresponding standing wave mode (one dot in the 1D K-space). Another answer works for 3D case, where the K-space is 3D, so more than one K-modes in the 3D K-space can have the same frequency. Therefore,... | https://physics.stackexchange.com |
53,457 | [
"https://datascience.stackexchange.com/questions/53457",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/75687/"
] | I have trained a model for CNN and I am getting the error on the dense layer.
Model code:
<pre><code>def model(input_img):
conv1 = Conv2D(5, (3, 3), padding='same')(input_img) #28 x 28 x 32
conv1 = BatchNormalization()(conv1)
pool1 = MaxPooling2D(pool_size=(2, 2))(conv1) #14 x 14 x 32
relu1 = Activation('relu')(pool1... | You need to <strong>flatten</strong> your tensor before feeding it to the <code>Dense</code> layer.
<pre><code>from keras.layers import Flatten
def model(input_img):
conv1 = Conv2D(5, (3, 3), padding='same')(input_img) #28 x 28 x 32
conv1 = BatchNormalization()(conv1)
pool1 = MaxPooling2D(pool_size=(2, 2)... | When I tried flattening the new summary
<pre><code>Layer (type) Output Shape Param #
=================================================================
input_1 (InputLayer) (None, 242, 242, 1) 0
_________________________________________________________________
con... | https://datascience.stackexchange.com |
65,276 | [
"https://physics.stackexchange.com/questions/65276",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/9612/"
] | We have a uranium-236 nucleus that fissions into two equal fragments, and I'm supposed to find the electrical potential energy just as the two fragments split apart. No other information is provided.
I am very confused about this problem for two reasons. First, U-236 is electrically neutral, with exactly 92 protons a... | Like dmckee says, the potential energy of electrons in an atom doesn't really compare to the energy of the nucleus. Since the nucleus is so tightly packed, and (in the case of Uranium) contains so many protons, they have a lot of potential energy—it takes a lot of work to "push" them together. The <strong>strong force<... | Has your instructor (or your book) mentioned how much <em>bigger</em> a atom is than a atomic nucleus? On order of 10000 times.
Moreover, except for the $s$-shell electrons, most electron never come very close to the center (the $p$, $d$, etc shells all have nodes at $r=0$) so at the moment of fission the nuclei are s... | https://physics.stackexchange.com |
614,739 | [
"https://math.stackexchange.com/questions/614739",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/108874/"
] | $A\in\mathbb K^{n,n}$
We choose $a$ columns and $b$ rows, where $a+b>n$. When a chosen row and column cross, the entry of matrix at that point is equal to $0$, for example:
$n=5$, chosen columns$=\{2,3,4\}$, chosen rows$=\{1,3,5\}$.
\begin{bmatrix}
q & 0 & 0 & 0 &t\\
a & s & d & f &... | Since the determinant is defined by a sum over all permutations, you can show the value is $0$ if every permutation matrix (with one row chosen in each column to have a $1$, such that also every row has a single $1$) must have at least one entry $1$ in a position where $A$ has a $0$. To show that this is the case for a... | Hint: By reindexing the columns and rows, we may assume that $A$ is in the form of
$$
A=\pmatrix{X_{(n-b)\times a}&Y_{(n-b)\times(n-a)}\\ 0_{b\times a}&Z_{b\times(n-a)}}.
$$
What is the maximum rank of $X$ (note that $a+b>n$)? What is the maximum column rank of $A$?
| https://math.stackexchange.com |
118,330 | [
"https://stats.stackexchange.com/questions/118330",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/57193/"
] | A random sample $X_{1},...,X_{n}$ is pulled from a gamma distribution. Are there jointly sufficient statistics based on these observations for the two unknown parameters?
The definition of a gamma distribution is that its probability density function $f$ is nonzero only for positive arguments, where it is given by
$$... | The sufficient statistics is $\left(\prod_{i=1}^n X_i, \sum_{i=1}^n X_i \right)$. To see this, note the likelihood can be expressed as
\begin{eqnarray}
&&L(X_1,\ldots X_n) \\
&=& \prod_{i=1}^n \frac{X_i^{\alpha-1}}{\beta^\alpha \Gamma(\alpha)} e^{-X_i/\beta} \\
&=& \frac{1}{\beta^{n\alpha} \Gam... | Sufficient statistics are defined in terms of parameters. Jointly sufficient statistics, are together sufficient for one or more parameters.
Recall that sufficiency is defined typically in terms of the joint distribution of the sample conditioned on the sufficient statistic; therefore joint sufficiency is obtained ... | https://stats.stackexchange.com |
161,453 | [
"https://softwareengineering.stackexchange.com/questions/161453",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/60214/"
] | I've been trying to read through the RoR API to try to learn things that the tutorial missed, and I haven't been able to follow it at all. The only time I've read documentation was when I needed to look up a Python module, and that was easy to understand, but I can't understand the docs for Rails. How do I read through... | For a start, you don't learn a language (or how to use a library) from a reference pages. That what the tutorials are for starters.
For more advanced topics, if tutorials are missing, find good blogs, or a good book.
