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 |
|---|---|---|---|---|---|
24,352 | [
"https://datascience.stackexchange.com/questions/24352",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/41414/"
] | What happens if my data/feature is not normal? Can I still use machine learning algorithms to utilize such data for predictions?
I noticed in many data sciences courses, there is always a strong assumption of using a normal/Gaussian data. I have always wonder why this is so, and most people would say that due to centr... | There are models that do not make assumption that the underlying data distribution is a normal distribution.
For example, support vector machine just cares about the boundaries of the separating hyperplane and do not assume the exact shape of the distributions. Decision tree models also do not make such assumption.
... | Gaussian models are often used (and maybe sometimes over-used) because of their mathematical convenience (many statistical models can be found as built-in functions, when based on the Gaussian distribution, in some libraries such as mixture models, hidden Markov models,...). Also, when one has no idea about what distri... | https://datascience.stackexchange.com |
136,362 | [
"https://stats.stackexchange.com/questions/136362",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/68170/"
] | I'm interested in generating random arrivals that should simulate the call arrivals of a call center. I chose to use a Poisson distribution, but the greatest problem comes with the fact that it's a discrete distribution.
So I thought that I could use it to generate an arrival rate in a time frame of 1 second; this w... | <ol>
<li>If it's a Poisson process, the inter-call time is exponential with mean equal to the inverse of the rate. It's probably easier at each step to simply generate the time to the next call than generate a number of calls in an interval and then try to place them in that interval.
If you really want do it the way y... | The key to efficiently generating poisson distributed events is to realize the any number of events that exist within any interval occur independently. In other words,the occurrence time of each event is uniformly distributed in the interval. Each of n events with average arrival rate of mu occur uniformly in the inte... | https://stats.stackexchange.com |
339,962 | [
"https://physics.stackexchange.com/questions/339962",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/59234/"
] | $2+1$-dimensional Einstein gravity has no <em>local</em> degrees of freedom. This can be proved in two different ways:
<ol>
<li>In $D$-dimensional spacetime, a symmetric metric tensor <em>appears to have</em> $\frac{D(D+1)}{2}$ degrees of freedom satisfying $\frac{D(D+1)}{2}$ <em>apparently independent</em> Einstein f... | Let's start with a simpler example: $1+1$ dimensional gravity. This is actually a pretty important example to understand because all of string theory takes place in this framework!Within $1+1$ dimensional gravity, just as in $2+1$ dimensions, there are no local interactions. Thus, it seems like a pretty good starting p... | Bob Knighton's answer is very detailed. But I want to add a few remarks. You can try to prove this identity
$$ R_{\mu\nu\rho\sigma} = \frac{R}{D(D-1)} (g_{\mu\rho}g_{\nu\sigma}-g_{\mu\sigma}g_{\nu\rho}). $$
Then, it's straightforward to show that for 1+1 spacetime, the Einstein tensor $R_{\mu\nu} - \frac{1}{2}Rg_{\mu... | https://physics.stackexchange.com |
374,137 | [
"https://softwareengineering.stackexchange.com/questions/374137",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/184113/"
] | I'm a newbie coder. I find it troublesome to declare a variable in 1 function and not be able to access it in other functions. I have to make many of my variables global just to get my code to work. But a lot of people say that the global state is evil. I don't understand the purpose of having limited scope, anyway.
S... | Engineering is, abstractly, managing complexity.
Software Engineering is, abstractly, managing complexity in <strong>software!</strong>
Scope is a tool to help manage complexity, like any tool it can be used or abused, and sometimes can be overkill.
Without scope, you would have to track the entire state of the prog... | Minimizing your use of global variables means that you don't have to think about how these variables are interacting with your functions.
How many different places in your code are writing to that global variable? Your global variable is the center of a spider web; every place it touches is adding unnecessary complexi... | https://softwareengineering.stackexchange.com |
324,992 | [
"https://softwareengineering.stackexchange.com/questions/324992",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/55003/"
] | As someone used to C++ and new to JavaScript, I find this behavior odd. Whether a program runs directly on the platform like C++ ones, or it runs at a higher (or deeper?) level like JavaScript ones, conceptually, a program a program and an exception is an exception. Then why does JavaScript have this behavior? Is JavaS... | A major difference between C++ programs and Javascript scripts is that a C++ program typically runs for a much longer time than a Javascript script.<br>
A C++ program with a GUI executes continuously while you are working with the program. A Javascript script on the other hand only executes for a short time to respond... | That's not true at all. The JS exception is not uncaught in the slightest. It's simply caught by the browser. A C++ UI library can trivially produce the same effect by calling the onClick handler inside a try/catch.
The difference in behaviour has nothing to do with language - it's all library.
| https://softwareengineering.stackexchange.com |
484,976 | [
"https://electronics.stackexchange.com/questions/484976",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/244618/"
] | I need 12V for my system and I want to use 18650 cell. Problem is, that everywhere I looked, only boost converters are sold, which only multiply input voltage.
| That is because the edges of the square wave is identical regardless of the rate of when the edges happen. So what happens at the edge does not depend on the frequency of the square wave.
| Here is the logic of solving math problems using the frequency domain:
<ul>
<li>This differential equation stuff is <em>hard</em>. In fact, it's practically impossible, and there's all this <em>housekeeping</em> mixed in. I wish there were a better way!</li>
<li>Oh look, if I'm analyzing a linear, time-invariant sys... | https://electronics.stackexchange.com |
56,045 | [
"https://dba.stackexchange.com/questions/56045",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/30732/"
] | My SQL Server's instance name is <strong>SQLEXPRESS</strong> and SQL Server Service Name looks like <strong>MSSQL$SQLEXPRESS</strong>. Is there any relation between instance name and service name? I'm trying to <strong>check SQL Server Service Status by name</strong> and I wonder can SQL Server Service name be differen... | Yes, the service name is always <code>MSSQL$<Instance Name></code> for a named instance and <code>MSSQLSERVER</code> for a default instance. I don't believe either can be altered or overridden, nor can I think of any reason why you'd want to.
You can enumerate the installed instances on a server via the registr... | Mark showed you a way to get this information directly from the registry, but another way to do this would be through WMI, consumed by PowerShell:
<pre><code>Get-WmiObject -ComputerName "YourDestinationServer" -Namespace "root\microsoft\sqlserver\computermanagement11" -Class "SqlService" |
Where-Object {$_.SQLServ... | https://dba.stackexchange.com |
455,383 | [
"https://physics.stackexchange.com/questions/455383",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/181339/"
] | Why do Spin 1/2 particles when turning them by 360 deg get a phase factor of -1 and a loop of 720 deg leads to the identity while for spin 1 particles a loop of 360 deg gives already the identity?
| It turns out the it's not the rotational group <span class="math-container">$SO(3)$</span> that is important in QM but it's universal cover, which happens to be a double cover and in this context is called the spin group, <span class="math-container">$Spin(3)$</span>.
This is also true for relativistic QM when it's no... | You ask for "why". Well the reason is that the rotation operator in matrix form does that.
For a spinor <span class="math-container">$\left( \begin{array}{} a \\ b \end{array} \right)$</span>, you find that the rotation operator about an axis defined by the unit vector <span class="math-container">$\hat{n}$</span> alo... | https://physics.stackexchange.com |
365,853 | [
"https://softwareengineering.stackexchange.com/questions/365853",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/48380/"
] | I am writing a simulation engine consisting of a number of components, each of which operates on a fixed set of shared buffers.