Having said that, reference pages are there to see details of a function (for example parameters and ... | The way to do it, if you insist on pulling info from the API w/o using as what it really is - a reference manual - would be to come up with a small program for each item in the reference/API docs and actually create code for it. In other words, to learn code, you must code, end of the day, that's the only real solutio... | https://softwareengineering.stackexchange.com |
203,404 | [
"https://security.stackexchange.com/questions/203404",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/199367/"
] | Suppose I have a <strong>server A</strong>, and that there is a <strong>website W</strong> hosted on A. The HTML of W contains:
<pre><code><img src=https://www.domainD.com/testT.jpg>
</code></pre>
Then I have a computer C, that accesses W.
Will <strong>computer C</strong> directly ask <code>domainD</code> for... | HTTP is <strong><em>Hyper Text</strong> Transfer Protocol</em>. Hyper text stands for the ability to aggregate informations from different sources. If you advertise an URL in a web page, the browser will use that URL to fetch the information piece. This is inherent to the protocol. Full stop here.
<strong>But</strong>... | In your example, computer C would directly access domain D, to obtain the image.
As you noted in your question, it's an <strong>external</strong> resource. This means, your website W has no control over the content on that host.
Clients can try to protect themselves, as @Tobi-nary has stated in his answer.
The othe... | https://security.stackexchange.com |
1,632,928 | [
"https://math.stackexchange.com/questions/1632928",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/309264/"
] | Find the sum $$\sum _{ k=1 }^{ 100 }{ \frac { k\cdot k! }{ { 100 }^{ k } } } \binom{100}{k}$$
When I asked my teacher how can I solve this question he responded it is very hard, you can't solve it. I hope you can help me in solving and understanding the question.
| \begin{align}
\sum\limits_{k=1}^{100} \frac {k\cdot k!}{100^k} \frac{100!}{k!(100-k)!} &= \frac{100!}{100^{100}} \sum\limits_{k=1}^{100} \frac{k\cdot100^{100-k}}{(100-k)!}\\
&= \frac{100!}{100^{100}} \sum\limits_{k=0}^{99}\frac{(100-k)\cdot 100^k}{k!}\\ &=\frac{99!}{100^{99}} \sum\limits_{k=0}^{99}
\left( \... | Using the notation $n^\underline{r}=\overbrace{n\ (n-1)\ (n-2)\cdots(n-r+1)}^{r\text{ terms}}$ for the falling factorial , we have
$$\begin{align}
\sum_{k=1}^n\frac {k\cdot k!}{n^k}\binom nk&=
\sum_{k=1}^n\frac {\color{blue}k\cdot k!}{n^k}\cdot \frac {n^\underline{k}}{k!}\\
&=\sum_{k=1}^n\frac {n^\underline{... | https://math.stackexchange.com |
1,045 | [
"https://chemistry.stackexchange.com/questions/1045",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/566/"
] | I'm trying to find the oxidation number of $ \ce N$ in $ \ce{(NH4)2SO4}$.
The answer is supposed to be $-3$ but I can't figure out the logic behind this.
| Ammonium sulfate is an ionic compound, composed of two ammonium ions ($\ce{NH_{4}^{+}}$) and one sulfate ion ($\ce{SO_{4}^{2-}}$). As such, you can neglect the sulfate entirely from your consideration of the oxidation state of the nitrogen, as well as treating each ammonium ion as a separate entity. Given the total cha... | To easily determine the oxidation number on an individual atom in an ion it is necessary to write an equation.
First determine what the oxidation number of your known atoms are.
In this case, we know the oxidation number for H is +1.
Then set this value equal to the overall net charge of the ion.
In this case, it i... | https://chemistry.stackexchange.com |
209,629 | [
"https://dba.stackexchange.com/questions/209629",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/153399/"
] | I have a table say table1 with three columns lets name them col1 col2 and col3. I have a suspicion that col2 and col3 have some values that are identical i.e. to say there are some rows where col2 = col3. In case, if for these rows col1 is the same I will have no problem in my application. But how to check for those wh... | You mean something like
<pre><code>SELECT col2, col3 FROM table WHERE col2 = col3 GROUP BY col2, col3
HAVING COUNT(DISTINCT col1) > 1;
</code></pre>
Would show you the col2/col3 combinations where col2 = col3 but col1 differs between those rows.
| <blockquote>
Akina: Сorrect me if I'm wrong. You want 1) Eject all records with col3 field values which not exists in any record in col2 field. 2) Select DISTINCT col1 for the remaining records.
Andy Joe: @Akina col3 values which does exist in col2
</blockquote>
Variant 1:
<pre><code>SELECT DISTINCT t1.col1
FROM table1... | https://dba.stackexchange.com |
11,134 | [
"https://mechanics.stackexchange.com/questions/11134",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/4376/"
] | For the past couple of months, I've been having trouble filling my gas tank. I have a 2003 Hyundai Elantra, which has a 55-liter tank (approximately 14.5 US gallons).