In practice, the simulation will run entirely on the GPU. When developing a component however, it is easier to copy the buffers from the GPU, execute the component on the CPU, and write the u... | The way I picture your system, based on the given description, is as a set of worker components that read values from zero or more input buffers and write their results to zero or more output buffers. Besides these worker components, there is a management/configuration part that creates the components and buffers and c... | If your goal is to separate the application call from the hardware you are OK. However, if your goal is to work with P/Invoke then you are introducing problems.
This is a case where you might wrap internal representation with an external interface. If you choose to do that, you are doing <strong>Composition</stron... | https://softwareengineering.stackexchange.com |
570,729 | [
"https://physics.stackexchange.com/questions/570729",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/264677/"
] | <blockquote>
Suppose <span class="math-container">$F$</span> is independent of velocity,so Newton's law can be
expressed as : <span class="math-container">$m \ddot{\mathbf{x}}(t)=\mathbf{F}(\mathbf{x}(t)) .$</span>
Then an energy function of the form <span class="math-container">$$ E(\mathbf{x}, \dot{\mathbf{x}})=\frac... | You already have proved the "only if" part. What your derivation shows is that
<span class="math-container">$$\frac{d}{d t}\left(\frac{1}{2} m|\dot{\mathbf{x}}(t)|^{2}+V(\mathbf{x}(t))\right)$$</span>
equals zero only if
<span class="math-container">$$\mathbf{F} = -\nabla V.$$</span>
In other words, your work... | Let look at this example one dimensional
Kinetic Energy is
<span class="math-container">$$T=\frac{m}{2}\,\dot{x}^2$$</span>
and Potential Energy is
<span class="math-container">$$ U=U(x)$$</span>
with Euler Lagrange you get
<span class="math-container">$$m\,\ddot{x}+\frac{\partial}{\partial x}\,U(x)=0$$</span>
thus acc... | https://physics.stackexchange.com |
28,652 | [
"https://electronics.stackexchange.com/questions/28652",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/8139/"
] | I have 53 DIO lines in my circuit. I am designing a multisheet schematic in eagle, and i was thinking about using the "supply" connections as I typically do to connect my supply lines, and a different "supply" symbol with the value and name of the DIO line to connect my DIO pins. However when I do this eagle gives me t... | The DGND and other supply symbols connect everything to which they're connected to the same net. This is helpful with common stuff like ground and power, but it's confusing for other nets. Furthermore, you'd need 53 separate symbols for each of your DIO nets, which would not be readable.
Instead, you should use nam... | First, you should <b><i>always</i></b> make explicit power and ground connections. I know Eagle makes implicit connections for you in some cases, but that is dangerous and relying on that feature is really irresponsible.
Second, what you want is called a "bus" in Eagle. It's a way of grouping a bunch of nets togethe... | https://electronics.stackexchange.com |
343,050 | [
"https://physics.stackexchange.com/questions/343050",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/126543/"
] | What is <strong>a test charge</strong>?
What is <strong>a point charge</strong>?
What is the difference between <strong>a test charge</strong> and <strong>a point charge</strong>?
| Since your second question has been answered in the comments, I will answer your first question.
Let's examine in words what $\Delta U=Q+W$ means: "Any change in internal energy arises from a flow of heat into/out of the system and/or work done by/on the system." Put differently: "The only two ways internal energy can... | The equation of the first law of Thermodynamics does <em>not</em> directly imply the conservation of energy; rather the first law of Thermodynamics is a consequence of the <strong>conservation of energy</strong> when applied to Thermodynamics( systems involving heat, temperature etc.)
The conservation of energy was kn... | https://physics.stackexchange.com |
1,507,526 | [
"https://math.stackexchange.com/questions/1507526",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/170847/"
] | Let $S$ be the portion of the sphere $x^2+y^2+z^2=9$, where $1\leq x^2+y^2\leq4$ and $z\geq0$. Calculate the surface area of $S$
Ok i'm really confused with this one. I know i have to apply the surface area formula but and possibly spherical coordinates but i can't seem how to get the integral out.
The shape. I thoug... | Cylindrical coordinates are the way to go!
Recall that if you have a surface S the surface integral is equal to
\begin{equation}
\int\int f(x,y,z) dS
\end{equation}
Well, you can represent z as a function of x and y.
Also recall that dS stands for the "arc-length" at that point.
Therefore, you can rewrite the integr... | The surface $S$ in question is a spherical zone. Its area can be found by elementary means: If $R$ is the radius of the sphere and $h$ is the $z$-height of the zone then the area $\omega(S)$ is given by $$\omega(S)=2\pi R h\ .$$
As $R=3$ and $h$ is easily computed as $h=\sqrt{9-1}-\sqrt{9-4}$ we obtain $$\omega(S)=6\pi... | https://math.stackexchange.com |
103,695 | [
"https://mathoverflow.net/questions/103695",
"https://mathoverflow.net",
"https://mathoverflow.net/users/22189/"
] | Let me be more precise than the title. (This will be my last attempt to do something with abelian varieties. Sorry for all the basic questions. The answers have been great!)
Let $A$ be a simple abelian variety over a field $k$. Let $g\geq 2$ be the dimension of $A$.
Does there exist an integer $n\geq 1$ such that $A^... | No (I suppose that $k$ is algebraically closed). This is because Poincaré's complete reducibility theorem contains a unicity statement for the intervening factors (up to isogeny). See Mumford, Abelian varieties, p. 173-174.
| In fact, it is no for completely elementary reasons. If $A$ is simple and
$B\subset A^n$ is an abelian variety with $\dim B < g$, then $Hom(B,A^n)=Hom(B,A)^n$ is necessarily zero. So $B=0$.
| https://mathoverflow.net |
114,893 | [
"https://mathoverflow.net/questions/114893",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13441/"
] | A Peano curve is a continuous map $[0,1]\to [0,1]^2$ whose image is the whole square.
I would like to know if on can obtain "holomorphic" Peano curves. Namely, is it possible to find a continuous map $\phi$ from the unit disk $|z|\le 1$ to $\mathbb C^1$ such that
$\phi$ is holomorphic for $|z|<1$ and the image o... | Here it is:
MR0015154
Salem, R.; Zygmund, A.
Lacunary power series and Peano curves.
Duke Math. J. 12, (1945). 569–578.
| Define $$\phi(z):=\frac{1}{2\pi i}\int_{S^1}(\zeta-z)^{-1}\cdot \varphi(\zeta)d\zeta$$
for $|z|<1$, where $\varphi: S^1\to\mathbb{C}$ is a Peano curve (i.e. its image has nonempty interior), and $\phi(z):=\varphi(z)$ for $z\in S^1$. [<strong>Edit</strong>: this construction doesn't work because $\phi$, as I define... | https://mathoverflow.net |
25,779 | [
"https://cstheory.stackexchange.com/questions/25779",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/17410/"
] | A colored graph can be described as tuple $(G,c)$ where $G$ is a graph and $c : V(G) \rightarrow \mathbb{N}$ is the coloring. Two colored graphs $(G,c)$ and $(H,d)$ are said to be isomorphic if there exists an isomorphism $\pi : V(G) \rightarrow V(H)$ such that the coloring is obeyed, i.e. $c(v) = d(\pi(v))$ for all $v... | The problem you describe has definitely been considered (I remember discussing it in grad school, and at the time already it had been discussed long before then), though I can't point to any particular references in the literature. Possibly because it is linearly equivalent to uncolored graph isomorphism, as follows (t... | I read your last comment in the Joshua's correct answer; if you need to transform EQ-GI to colored GI (i.e. you are in trouble with the colors assigned to the equivalence classes) you can use the following reduction:
Suppose that the starting graphs are $G_1 = (V_1, E_1)$, $G_2 = (V_2, E_2)$ and there are $q$ equivale... | https://cstheory.stackexchange.com |
395,159 | [
"https://physics.stackexchange.com/questions/395159",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/6581/"
] | Suppose you given conductors $L_i$ with given geometry in space and the information that the conductor $L_i$ has the total charge $Q_i$ ($i = 1,\dots,n$). Suppose further that there are no additional charge density outside of the $L_i$.
I want to calculate (numerically) the resulting electrostatic surface charge distr... | As we go up in the atmosphere , the number of molecules per unit volume decreases . The quantity of heat per unit volume or the heat density is low . But the translational kinetic energy per molecule is quite large. As the kinetic temperature is the measure of translational kinetic energy, so the kinetic temperature is... | "In the upper part of the atmosphere ... one feels severe cold" - I guess this statement requires some qualification, as this depends on whether one is exposed to sun radiation.
In the upper atmosphere (thermosphere starts at about 85 km), the air density is negligible for most purposes, and I don't think anybody has ... | https://physics.stackexchange.com |
65,672 | [
"https://math.stackexchange.com/questions/65672",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/11976/"
] | I am really sure that if two sets have the same power set, then they are the same set. I just am wondering how does one exactly go about proving/showing this?
I'm usually wrong, so if anyone can show me an example where this fails, I'd like that too.
The homework just asks for true/false, but I'm wanting to show it i... | Suppose <span class="math-container">$A \neq B$</span>. Without loss of generality, there exists an <span class="math-container">$x \in A$</span> such that <span class="math-container">$x \notin B$</span>. Then <span class="math-container">$\{x\} \in \mathscr{P}(A)$</span> whereas <span class="math-container">$\{x\} \n... | To add on William's answer with a positive proof, first one has to note the following observation:
$$A=\bigcup\{B\mid B\subseteq A\}$$
To prove this, the inclusion $A\subseteq\bigcup\{B\mid B\subseteq A\}$ is trivial since $A\subseteq A$, so we take $A$ into the union. In the other direction, since every $B$ in the u... | https://math.stackexchange.com |
488,672 | [
"https://math.stackexchange.com/questions/488672",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/93961/"
] | I am in high school, and we started learning De Moivre's formula. I had some problems with my homework concerning rooting of z. So far, this is what I know about the formula:
<span class="math-container">$\sqrt[n]{z}= \sqrt[n]{r}\left (\cos \left(\dfrac{\phi+2k\pi}{n} \right)+i\sin \left(\dfrac{\phi+2k\pi}{n} \right) ... | You can either argue that since $\;\dim_{\Bbb R}\Bbb R^3=3\;$ then the maximal number of lin. ind. vectors is three and thus your four vectors <strong>must</strong> be lin. dependent, or else do what you did and observe tha the condition $\,a_1=-a_2=-a_3=-a_4\;$ does <strong>not</strong> force all the coefficients to b... | There is always a simple way to show this. Consider the matrix with columns the vectors you mentioned.
<span class="math-container">$A=\begin{pmatrix}
1 & 0 & 0 & 1\\
1& -1 & 1 & 1 \\
2& -2 &3 & 1 \\
\end{pmatrix}$</span> and try to find non-zero solutions in <span ... | https://math.stackexchange.com |
40,806 | [
"https://chemistry.stackexchange.com/questions/40806",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/22961/"
] | I cannot figure out a question on my review sheet. The full question is:
<blockquote>
Methane (<span class="math-container">$\ce{CH4}$</span>) is a gas at room temperature but chloroform (<span class="math-container">$\ce{CH3Cl}$</span>) is a liquid. Explain why changing just one <span class="math-container">$\ce{H}... | Yes, I think that is the right answer expected for this question.
<hr>
<strong>Three factors to consider.</strong>
(1) Most importantly there four intermolecular forces which effect BP
Ionic bonds > Ion-dipole interactions > H bonding > dipole-dipole interactions > Van der Waals dispersion forces.
(2) Increasin... | The answer to predict boiling points of the four substances would indeed be expected to be given as:
<blockquote>
<span class="math-container">$\ce{CH3Cl}$</span> is a dipole. The dipole-dipole interactions are much stronger than the van der Waals interactions present in methane, so it’s boiling point is much higher.
W... | https://chemistry.stackexchange.com |
96,681 | [
"https://physics.stackexchange.com/questions/96681",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/24451/"
] | I do not understand why it's supposed to be vanishing. Rather than discussing the question in its full generality I prefer to consider the following scenario, which I think sums up anything that's actually important for my level and my purpose, but keep in mind the real point of the question.
Consider a system of six ... | The answer is that the antisymmetry of the state implies that the total angular momentum vanishes. Let's start with the simplest example, two spin-1/2 states. We can form a two-particle state with $S_z=0$ as $|1/2\rangle|-1/2\rangle$, or as $|-1/2\rangle|1/2\rangle$, but neither of these has vanishing total angular mom... | I'm not totally understanding the question, but I think the critical aspect here is that in atoms, the energy gap between successive levels is much greater than the "thermal" energy of the electrons. So the energy levels really do have to fill up pairwise, with each pair of electrons forming a singlet state with spin z... | https://physics.stackexchange.com |
176,416 | [
"https://mathoverflow.net/questions/176416",
"https://mathoverflow.net",
"https://mathoverflow.net/users/23772/"
] | Can anyone provide a proof of the equidistribution theorem using Weyl's criterion for the case of $c*a \,\,\, \text{(mod 1)}$ where $c=2^n: \,\,\, \forall n \in N_0$ for irrational algebraic $a$? The original equidistribution theorem is for the case that $c = n: \,\,\, \forall n \in N_0$. Much thanks in advance.
| You are asking whether a number $a$ is a normal number in base 2 or not. This is an extremely complicated problem, and very far from being solved. Generally speaking, there exist several constructions of normal numbers, but we don't have any tool to determine whether a given number is normal or not. It is (sometimes) c... | For the coefficients $2^n$ the equidistribution theorem fails. In fact it is easy to exhibit an irrational $a$ such that the sequence $(2^na)_{n=0}^\infty$ is not even dense in $(0,1)$ modulo $1$. For example, take an $a\in (0,1)$ whose binary expansion consists of increasing blocks of $1$'s seperated by $0$'s:
$$ a=0.... | https://mathoverflow.net |
165,292 | [
"https://security.stackexchange.com/questions/165292",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/153484/"
] | I was using my company's Wifi while I was trying to search inappropriate things. But some pages were blocked. I stopped when I read the block pages saying that "company's name has blocked this site" or something similar. Will this alarm on their computers?
| Yes, all traffic that goes through their internet (and blocks) will be <em>logged</em>.