When I buy gas, the pump clicks off after dispensing only two or three gallons. Knowing the tank can't possibly be full, I keep working on filling the t... | I finally took the car to a shop. It turns out that the problem was the charcoal canister, which needed to be replaced.
| Sound like you refueling control valve may be bad. This is a one way valve that connects the fuel tank to the EVAP Canister. It's purpose is to send vapors to the canister instead of the air when you are refueling. If it's plugged up it will not allow vapors to escape fast enough and cause the pump to shut off.
| https://mechanics.stackexchange.com |
138,282 | [
"https://mathoverflow.net/questions/138282",
"https://mathoverflow.net",
"https://mathoverflow.net/users/20757/"
] | What integers are not in the range of $a^2+b^2+c^2-x^2$ (for all integer combinations of a, b, c, and x)? This form is similar to that of Lagrange's Four-Square Theorem, for which the answer would be "none". The generalization by Ramanujan only seems to cover non-negative coefficients.
| With indefinite forms, it is possible for ternary forms to be universal. Indeed, all are known. References are given in <em>Modern Elementary Theory of Numbers</em> by Leonard Eugene Dickson, (1939). With any integer $M$ and any <strong>odd</strong> $N,$ they are equivalent to (by an invertible linear change of varia... | Since Gerry Myerson is too humble to take answer credit, I'll
make it even simpler and close out my stupid question:
$0^2+(x+1)^2-x^2=2x+1$ ranges all odds, so $1^2+(x+1)^2-x^2$ ranges all evens.
Just 3 integers are enough (a is 0, b is 0 or 1, c is x+1).
| https://mathoverflow.net |
309,611 | [
"https://physics.stackexchange.com/questions/309611",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/144323/"
] | The differential equation for a simple pendulum can be given as,
$$\frac{\mathrm{d}^2\theta}{\mathrm{d}t^2} + \frac{g}{l}\sin\theta = 0$$
In some notes I found that $g/l$ can be assumed as $1$ (i.e $g/l = 1$) without loss of generality, and this can be rewritten as
$$\frac{\mathrm{d}^2\theta}{\mathrm{d}t^2} + \sin\t... | This all comes down to having the freedom to choose units for the quantities.
Recall that a physical quantity can be written as a product of a number and a unit. In this case, you have several examples of physical quantities: $\theta$, $g$, $l$, and $t$. For example, in the case of $l$, if the pendulum is $0.75\ \math... | I think they're just choosing a time scale. Note that the units of $\frac{g}{\ell}$ are $\left(\frac{\rm m}{\rm s^{2}}\right)\frac{1}{\rm m} = \frac{1}{\rm s^{2}}$.
So, if you replace the second with a unit of time equal to $\sqrt{\frac{\ell}{g}}$, then in that system of units, we have $\frac{g}{\ell} = 1$
| https://physics.stackexchange.com |
50,928 | [
"https://softwareengineering.stackexchange.com/questions/50928",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/4603/"
] | How do people deal with profanity in source code and VCS comments. Keep or delete?
What about soft-expletives like WTF or Arrgggh?
Is unprofessional, offensive or something to be shrugged off?
| <strong>It should be gently discouraged</strong>
..you cannot possibly know who will get to see the source code over its' lifetime.
While it is all part of the job to get frustrated with a particularly complex or old piece of code and want to sound off about it, putting expletives/rants/ASCII art/bad jokes/offensive ... | If you're selling your source code (i.e. you're a component writer), it probably ought not be in there.
If it's a matter of prudishness, then well whatever, it's up to you.
If you see someone writing a lot of WTF's then maybe it's a sign that you should talk to them about the problems that they're having.
If someone... | https://softwareengineering.stackexchange.com |
14,559 | [
"https://bioinformatics.stackexchange.com/questions/14559",
"https://bioinformatics.stackexchange.com",
"https://bioinformatics.stackexchange.com/users/9010/"
] | I have 10 samples from a RNAseq experiment (5 control, 5 disease), I have performed a cluster analysis for the samples and for the genes (4000 genes aprox) to see how they cluster (to see which samples are similar and which genes have similar expressions).
I was wondering if in terms of statistics it makes any sense to... | First of all, I am not a statistician but have been performing RNA-seq analysis for a while, here is my take:
<ul>
<li>I think performing PCA on the samples makes sense in terms of mathematics. What I mean is you can compute eigenvectors and subsequently principal components either on your genes or on your samples.
</l... | If you use, say, R's prcomp, you can use <code>my_pca_object$x</code> to get PC coordinates for the samples, and <code>my_pca_object$rotation</code> to get how much each gene contributes to each PCA. (You might need to transpose your transformed count file to get it to work right)
| https://bioinformatics.stackexchange.com |
320,039 | [
"https://softwareengineering.stackexchange.com/questions/320039",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/230724/"
] | So i am creating my first larger scale application (by larger scale i mean something i see myself publishing in the app store) and i am not sure of how to handle user authorization.
The client will consist of a application for android and iphone, and they make HTTP requests on a server.
My data is stored in a postgreS... | First off, the token approach seems sound for your case. One option is to encrypt user information (e.g. id) into the token. On the server side, you can then keep things stateless. Realize that no matter the details of how it is generated, this token is sensitive. If someone has it, they can use it to pretend to be... | Don't really know the full use case but this really screams using a session to me. Normally these are implemented with a unique ID sent to the client in the form of a cookie and stored on the server in an in memory database like <code>redis</code> or <code>memcached</code>.