What will trigger an <em>alarm</em> is something only your IT department can tell you. Every company (and IT dept) is different). In my company, you would have HR approaching you very soon...
| It has been logged because clearly there is a proxy server present.
That doesn't mean it will alarm anything, many companies enforce this kind of blocking just to block the access to inappropriate sites, not to take action against the people who tried to, so in this case the alarms may not be even set because nobody ... | https://security.stackexchange.com |
281,289 | [
"https://mathoverflow.net/questions/281289",
"https://mathoverflow.net",
"https://mathoverflow.net/users/114589/"
] | Let $\phi:{\mathbb{N}}\rightarrow {\mathbb{N}}$ be a bijection. Can we extend the notion of parity (of a finite permutation) to $\phi$ ?
In other words, Can we define a group homomorphism $\Lambda $, between the group of all bijections of $\mathbb{N}$ to the group {1,-1,$\cdot$} such that $\Lambda(\psi)=-1$ if $\ps... | It would be easier, and equivalent, to consider $\mathbb{Z}.$ But I'll stick to $\mathbb{N}.$
Consider $\sigma=(2\ 3)(4\ 5)(6\ 7)\cdots$ (so $0$ and $1$ are fixed points) and $(0\ 1)\sigma.$ They have the same cycle type but should not have the same parity. Note that fixed points and the particular ordering of $\math... | The signature homomorphism, defined on finitely supported permutations, does not extend to the group of all permutations.
To show this, it's enough to write a transposition as a commutator. Namely, call X-element a permutation consisting of infinitely many cycles of each finite length (and no infinite cycle). Then it'... | https://mathoverflow.net |
74,764 | [
"https://softwareengineering.stackexchange.com/questions/74764",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/33/"
] | I am a recent (as of yesterday) college grad - BS in Computer Science. I've been a huge fan of version control ever since I got mad at an assignment I was working on and just started from scratch, wiping out a few hours worth of actually good work. Whoops!
Since then, I've used Bazaar and Git (and SVN when I had to fo... | Whenever I have something that works (meaning, doesn't break anything for anyone else) I'll do a check-in. I write most of my stuff test first, so that means every time I have a new test that passes, I check-in.
In practice that means a few times per hour. At least a couple of times every hour, with 5 being quite a bi... | You shouldn't commit based on a time basis, but on a feature basis. Whenever you add a new feature that's worth committing, commit. You added a working method? Commit. You fixed a typo? Commit. You fixed a file's wrong indentation? Commit. There's nothing wrong committing small changes, as soon as the commit is relevan... | https://softwareengineering.stackexchange.com |
128,176 | [
"https://mathoverflow.net/questions/128176",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9317/"
] | I apologize as this question is not really mathematical, and therefore perhaps not
well-suited for this site. Please feel free to close it if you think it is not. My reason
for asking it here is that I am not satisfied (that is not convinced in any sense)
by many discussions relative to that question I have seen on var... | This question seems a bit vague, but one answer is that there are cryptosystems such as NTRU that are based on (special cases) of the closest vector problem (CVP). At present, quantum computers would not significantly speed up the solution of the CVP. If I understand correctly, they would require doubling the length of... | There is a very good book that you can find your answer there completely. This book's name is:
"Post-Quantum Cryptography" by "Daniel J. Bernstein, Johannes Buchmann and Erik Dahmen".
As a part of this book, today we know that these cryptosystems can be broken by quantum computers:
$1)$ RSA public key encryption
$... | https://mathoverflow.net |
152,322 | [
"https://mathoverflow.net/questions/152322",
"https://mathoverflow.net",
"https://mathoverflow.net/users/33900/"
] | Let $M$ be a $ \mathbb{Z}_{p}[[T]] $-module and $X=Hom(M,\mathbb{Q}_{p}/\mathbb{Z}_{p})$ be the dual of $M$. Let $X[p^n]$ denotes the $p^n$-torsion points of $X$. Is $X/X[p^n]$ the dual of $M[p^n]$ $?$ If not, then whose dual is $X/X[p^n]$ in terms of $M$ $?$
| As @S.Carnahan shows. this is not true.
Perhaps the statement you want is that the dual of $M[p^n]$ is $X/p^nX$?
Take the exact sequence
$$0\to M[p^n] \to M \to M \to M/p^nM \to 0,$$
where the middle map is multiplication by $p^n$, and dualize it.
<strong>Edit:</strong> This also shows that $X/X[p^n]$ is the dual ... | Let $M = \mathbb{Z}_p$ with $T$ acting as $0$. Then (if I'm not missing anything) $X \cong \mathbb{Q}_p/\mathbb{Z}_p$, and $X/X[p^n] \cong X \neq 0$, while $M[p^n] = 0$.
| https://mathoverflow.net |
329,416 | [
"https://softwareengineering.stackexchange.com/questions/329416",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/81299/"
] | Given a list of items, I want to break it up into four groups with as equal length as possible. The items need to stay grouped by the first letter in each item as well.
26 letters / 4 groups would generally cover 6.5 letters in each group. If we had an equal amount of items starting with the same letter in each group ... | Create 4 lists for the results and 26 lists to hold the interim items by initial letter then apply this pseudo-code:
<pre><code>foreach item in masterlist
append item to initial letter list
increment total counter
average bucket size = total/4
iterate letter buckets in order
if current results bucket siz... | Not being given any other requirements and<br>
assuming you want to stick just first letters and<br>
assuming you will stick to a number of groups that is a power of 2:
<ul>
<li>Sort the list alphabetically</li>
<li>Cut it in as close to half as you can</li>
<li>Cut those two pieces in as close to half as you can</li>... | https://softwareengineering.stackexchange.com |
37,993 | [
"https://mathoverflow.net/questions/37993",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9068/"
] | Let P be an arbitrary probability space.
I would like to find a compact topological group $G$ so that the Haar probability measure on $G$ admits a measurable map to the probability space $P$.
By a measurable map, I mean a function which lifts measurable sets to measurable sets of the same measure. That is, $f : Q \l... | It is possible to find the following: A compact abelian group G with Haar measure $\mu_G$, a subset $S\subseteq G$ of full outer Haar measure and a measurable function $f\colon S\to X$ with $\mu_P(E)=\mu_S(f^{-1}(E))$ for measurable $E\subseteq P$. In fact, as you mention, G can be taken to be a large enough product of... | I don't know about an arbitrary probability space, but if $S$ is a Borel space, and $\mu$ is a probability measure on $S$, then there exists a map on $f:((0,1],\lambda)\to S$ whose law is $\mu$. Here $(0,1]$ is the circle group and $\lambda$ the Lebesgue measure. This result follows, for instance, from the existence th... | https://mathoverflow.net |
35,778 | [
"https://physics.stackexchange.com/questions/35778",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/11062/"
] | Both the General & Special Relativity discarded Newtonian mechanics of absoluteness. According to Einstein's view, Time, Mass, Length and Space are interdependent. So, Did Relativity discarded only <em>absoluteness</em> in space and mentioned that all motions are <strong>relative</strong>... What else suffocated in... | With SR, the absoluteness of simultaneity was discarded, i.e., two events may have the same time coordinate in one inertial frame but not in relatively moving others.
In GR, where the geometry of a general spacetime evolves, the very notion of simultaneous is arbitrary. From "Gravitation" by MTW:
<blockquote>
In N... | In short Newtonian mechanics with Galilean relativity allowed that all observer could agree on both
<ul>
<li>The spatial distance $\mathrm{d}r^2 = \mathrm{d}x^2 + \mathrm{d}y^2 + \mathrm{d}z^2$ </li>
<li>The time difference $\mathrm{d}t$ between two events</li>
</ul>
Special relativity holds that neither of these dif... | https://physics.stackexchange.com |
37,961 | [
"https://softwareengineering.stackexchange.com/questions/37961",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | I'm trying to lead a software team that is falling behind. One of the main problems is that whenever something is mildly difficult, I end up having to assign it to myself. I had one other developer with moderate skills and half an intern. Unfortunately, the other developer's skills do not include design.
So I begge... | <blockquote>
<em>Would it have been more reasonable to go help this guy who's been writing C++ for 7 years figure out how to correctly return a reference to an object that isn't destroyed the moment it's returned?</em>
</blockquote>
I gave all my C++ books away several years ago, while swearing that I'd never tou... | This sort of issue is the bread and butter of management. One question all managers need to ask is, "Do my people have the skills needed to do the job?" If the answer is "no", a good manager doesn't scream or quit - a good manager goes about rectifying the situation.
Here's one observation - C++ is not a trivial langu... | https://softwareengineering.stackexchange.com |
59,683 | [
"https://dsp.stackexchange.com/questions/59683",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/43593/"
] | Given a discrete-time finite-support signal x[n]
<span class="math-container">$$x[n] = \left\{ {\begin{array}{*{20}{l}}
{{{( - 1)}^n}n}&{{\rm{ }}n = 1,2,3}\\
0&{{\rm{otherwise}}}
\end{array}} \right.$$</span>
And consider also its periodic repetition is
<span class="math-container">$$y[n] = \sum\nolimits_{k... | ...And now for a differing opinion....
The OP's representation of bandpass white noise as
<span class="math-container">$$n(t) = n_I \cos(2\pi f_ct) - n_Q \sin(2\pi f_ct)\tag{1}$$</span> is inadequate; because each sample path of this noise process is a <em>pure sinusoid</em> of <em>fixed</em> frequency <span class="ma... | <span class="math-container">$$ -\frac{\pi}{2}\le \mathrm{arctan}(x)\le \frac{\pi}{2} \quad x\in (-\infty , \infty) $$</span>
so as asked, no.
Perhaps
<span class="math-container">$$ Y(f)=|H(f)|^2 X(f) $$</span>
where <span class="math-container">$H(f)$</span> is your narrow band filter, would imply that the rando... | https://dsp.stackexchange.com |
1,015,927 | [
"https://math.stackexchange.com/questions/1015927",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/182422/"
] | If we have two solutions to a quadratic equation which are
$L_1=-a+\sqrt{a^2-b^2}$ and $L_2=-a-\sqrt{a^2-b^2}$ and the only fact we are given is that $a,b>0$,
<strong>Is it possible to know if $L_1$ and $L_2$ can be of opposite signs if
$\sqrt{a^2-b^2}>0$?</strong>
We obviously know $L_2$ would be negative b... | Since $L_1 L_2=b^2>0$, they cannot have opposite signs.
| The product is
$$L_1L_2=a^2-(a^2-b^2)=b^2\ .$$
If $L_1$ and $L_2$ are real then their product is positive and one of them is negative, so the other is also negative.
| https://math.stackexchange.com |
524,265 | [
"https://electronics.stackexchange.com/questions/524265",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/201972/"
] | I have read that frequency modulation has the advantage that it can be demodulated non-coherently while phase modulation can only be demodulated coherently.
I don't find any reason to support this statement.
If the frequency variation of a cosinusoid carrier can be found, why can't its phase as a function of time be ob... | The phase of a signal is only defined with respect to a reference. If the reference cannot be communicated, then the phase is meaningless.
Often when phase modulation is used, it's treated as Differential Phase Modulation. It's not the absolute phase of any symbol that's relevant, it's the change of phase since the las... | FM can be demodulated for ex. with a filter which converts frequency variations to amplitude variations. Add a rectifier (=crystal detector) and the demodulator is ready. And it's non-coherent because it's not based on mixing with the carrier.
Phase modulation can be seen also as FM as you can see if you know the math ... | https://electronics.stackexchange.com |
161,360 | [
"https://stats.stackexchange.com/questions/161360",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/54659/"
] | I don't have much experience with data analysis algorithms (data mining, machine learning, if you like) and I'm interested if some could share their experience with practical usage of Silhouette in cluster validation/interpretation.
Concretely, is it practical to use it in case of big data? My question comes from the ... | <blockquote>
I want to produce silhouette I need to calculate 10^8 distances
</blockquote>
So this question is rather about (resources for) computation a big square distance matrix than about Silhouette criterion. Yes you need all the distances to be able to compute silhouette values: this criterion is matrix-based.... | If you are using k-medoids and DTW, you should first compute a distance matrix anyway.
PAM (k-medoids) needs a lot of distance computations; DTW is also fairly expensive. So it really pays off to compute the distance matrix and maybe even store it on disk.
But after that, Silhouette is not very expensive anymore.
| https://stats.stackexchange.com |
190,891 | [
"https://softwareengineering.stackexchange.com/questions/190891",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/84619/"
] | Although Joda is feature rich and more sophisticated than standard Java time, it may not always be the best thing to use. How do I decide if I should use Joda Time or Java Time in any Java code?
Is there some kind of guideline which tells us how to pick the right one depending on our requirements?
| Joda Time is such an improvement over the Java time library that it is almost always the right choice, apart from the following exceptions:
<ol>
<li>When it is difficult or undesirable to add third party dependencies to your project</li>
<li>When its use in a public interface would cause issues, e.g. getting an ORM to... | The Java standard date API is so fundamentally broken that I have often considered simply adding Joda Time to the library extensions of the JVM so that it loaded on the classpath by default with the rest of the Java API.
If you have ever been tasked with retrofitting internationalization and time zones into a legacy J... | https://softwareengineering.stackexchange.com |
525,050 | [
"https://physics.stackexchange.com/questions/525050",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/240914/"
] | I would like to know if an object will fall towards the sun if its horizontal speed is <span class="math-container">$0$</span> at earth's distance.
<span class="math-container">$G =$</span> gravitational constant<br>
<span class="math-container">$m_1 =$</span> mass of object = 70 kg<br>
<span class="math-container">$... | <strong>Yes</strong>, indeed it does.
The astronaut, in this scenario, is above a fixed (I'm going to ignore the Sun's rotation for simplicity) point on the Sun's surface, even if the "height" is profound (150 <em>giga</em>meters) and so begins to fall. For the same reason that if you are placed at a fixed point of he... | Yes, when something goes into orbit it needs to gain a lot of speed, if it doesn't have enough already.
| https://physics.stackexchange.com |
323,068 | [
"https://dba.stackexchange.com/questions/323068",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/158432/"
] | Table definition:
<pre><code> Table "public.transactions"
┌────────────────────────────┬──────────────────────────┬───────────┬──────────┬───────────────────────────────────────────────────────┐
│ Column │ Type │ Coll... | With the following SQL I have managed to get proper running balance for debit and credit of each specific account. Thanks to contributors.