When a user logs a new object will be adde... | https://softwareengineering.stackexchange.com |
210,205 | [
"https://dba.stackexchange.com/questions/210205",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/153820/"
] | I am trying to do a simple SELECT on a large table, but it is not being run in parallel:
<pre><code>my_db=> explain (analyze, buffers) select value from my_table;
Seq Scan on my_table (cost=0.00..94433357.34 rows=5441810434 width=4) (actual time=0.029..1519364.787 rows=4897721407 loops=1)
Buffers: shared hit=112... | The query leader is the only process that communicates with the front end. All the SELECTed data for the non-aggregated version of the query has to be marshalled up from the parallel workers to the query leader. That is expensive, so using parallel query here would almost certainly be counter-productive. You might b... | A simple explanation to your question is the a logical abstraction.
What is faster?
<h3>1. Parallel Execution</h3>
<ol>
<li>Analyse query</li>
<li>Determine which index to use</li>
<li>Split the query into parallel reads</li>
<li>Consolidate query results</li>
<li>Present consolidated data</li>
</ol>
<h3>2. Serial E... | https://dba.stackexchange.com |
6,713 | [
"https://electronics.stackexchange.com/questions/6713",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1225/"
] | How do these electronic calipers work?:
<img src="https://i.stack.imgur.com/AtTpr.gif" alt="Caliper">
I know they work by measuring the capacitance of the running track, somehow. But how do they use capacitance to measure distances - is it a linear relationship of capacitance to distance, or is there something else g... | Its position to capacitance ratio to frequency ratio to value conversion. The key is using unevenly patterned conductors in proximity of two capacitors. The circuit has slow response, but works remarkably as caliper.
| Just had some fun trying to scope the signals, something really funky is going on there.
"Here is a good web page" <- that page? wrong! not what is happening there at all, there is only one input signal, not sin and cos
"The key is using unevenly patterned conductors in proximity of two capacitors." <-- wrong a... | https://electronics.stackexchange.com |
22,016 | [
"https://datascience.stackexchange.com/questions/22016",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/37546/"
] | When I reopen a project I am working on in the Jupyter Notebook, and trying to add code, the cell restarts at '1' and the only way I can continue to work with my previous objects present is by rerunning all the code. Is there a better way?
| In Hadoop framework, there are multiple way to analyze the data. This depends on your use case, expertise and preference. Hive <code>EXTERNAL</code> tables are designed in a such way that other programmer can also share the same data location from other data processing model like Pig, MapReduce Programming, Spark and o... | In hive if you are doing using <code>drop</code> to drop a table and if the table is external table then it will only delete the table.
When you are creating table it creates a directory in hadoop with the path you specified. But if you are not giving any path it will take the default directory (like: <code>/user/hive... | https://datascience.stackexchange.com |
137,621 | [
"https://dba.stackexchange.com/questions/137621",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/92682/"
] | I want to preface this post by saying that I am a SQL(ite) newbie. My main goal is to find the opening/closing/high/low/average prices of each 5 minute interval of these stock prices. I can get the high/low working with min/max and the group by query but I am running into problems with the opening/closing. My database ... | You first query is OK although not entirely correct.
<ul>
<li>You need to be careful with <code>GROUP BY</code> and not have any column in the <code>SELECT</code> list that is not also in the <code>GROUP BY</code> list. So, add the <code>symbol</code> in the group by list.</li>
<li>Next, the <code>LIMIT</code> needs ... | With correlated subqueries, it would look like this:
<pre><code>SELECT Symbol,
MIN(DateTime) AS MinDT,
MIN(Price) AS MinPrice,
MAX(Price) AS MaxPrice,
AVG(Price) AS AvgPrice,
(SELECT Price
FROM stocks AS s2
WHERE s2.Symbol = stock.Symbol
AND s2.DateTime = ... | https://dba.stackexchange.com |
9,104 | [
"https://computergraphics.stackexchange.com/questions/9104",
"https://computergraphics.stackexchange.com",
"https://computergraphics.stackexchange.com/users/11114/"
] | I have a noob level question about RGB images-
Pixels in RGB images are in the range of (0-255), so technically each channel ranges from 0(black) to 1(white), then why we say that each image has a Red, Green, Blue channel component, although they are only Gray channel. In short, how the image is formed?
| Each channel ranges not from <em>black</em> to <em>white</em>, but from <em>off</em> to <em>full intensity</em>. What colour is meant by <em>full intensity</em> is down to convention and the presentation technology.
For example, a given image file format might say there are three bytes, of which the first is the red c... | CRT monitors are a thing of the past, but I think they are the best example to describe to you "how the image is formed".
Each pixel on the monitor is actually a group of 3 phosphors. A green phosphor, a red phosphor and a blue phosphor. These phosphors will glow at a certain intensity when they are charged. Inside the... | https://computergraphics.stackexchange.com |
139,012 | [
"https://security.stackexchange.com/questions/139012",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/34553/"
] | <h2>Assumimg that...</h2>
<ul>
<li>the target is some server (> 2010) that could be running any OS</li>
<li>the attacker has gained access to everything remotely, (with maybe some physical access as well)</li>
</ul>
Is it possible for an attacker, through only software means, to leave an irreversible software artifac... | If we are talking about any theoretical possibilities (outside of basic, that would be purged during BIOS and OS wipe):
- Attacker can change firmware of the hardware. Most lucrative would be network adapter and storage device, but others might be targeted as well.
Cannot think of anything else, if we are restricting... | There was a paper at the CCC conference a few years ago discussing modifying hard disk controller firmware to allow the disk controller to silently replace bits of data between the platter and the main machine.
Conclusion was that some of the things have multi core ARMs and do not fully use them, so actually the atta... | https://security.stackexchange.com |
6,316 | [
"https://computergraphics.stackexchange.com/questions/6316",
"https://computergraphics.stackexchange.com",
"https://computergraphics.stackexchange.com/users/7462/"
] | From the sources that I have read about deferred rendering they all mention "handling transparency is hard" without much more information.
However a solution that I see is, handle the scene once without the transparent geometry, once assuming the geometry is fully opaque, then interpolate between the 2 based on the t... | PaulHK is right in what he said: you have to consider that there may be more than 2 transparent objects behind each other.
Also, the idea of deferred shading is to render the geometry only once to be more efficient. If you render the geometries multiple times, you lose (part of) your efficiency. Moreover, the lighting... | A fundamental assumption of deferred shading is that there will be only one surface, and therefore only one depth, at a given pixel.
An effect that contradicts that assumption will require some sort of special handling in a deferred renderer. Translucency, because it allows to see through multiple layers, is such an e... | https://computergraphics.stackexchange.com |
15,098 | [
"https://quantumcomputing.stackexchange.com/questions/15098",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/13563/"
] | It appears that controlled-<span class="math-container">$U$</span> type operation is the bedrock to many quantum algorithms, for instance, phase estimation and amplitude estimation. These algorithms systematically employs the controlled-<span class="math-container">$U$</span> type operation on the a state, say <span cl... | We know that operators are applied on qubits. But sometimes it does not make sense to ask the state on which we apply an operator, say <span class="math-container">$U$</span>. For instance, take the two-qubit entangled state <span class="math-container">$|\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)$</span>.... | <blockquote>
It appears in the most general case the resulting state of the control bit and the oracle register needs to be viewed as one state.
</blockquote>
Yes, absolutely. This is rather the point of quantum computation - for any interesting computation, there will be entangling steps that mean you cannot view the ... | https://quantumcomputing.stackexchange.com |
574,707 | [
"https://physics.stackexchange.com/questions/574707",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/272854/"
] | I don't quite get the concept of drift velocity. According to definitions, <strong>it is the net velocity with which the electrons are drifted in a direction opposite to the applied electric field</strong>. Is the thermal velocity included in that or is it different? According to what I have read drift velocity goes to... | Degeneracy occurs when a system has more than one <em>state</em> for a particular energy level. Considering the three dimensional harmonic oscillator, the energy is given by
<span class="math-container">$$E_n = (n_x + n_y + n_z) \,\hbar \omega + \frac{3}{2},$$</span>
where <span class="math-container">$n_x, n_y$</span>... | The 1D harmonic oscillator Hamilton is given by <span class="math-container">$$H=\left(n+\frac{1}{2}\right)\hbar\omega$$</span>
where <span class="math-container">$\omega$</span> is the frequency and <span class="math-container">$n$</span> is a natural number.
As you can see the Hamiltonian is independent of spin <span... | https://physics.stackexchange.com |
889,393 | [
"https://math.stackexchange.com/questions/889393",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/160811/"
] | Suppose V and W are finite dimensional. Let $v \in V$. Let
$E = {T \in L(V, W): Tv = 0}$ where L(V, W) is the set of all linear transformations from a vector space V to a vector space W. Show that E is a subspace of L(V, W). What is dim E?
For the proof that E is a subspace I said:
It is obvious that E contains the ... | Let $v_i$ be a basis for $V$ and $w_j$ be a basis for $W$. Define $T_{mn} $ by
$T_{mn} v_i = \delta_{mi} w_n$. It is straightforward to verify that the $T_{mn}$ for a basis for $L(V,W)$, hence $\dim L(V,W) = (\dim V) (\dim W)$.
First, if $v=0$, we see that $E = L(V,W)$, hence $\dim E = (\dim V) (\dim W)$.
Now suppos... | I think you want to show the set $E := \{T \in L(V,W) : T(v) = 0\}$ of $T$ killing a fixed $v$ is a linear subspace of $L(V,W)$, right? Then your proof should involve $T_1 + T_2$ and $cT_1$, for $T_1, T_2 \in E$ and $c$ a scalar, rather than $v_1 + v_2$ and $cv$.
For the dimension, one way to go is to pick a basis of ... | https://math.stackexchange.com |
296,336 | [
"https://physics.stackexchange.com/questions/296336",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/100917/"
] | It is pretty straight forward how light is redshifted in an expanding universe, yet I still can't understand why the De'Broglie wavelength of a massive particle isn't redshifted in an expanding universe. There is no proper notion of conserved mass energy in the expanding universe (without considering gravitational ener... | The de Broglie wavelength of a massive particle <strong>is</strong> redshifted in an expanding universe.
The de Broglie wavelength is given by:
$$ \lambda = \frac{h}{p} $$
so a red shift of the de Broglie wavelength simply means that the momentum is decreasing, which for a massive particle means that its velocity re... | The difference between massless and massive particles in the expanding Universe is in their energy densities. Since the energy of heavy particle comes almost entirely from its mass, the energy density behaves as $\frac{1}{r^3}$, while the energy of the massless one comes from its wavelength, which changes as the Univer... | https://physics.stackexchange.com |
198,049 | [
"https://mathoverflow.net/questions/198049",
"https://mathoverflow.net",
"https://mathoverflow.net/users/21815/"
] | Let $S$ be a smooth projective surface over $\mathbb{C}$. (I guess this can be more general—higher dimension, other ground fields, non-projective, maybe even singular?—and I'dd like to hear that.) Let $s \in S$ be a point. Let $\beta \colon X \to S$ be the blowup of $s \in S$. Suppose that $H^{i}(S, T_{S})$ is known fo... | The answer is the following and can be found in Hartshorne's book <em>Deformation Theory</em>, see in particular Exercise 10.5 page 83.