<pre><code>WITH DATA AS ( SELECT transactions_id, transactions_date::date as "Date", transactions_name, account_name(transactions_fromaccount) AS "From account",... | When you have a calculated column in your SELECT, like this:
<pre><code>SELECT
...
some_expression AS "alias",
...
FROM
...
</code></pre>
and you want to re-use its result in that same SELECT, the most generic solution is to rewrite the query as a derived table, so that you can reference the <code>&qu... | https://dba.stackexchange.com |
44,277 | [
"https://dba.stackexchange.com/questions/44277",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/10325/"
] | I upgraded my SQL Server 2008 R2 to SQL Server 2012, and I had noticed a new feature was added: <code>Sequence</code>.
I don't know the reason of adding sequences when there is an <code>identity</code> property.
Can someone elaborate on what this feature is useful for?
| Some examples
A sequence:
<ul>
<li>allows you know the new number before you actually write to the table<br>
Example: how to get the IDENTITY value in a BEFORE TRIGGER</li>
<li>one sequence can be used for more then one table<br>
A.k.a get a value that will be unique across many tables without supertype/subtype</li>
... | <blockquote>
Can someone elaborate on what this feature is useful for?
</blockquote>
Generating sequences, is that not obvious?
Stuff like account numbers, order numbers, order numbers - that may not even be used as identity as in identity column.
| https://dba.stackexchange.com |
44,449 | [
"https://quant.stackexchange.com/questions/44449",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/36637/"
] | I have a formula for intermediate european option price calculated at, say, m-th possible tree value.
<span class="math-container">$S_n^{(m)}$</span> is a price at node after going up <span class="math-container">$n$</span> times and down <span class="math-container">$n - m$</span> times
<span class="math-container">$... | Assuming continuously compounded returns for a multi-period model with <span class="math-container">$N$</span> being the number of periods:
<span class="math-container">\begin{cases}
&\log u \quad \text{with probability q}\\
&\log d \quad \text{with probability 1-q}
\end{cases}</span>
given the stock price at... | I think stuff does not cancel out because there was a mistake in the initial formula, which should instead read:
<span class="math-container">$exp(r \delta t) V(S,t)=pV(uS,t+\delta t)+(1-p)V(dS,t+\delta t)$</span>
Developing the function V to second order Taylor terms:
<span class="math-container">$exp(r \delta t) V... | https://quant.stackexchange.com |
599,523 | [
"https://stats.stackexchange.com/questions/599523",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/68301/"
] | Is there an intuitive way to remember if we get an upper bound or lower bound for a parameter when inverting a one-sided hypothesis test? In Casella & Berger, it is written:
If we have <span class="math-container">$H_0: \mu = \mu_0, H_1: \mu < \mu_0$</span> then "<span class="math-container">$H_1$</span> sp... | The authors are not ambivalent here.
If <span class="math-container">$\mathcal H_1: \mu<\mu_0, $</span> what should the test function look like? It must reject the null hypothesis <span class="math-container">$\mathcal H_0: \mu=\mu_0 $</span> if <span class="math-container">$\bar x$</span> of a certain <span class="... | Recall that a confidence interval collects all hypothesized values for which the corresponding null could not have been rejected given the sample at hand.
So suppose you observe a sample mean of, say, <span class="math-container">$\bar{x}=1$</span> and you test the above null that <span class="math-container">$\mu\geq\... | https://stats.stackexchange.com |
522,533 | [
"https://electronics.stackexchange.com/questions/522533",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/250135/"
] | We have run into a requirement where we need to terminate the charging of our Lithium Polymer battery when the battery temperature exceeds the manufacturer rated temperature.
My immediate reaction is to wire in a thermocouple to the battery pack and run that into the MCU input which would then might toggle some sort of... | If the signal is represented as a voltage <span class="math-container">\$v(t)\$</span> or a current <span class="math-container">\$i(t)\$</span> and it is connected to a (1 ohm) resistor, the power dissipated in the resistor is proportional to <span class="math-container">\$v^2(t)\$</span> or <span class="math-containe... | <span class="math-container">$$ P = \frac{V^2} R $$</span>
If you're driving a constant resistance then the power is proportional to the square of the voltage.
You can rewrite the equation substituting, from Ohm's Law, <span class="math-container">\$ V = IR \$</span>:
<span class="math-container">$$ P = \frac {V^2} R =... | https://electronics.stackexchange.com |
70,028 | [
"https://softwareengineering.stackexchange.com/questions/70028",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/18541/"
] | A couple of months ago I moved to Germany. Taking some projects on my own, I've recently had the opportunity to develop with a company-based framework, that was very well documented, but in German. My German is pretty good, however my programming terminology is somewhat lacking.
Long story short, I was wondering, how... | Personally, I tend to write all variable/function/class names, comments and documentation in English. And no, it's not my native language (Dutch is).
There are several reasons for this:
<ul>
<li>As others have said, English is the de facto <em>lingua franca</em> of programming. If you're working in an international t... | Documentation for programmers or documentation for users?
Anyways, it doesn't matter. Yes in both cases. For users, naturally, in whatever language is required. For programmers, english is <em>lingua franca</em> nowadays, but it still goes.
<em>Why on earth would it be a bad habit? Coming from an english speaking co... | https://softwareengineering.stackexchange.com |
272,378 | [
"https://electronics.stackexchange.com/questions/272378",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/122317/"
] | For a signal with amplitude,
$$V = A\sin (\omega t)$$
any idea at what point the maximum slope (gradient, dv/dt) is? I have gone through the method of differentiating which yields
$$A\omega \cos(\omega t) \tag{i}$$
and then doing a second differential, which yields
$$-A \omega^2 \sin (\omega t) \tag{ii}$$
Equati... | The maximum slope for a sine wave that has no offset and an ampliutde \$A_0\$ occurs exactly during the zero crossings. Its value is simply \$A_0 \omega\$
The derivation is
$$
\frac{d}{dt} A_0 \sin (\omega t) = A_0 \omega \cos(\omega t)
$$
which gives the slope of the sine wave.
The maximum of the cosine is 1. There... | Perhaps I could not understood well, but I think you done a mistake (or two).
The maximum of the <em>slope</em> is where <em>its</em> (of the slope) derivative is 0, then you should take the slope (the first derivative), derive it and put this second derivative equal to zero.
P.S. You also differentiating wrong:
... | https://electronics.stackexchange.com |
40,459 | [
"https://dba.stackexchange.com/questions/40459",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/3698/"
] | We have a process that generates an inventory report. On the client side, the process splits of a configurable number of worker threads to build a chunk of data for the report that corresponds to one store out of many (potentially thousands, typically dozens). Each worker thread calls a web service that executes a st... | Assuming you can isolate the problem to the generation of identity values (try removing that column as a test), what I would recommend is this:
<ol>
<li>Remove the <code>IDENTITY</code> property from the column in the final table.</li>
<li>Generate identity values in each of the #Temporary tables.</li>
<li>When loadin... | (Updated February 2019)
This is an old post, that said I've finally managed to convince Microsoft that the very fact this happens is indeed a defect.