We work over an algebraically closed field $k$. Then there is an exact sequence of sheaves $$0 \to \beta_*T_X \to T_S \to k_s \oplus k_s \to 0,$$ inducing an exact sequence in cohomo... | Let $S$ be a surface and $Z=\{p_1,...,p_n\}\subset S$ be a reduced subscheme of dimension zero. Let $\epsilon:\widetilde{S}\rightarrow S$ be the blow-up of $S$ at $Z$. Consider the exact sequence
$$0\mapsto \epsilon^{*}\Omega_{S}\rightarrow \Omega_{\widetilde{S}}\rightarrow i_{*}\Omega_{E/Z}\mapsto 0$$
where $i:E\hookr... | https://mathoverflow.net |
79,531 | [
"https://mathoverflow.net/questions/79531",
"https://mathoverflow.net",
"https://mathoverflow.net/users/18384/"
] | Suppose X is a complete metric space, and $f:X↦X$ a continuous surjective function. Let D be a dense set. Suppose $f:D↦D$ is injective and $f^{-1}(D)=D$.
Is $f$ injective ?
Is there a family of metric spaces where you can conclude $f$ is injective?
| Sorry but I could not resist:
<img src="https://i.stack.imgur.com/pyVEI.png" alt="alt text">
The map is defined on $[0,1]\times[0,1]$, and can be written as
$$
f(x,y) = \begin{cases}
(x, (2-x)y) & \text{ if }y\leq 1/2, \\
(x, xy+1-x) & \text{ if }y> 1/2.
... | Here is another example which is easy to visualize. Let $X=[-1,1]^2$, $I$ be the segment between $(-1,0)$ and $(1,0)$ and $I_0$ its subsegment between $(-1/2,0)$ and $(1/2,0)$. There is a homeomorphism $f$ between $X\setminus I_0$ and $X\setminus \{0\}$ which sends $I\setminus I_0$ to $I\setminus\{0\}$ and extends cont... | https://mathoverflow.net |
122,923 | [
"https://mathoverflow.net/questions/122923",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7313/"
] | Let $\Gamma \subseteq PSL_2(\mathbb{R})$ be a Fuchsian group, possibly containing elliptic elements. Is it true that $N(\Gamma) / \Gamma$, where $N(\Gamma)$ the normalizer of $\Gamma$ in $PSL_2(\mathbb{R})$, is isomorphic to the automorphism group of $\Gamma \backslash \mathcal{H}^*$?
Here, $\mathcal{H}^*$ is the unio... | The compact Riemann surface $\Gamma\backslash\mathcal H^*$ may have authomorphisms that do not preserve the set of points corresponding to the cusps of $\Gamma$, so I believe the answer is no.
| How about $\Gamma = PSL_2(\mathbf{Z})$, where $N(\Gamma)/\Gamma)$ is the trivial group but the automorphism group of $\Gamma \setminus \mathcal{H}^*$ is infinite?
In general the best you can do is that you have a map $N(\Gamma) \to \mathrm{Aut}(\Gamma \setminus \mathcal{H}^*)$ whose kernel is $\Gamma$. If you have no ... | https://mathoverflow.net |
741,209 | [
"https://math.stackexchange.com/questions/741209",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/140690/"
] | A password is 8 characters long. Each character can contain 26 lower case or 26 uppercase letters or a integer from 0-9. What is the probability that an 8 character password contains exactly 1 OR 2 integers?
Please explain as the book answer is P = .630
Assuming that I could use (52^6*10^2+52^7*10)/62^8 was incorre... | Yes, this can be expressed in the language of linear algebra, as you seem to desire. Namely, over any infinite field $\,F\,$ the polynomials $\,\{X^i\}\,$ are basis of the polynomial function ring $\,K[X],\,$ hence $\ c+ aX = \langle c,a,0,0\ldots\rangle = \langle d,b,0,0\ldots\rangle = d+b X\,$ iff they have the same ... | Because the equality must hold for all values of $x$, if we let $x=0$ then we get $c=d $, then we let $x=1 $ to get $a+c=b +d$ but our previous findings give us that $a=b $. This generalises to polynomials of higher order, you just compare coefficients.
| https://math.stackexchange.com |
115,444 | [
"https://softwareengineering.stackexchange.com/questions/115444",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/34340/"
] | Arrays and pointers are not the same thing in C, although they are related and can be used similarly. So far we all agree.
However, I don't see why arrays were included in C, when pointers could have done their job perfectly.
I am not saying to remove the array notation (e.g, a[5] or int a[4] = {0,1,2,3};), which is... | Arrays are contiguous memory created on the stack. You can't guarantee contiguous stack memory without this syntactic sugar, and even if you could, you'd have to allocate a separate pointer in order to be able to do the pointer arithmetic (unless you wanted to do <code>*(&foo + x)</code>, which I'm not sure but it ... | Array notation is convenient, easier to read, and less prone to errors. It provides a formalism over pointers. It might be syntactic sugar, but we all need a little sweetness once in awhile, don't we?
As with all abstractions, you give up a little flexibility for the convenience that the abstraction provides.
| https://softwareengineering.stackexchange.com |
105,519 | [
"https://electronics.stackexchange.com/questions/105519",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/39903/"
] | I'm looking at a brand new foot pedal for a Tungsten Inert Gas (TIG) welder. This foot pedal uses cascading potentiometers to send a signal to the welder control system. I'm getting unusual results when I verify the pedal using a Volt Ohm Meter. I'm measuring resistance between the wiper terminal and 'ground' termina... | Given that you've said <code>R7</code> is set to 0 ohms, the two fixed terminals of <code>R6</code> are shorted together. When the wiper is at either extreme, its resistance to either fixed terminal will also be 0 ohms. When the resistance is 50%, both halves will be in parallel. Given that this appears to be a 50 k po... | Following your post of the schematic: Ah HAH. I think you may be getting thrown off by measuring the resistance to ground when two pots, and connections to Ground and +5V are involved (even though you no doubt had power off). Instead, with the pedal disconnected from the welder, attach a power supply (say +5V, or a 9V ... | https://electronics.stackexchange.com |
308,215 | [
"https://electronics.stackexchange.com/questions/308215",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/123349/"
] | <img src="https://i.stack.imgur.com/2DSE8.png" alt="enter image description here">
I was thrown off by a certain website while learning about a op amp Schmitt trigger design. The layout was the same inverting config as the above schematic but gave a confusing answer to calculating high threshold.
Vout=5v high
Vout=0v... | I find for some students, the angled components are visually confusing. Try redrawing the same schematic with only horizontal and vertical components to see if this helps you to analyze it.
For example, if you start on the right and straighten out the 6k resistor, you will notice it is in parallel with the series com... | Start from right to left. You can see that the rightmost diagonal <code>6K</code> resistor is connected in parallel to the <code>1K</code> and <code>2K</code> resistors. Calculate the equivalent and redraw. Suddenly you will figure out it is connected in series to another resistor. Calculate equivalent and redraw. And ... | https://electronics.stackexchange.com |
98,927 | [
"https://physics.stackexchange.com/questions/98927",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/19857/"
] | My teacher has for Bloch waves the notation $\langle \vec{r}|\vec{k} \rangle = e^{i\vec{k}\cdot \vec{r}}u_{\vec{k}}(r)$ and <em>uses it consistently</em>. However, does this not assume that there is an operator that has eigenstates $|\vec{k} \rangle$? If so, how would such an operator be defined?
| Sure, it is certainly possible to define a crystal momentum operator, although I haven't heard of people doing this.
You define it by saying that the eigenstates of this operator are Bloch states, and the eigenvalue of each Bloch state is its crystal momentum (translated into the first Brillouin zone). There is a uniq... | It turns out the Bloch states are eigenstates of the translational operator, <span class="math-container">$T(\vec{R}_{j})$</span>, namely, <span class="math-container">$T(\vec{R}_{j})\left\vert\vec{k}\right\rangle=e^{i\vec{R}_{j}\cdot\vec{k}}\left\vert \vec{k}\right\rangle$</span>, where <span class="math-container">$\... | https://physics.stackexchange.com |
252,114 | [
"https://security.stackexchange.com/questions/252114",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/248179/"
] | Assume I have a password manager that stores the credentials for a login to a 3rd party service. In this credentials the username, password and a TOTP-seed is stored and the current TOTP-token is displayed at all times and refreshed accordingly (Note that such a password manager does not exist).
Is authenticating to th... | In this case i would consider it a 1-factor authentication, but only from the client-side.
On the client side it would not much differ from using a password only, as each factor is not seperated from each other and can be accessed with the same password.
From a server-side view it can still be considered a 2-factor aut... | Yes, this degrades it to a <strong>single factor</strong> authentication.
Think of this as follows. How many problems need an attacker to solve to break authentication?
Consider examples: Suppose you have authentication that requires password and and a code sent via SMS. To break it, the attacker needs 1) to know you p... | https://security.stackexchange.com |
142,987 | [
"https://softwareengineering.stackexchange.com/questions/142987",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/48960/"
] | I'm looking to implement the command pattern in a web application (asp.net c#)... Since the commands come in text format from the client, what is the best way to translate the string to a command object? Should I use reflection? Currently I just assume the command that comes in matches the file name of a user control. ... | You could use a hash table to map from input strings to Execute methods.
| The best way to do this in just about any app is to use an IoC container. Then your command pattern looks something like:
<pre><code>public static class CommandLineActionFactory
{
public static ICommandLineAction GetAction(string actionName)
{
if (actionName == null) throw new ArgumentNullException(na... | https://softwareengineering.stackexchange.com |
134,984 | [
"https://physics.stackexchange.com/questions/134984",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57998/"
] | I'm just starting to learn about special relativity, and I'm a little bit confused about something. Take the example of an observer in $S$ on the ground observing a train move at constant velocity $v$ relative to $S$, an observer in $S'$ is on the train, and this observer in $S'$ flashes a light that reflects from the ... | I agree with your statements up through the claim that $t'<t$. That's all fine.