<strong><em>Update:</strong> MS Confirmed the defect and assigned it a bug # of 12628722.</em>
I had seen this post this past November 2018 when we to began to suffer ... | https://dba.stackexchange.com |
12,672 | [
"https://softwareengineering.stackexchange.com/questions/12672",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/2210/"
] | Imagine the following scenario:
You've detected that your (or someone else's) program has a bug - a function produces the wrong result when given a particular input. You examine the code and can't find anything wrong: it just seem to bog out when given this input.
You can now do one of two things: you either examine ... | Time/deadline pressures are one reason.
If you are up against a tight deadline and you've got your boss breathing down your neck (possibly literally!) then doing this and thinking "I'll come back and fix this later" is very tempting and might be the only thing you can do.
Of course the number of times you actually go... | <h1>Time</h1>
Is the #1 reason in my opinion. Although if the problem is codebase wise I might take more time to investigate it. Often my "bandage" fixes involve CSS or UI tweaks. I've written some pretty nasty inline CSS and JavaScript to deal with them quickly. Going back and fixing it is always an option if you get... | https://softwareengineering.stackexchange.com |
84,679 | [
"https://electronics.stackexchange.com/questions/84679",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7523/"
] | <strong>Context</strong>
I'm building a 7kW bidirectional two-stage switching converter. Each stage has its own control board and processor. The entire system runs off a common 24V rail.
<strong>Isolation stage</strong>
Two H-bridges on either side of a transformer, running at 18 kHz, 50% duty cycle, both sides swit... | The H-bridge on the high-voltage side of the isolation stage had a very high slope when the upper transistors were turning off. Adding an RC-series snubber across the windings limited this slope, and moved the problem to where only one processor was resetting, and that at 95% of rated current. Doubling the C (further h... | Congrats on finding a fix. Such intermittent problems are generally challenging.
The root cause could still be conducted EMI, with your snubber reducing the high-frequency generated noise on the buses and thereby fixing the problem.
Consider substantially increasing the filtering on your logic rails (including an LC... | https://electronics.stackexchange.com |
4,564,045 | [
"https://math.stackexchange.com/questions/4564045",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/995106/"
] | The negation of the definition of limit of functions is <span class="math-container">$\exists\epsilon>0\forall\delta>0\exists x\neq a(|x-a|<\delta \text{ and } |f(x)-f(a)|\geq\epsilon)$</span>. How do we use this to show for example that <span class="math-container">$lim_{x\rightarrow 3}x\neq 6$</span> or <spa... | Why is <span class="math-container">$\lim_{x\to 3} x \ne 6$</span>?
As <span class="math-container">$x$</span> gets very very close to <span class="math-container">$3$</span> we do not get very close to <span class="math-container">$6$</span>. We need to find a range were we can <em>always</em> pick an <span class="ma... | So the first limit is <span class="math-container">$lim_{x\rightarrow 3} x=6 $</span> and we need to show that <span class="math-container">$\exists\epsilon>0\forall\delta>0\exists x\neq 3(0<|x-3|<\delta \text{ and } |x-6|\geq\epsilon)$</span>.
Let <span class="math-container">$\epsilon=2$</span>. For <span... | https://math.stackexchange.com |
9,322 | [
"https://mathoverflow.net/questions/9322",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2689/"
] | Is there a definable (in Zermelo Fraenkel set theory with choice) collection of non measurable sets of reals of size continuum? More verbosely: Is there a class A = {x: \phi(x)} such that ZFC proves "A is a collection, of size continuum, consisting of non Lebesgue measurable subsets of reals"?
| (Edit.) With a closer reading of your question, I see that you asked for a very specific notion of definability.
If you allow the family to have size larger than continuum, there is a trivial <b>Yes</b> answer. Namely, let phi(x) be the assertion "x is a non-measurable set of reals". In any model of ZFC, this formula... | The following appears in On definability of non measurable sets, Harvey Friedman, Canadian Journal of Mathematics, Vol. 32, No. 3, 1980.
Let $M$ be the Solovay's model for $ZF + DC + V = L(R) +$ every set of reals is Lebesgue measurable etc. Let $\kappa$ be a regular cardinal of cofinality bigger than $\omega_1$ in $M... | https://mathoverflow.net |
237,596 | [
"https://dba.stackexchange.com/questions/237596",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/29483/"
] | I have a WSFC with SQL Server 2016 Enterprise Edition and 4 Availability Groups. Each server has 1 CPU with 6 cores @ 3.4GHz and 256GB of RAM.
Currently I have one instance on each, they serve 4 Availability Groups with a total of ~300 GB data in 95 databases.
I have the task of migrating more databases (35 databases... | After reading the input from Sean, I decided not to risk bogging down a well working cluster with possibly dire consequences. Since I wasn't sure I could overlook the collation difference, I installed a separate SQL Server on a virtual machine.
| <blockquote>
Each server has 1 CPU with 6 cores @ 3.4GHz and 256GB of RAM.
Currently I have one instance on each, they serve 4 Availability Groups with a total of ~300 GB data in 95 databases.
I have the task of migrating more databases (35 databases, 235 GB data) into this environment [...]
</blockquote>
Considering t... | https://dba.stackexchange.com |
10,715 | [
"https://scicomp.stackexchange.com/questions/10715",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/164/"
] | I have a question which I think should be pretty simple. I have written a subroutine in <code>Fortran</code> which will compute the Gradient at a point of the form
<code>subroutine get_gradient(xyz, Grad)</code>
where <code>xyz</code> is a <code>3x1</code> array and <code>Grad</code> is also a <code>3x1</code> array.... | For your example equation, taking the average approach, the local consistency error
$$
\frac{1}{h^2}[u(x-h) - 2 u(x) + u(x+h)]-f(\frac{1}{2}[u(x-h)+u(x+h)]) = \frac{1}{2}f_uu_{xx}h^2 + hot.
$$
will be of order $2$ (instead of order $3$). ($hot.$ means higher order terms)
Therefore, if your overall approximation is of... | If you look at it from a Galerkin perspective, the right side could also be approximated by
$$\frac16(f(u_{i-1})+4f(u_i)+f(u_{i+1})),$$
the Kepler formula, I believe. This would be valid for first sampling $f(u)$ and then approximating by a piecewise linear function. If the sampled $u$ is approximated piecewise linea... | https://scicomp.stackexchange.com |
689,251 | [
"https://physics.stackexchange.com/questions/689251",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/262541/"
] | When two operators switch have a complete set of simultaneous eigenstates, are the simultaneous eigenstates that are part of this complete set all the simultaneous eigenstates of the two existing operators?
Could there be other simultaneous eigenstates not belonging to this set?