Here I think is the issue you're running into:
The quantity $t'$ in the relationship above represents the time interval <em>as measured in frame $S'$.</em> It does <em>not</em> represent the number of ticks by the moving clock as measu... | It seems you feel that the example should be symmetrical because from each point of view (S or S'), time is running slower in the other. However, the experience is not symmetrical because as you said : S' is proper time and S is not.
If you make an other "experiment" of which S is proper time, then S will measure t2 a... | https://physics.stackexchange.com |
21,684 | [
"https://ai.stackexchange.com/questions/21684",
"https://ai.stackexchange.com",
"https://ai.stackexchange.com/users/31324/"
] | I often see that the state-action value function is expressed as:
<span class="math-container">$$q_{\pi}(s,a)=\color{red}{\mathbb{E}_{\pi}}[R_{t+1}+\gamma G_{t+1} | S_t=s, A_t = a] = \color{blue}{\mathbb{E}}[R_{t+1}+\gamma v_{\pi}(s') |S_t = s, A_t =a]$$</span>
Why does expressing the future return in the time <span cl... | Let's first write the state-value function as
<span class="math-container">$$q_{\pi}(s,a) = \mathbb{E}_{p, \pi}[R_{t+1} + \gamma G_{t+1} | S_t = s, A_t = a]\;,$$</span>
where <span class="math-container">$R_{t+1}$</span> is the random variable that represents the reward gained at time <span class="math-container">$t+1$... | David Ireland gives a fantastic answer, and I will provide an intuitive and gentle (but less rigorous) answer for those who are unfamiliar with the relevant statistical concepts.
<strong>Next reward <span class="math-container">$R_{t+1}$</span>:</strong> The next reward <span class="math-container">$R_{t+1}$</span> i... | https://ai.stackexchange.com |
90,490 | [
"https://stats.stackexchange.com/questions/90490",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/9162/"
] | I don't mean a value close to zero (rounded to zero by some statistical software) but rather a value of literally zero. If so, would it mean that the probability of getting the obtained data assuming the null hypothesis is true is also zero? What are (some examples) of statistical tests that can return results of this ... | It will be the case that if you observed a sample that's impossible under the null (and if the statistic is able to detect that), you can get a p-value of exactly zero.
That can happen in real world problems. For example, if you do an Anderson-Darling test of goodness of fit of data to a standard uniform with some dat... | In R, the binomial test gives a P value of 'TRUE' presumably 0, if all trials succeed and hypothesis is 100% success, even if number of trials is just 1:
<pre><code>> binom.test(100,100,1)
Exact binomial test
data: 100 and 100
number of successes = 100, number of trials = 100, p-value = TRUE <<&l... | https://stats.stackexchange.com |
37,683 | [
"https://stats.stackexchange.com/questions/37683",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/11405/"
] | I have some data that span several years: 2006-2010. I have run logistic regression to model the data. For the whole dataset, I get a 95% confidence interval for the <strong>odds ratio</strong> of a parameter of interest of
<pre><code>(0.34 - 0.47 )
</code></pre>
indicating a very significant effect. However, for e... | To expand on Peter Flom's answer (which is echoed in Michael Chernick's subsequent reply), this graphic may help the intuition.
<img src="https://i.stack.imgur.com/ANaN5.png" alt="Logistic plots">
The following <code>R</code> code shows how it was produced. Briefly, it generates 400 data points per year, with values... | In this case, it does not appear to have to do with sample sizes, since the CIs for the individual years do not even overlap with the CI for the whole period.
It's hard to say exactly what's going on. Your code would help - did the model for the full data set include year as a IV? What is your dependent variable? What... | https://stats.stackexchange.com |
176,407 | [
"https://softwareengineering.stackexchange.com/questions/176407",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/4517/"
] | While writing some predicates for collection filtering I have stumbled over the choice of the right words for the relation of the subject and the predicate (English is a foreign language for me). What I ended up writing was "Subjects <strong>matching</strong> this predicate..."
This seems to be incorrect, since predic... | I would use "Subjects satisfying this predicate".
Matches implies a pattern, rather than a condition. And "for which this predicate returns true," although the most accurate, sounds more technical than I think you intend.
Edit: Mike makes a good point that predicate is also very technical. Perhaps "Subjects satisfyin... | I think the terminology really depends on your intended audience.
If we're talking about code comments and API documentation then I would say your suggestion would be very accurate and understandable.
<pre><code>"For which this predicate returns true."
</code></pre>
If we're writing end user documentation I would av... | https://softwareengineering.stackexchange.com |
2,578,188 | [
"https://math.stackexchange.com/questions/2578188",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/379997/"
] | Prove that $x^2+x+2$ is maximal ideal in $F_3[x]$ ring.
I think of using the theorem that $B$ is maximal ideal in $A$ if $A/B$ is field. Particularly in this case we need to prove that $F_3[x]/(x^2+x+2)$ is field. Could you please help?
| Just verify that the polynomial does not have a root. If it was not maximal, it would have had a divisor of degree $1$, hence a root.
| Hints:
The quadratic's discriminant is $\;\Delta=1-4\cdot2=-7=2\pmod3\;$ . Now check that $\;2\;$ is a <em>non-quadratic residue</em> modulo $\;3\;$ .
| https://math.stackexchange.com |
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