For example, when we're searching for th... | Lets say <span class="math-container">$\psi$</span> denotes the fictional missing eigenstate. We consider 2 cases: (1) <span class="math-container">$\psi$</span> is orthogonal to the complete set of the current eigenfunctions <span class="math-container">$\phi_{i}$</span> and (2) <span class="math-container">$\psi$</sp... | This question can be answered without anything quantum: the set of things that have properties <span class="math-container">$A$</span>, <span class="math-container">$B$</span>, and <span class="math-container">$C$</span> is always contained within the set of things that have properties <span class="math-container">$A$<... | https://physics.stackexchange.com |
29,037 | [
"https://stats.stackexchange.com/questions/29037",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/11508/"
] | I'm working on a word-prediction/spelling-correction software project and I need to calculate the probability that a dictionary word is what the user meant to type, referred to as a "score". I found an article that explains how to score matches using statistical techniques, but I don't understand it 100% (I'm not stats... | Okay they say p-word is is the probability that come about from what is called the likelihood equation. The data is the given prefix. The likelihood is given the prefix the probability that to prefix corresponds to a given word. So for example suppose someone typed yuo. A very likely word would be you since o and u... | After thinking this over I realize the score formula is something like what I guessed and the distance term is not redundant. Let us concern the example of the yuo prefix again. Suppose p(you|yuo)=0.80 and P(your|yuo)=0.15 and P(yours|yuo)=0.05. now conisder another scenario where our data suggest that p(you|yuo)=0.... | https://stats.stackexchange.com |
750,706 | [
"https://math.stackexchange.com/questions/750706",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/92619/"
] | <span class="math-container">$f:\Bbb R \to\Bbb R $</span> is differentiable, <span class="math-container">$f(0)=0$</span> and <span class="math-container">$|f'(x)|\le|f(x)|$</span> for all <span class="math-container">$x$</span> then prove <span class="math-container">$f$</span> is identically zero.
I tried to use mea... | Iterate the estimate. Fix $x = x_0$ with $\lvert x\rvert < 1$, then for every $n \geqslant 1$, there is an $x_n$ (with $0 < \lvert x_n\rvert < \lvert x_{n-1}\rvert$) such that $$\lvert f(x)\rvert \leqslant \lvert x\rvert^n\cdot \lvert f(x_n)\rvert.$$ Deduce $f \equiv 0$ on $(-1,1)$. Use a similar argument to d... | First, I will show that $f$ is identically zero on $[0,1]$.
Suppose that $|f|$ attains a maximum at a point $m$, which is guaranteed by the Extreme Value Theorem. We can assume that $m < 1$, since
$|f(1)| \le |f(c)|$ for some $c \in (0,1)$.
It follows that
$|f(m)| \le m |f(c_m)|$, where $0<c_m < m$.
If ... | https://math.stackexchange.com |
411,970 | [
"https://softwareengineering.stackexchange.com/questions/411970",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/350250/"
] | I need to send a series of floats over a TCP socket.
Firstly, is it safe to assume that most platforms (e.g off the shelf Windows PC/Laptop) and architectures represent floats in the same way (i.e IEEE 754)?
If so, I was thinking of doing something like this:
<pre><code>float a = 29.054;
int* b = reinterpret_cast<in... | Customers generally at least begrudgingly understand if you can't reproduce a bug, especially if you have worked with them and made very visible attempts. What it usually takes to close such bugs is some sort of mitigation.
If it happens again, have you put something in place that will prevent data loss, give you more ... | Respond politely and honestly.
Document your attempts to reproduce the bug. Add logging capabilities if possible. Clean up the code around the bug to the best of your ability.
If this bug ever comes up again, you want to build up a backlog of evidence on how to fix it.
Sometimes you'll fix the bug while working on othe... | https://softwareengineering.stackexchange.com |
190,116 | [
"https://softwareengineering.stackexchange.com/questions/190116",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/73508/"
] | I have come across the following problem many times in various guises in my programming career. As a simple example, consider the following:
Let's say there is a method (B) that could differ depending on customer requirements. This could be for any number of reasons. Common sense tells you that as things are now, you ... | In general, <strong>business logic</strong> tends to be similar by coincidence. On the other hand, <strong>program logic</strong> (meaning the structure and flow of your application) tends to be similar by convention.
If you think about different types of business entities, they're all going to have a <code>fileTaxRet... | <blockquote>
Are there any rules of thumb that can be applied in such cases or does every case have to be taken on its merits?
</blockquote>
There are at least one or two dozen different kind of solutions for that kind of problem, and to choose the "best" one (whatever that means) depends on the details of the speci... | https://softwareengineering.stackexchange.com |
265,549 | [
"https://math.stackexchange.com/questions/265549",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/39770/"
] | $$ \left\{ x \in\mathbb{R}\; \middle\vert\; \tfrac{x}{|x| + 1} < \tfrac{1}{3} \right\}$$
What is the supremum and infimum of this set? I thought the supremum is $\frac{1}{3}$. But can we say that for any set $ x < n$ that $n$ is the supremum of the set? And for the infimum I have no idea at all. Also, let us co... | Let $x$ be negative. then $\dfrac{x}{|x|+1}$ is negative, and in particular $\lt \dfrac{1}{3}$.
So there is no infimum. (But some people allow the symbol $-\infty$ as an infimum.)
For the supremum, note that there are positive $x$ such that $\dfrac{x}{x+1}\lt \dfrac{1}{3}$.
Since $\dfrac{x}{x+1}=1-\dfrac{1}{x+1}$, o... | For $x\geq 0$, the condition $\frac{x}{|x|+1}<1/3$ is equivalent to $x<x/3+1/3$, which in turn is equivalent to $x<1/2$.
So the supremum of your set is $1/2$.
For $x\leq 0$, we have that $\frac{x}{|x|+1}<1/3$ is equivalent to $x<-x/3+1/3$, and then to $4x<1$, which is true for every nonpositive numbe... | https://math.stackexchange.com |
202,525 | [
"https://mathoverflow.net/questions/202525",
"https://mathoverflow.net",
"https://mathoverflow.net/users/62562/"
] | Edit: As David Eppstein points out (in his answer below) the assumption that the graph is non-planar is redundant.
Thank you to everyone who answered/commented.
<hr>
I have a problem about geometric embeddings of graphs for which the case I cannot prove is when the (simple, connected) graph is 4-regular, non-planar... | A random 4-regular graph will have large girth and will, I expect, not be planar. This suggests that that there are a lot of the graphs you want, and they have no particular special properties. Markus Mehringer's program genreg will produce 4-regular graphs quickly and, as $n$ increases. Brendan McKay's geng program ca... | The graph from the page provided by user35593 is indeed non-planar:
<pre><code>sage: g = Graph(':R____```aDaEaFbDbEGbFHcDLcEIJcFGhJOiKMP')
sage: g.order()
19
sage: g.is_regular(4)
True
sage: g.girth()
5
sage: g.is_planar()
False
</code></pre>
| https://mathoverflow.net |
344,807 | [
"https://softwareengineering.stackexchange.com/questions/344807",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/128967/"
] | Given the interfaces that major OSes (Windows, macOS/OS X/Mac OS X, Linux) provide to file systems, can file systems be designed and implemented in a way that is largely independent of OS?
I'm not at all an expert on file systems and I've never implemented one but I am an enthusiastic user of file systems. My naive ex... | I will give you an example that shows that the answer to your question is both "Yes" and "No": <em>FUSE</em>.
FUSE stands for <em>Filesystem in Userspace</em>. FUSE is a Linux kernel filesystem driver that doesn't actually implement a filesystem; instead, it provides an abstraction layer, an API, and an ABI that expor... | Yes, they can, the reason they usually aren't is simply because the people in control of the various OSs often are not interested in making things compatible with other platforms. Linux has drivers for a wide variety of filesystems, including NTFS, and there are ext2/3 drivers for Windows as well.
Microsoft created N... | https://softwareengineering.stackexchange.com |
1,233,806 | [
"https://math.stackexchange.com/questions/1233806",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/140361/"
] | <blockquote>
Let $r,s,t\in\mathbb{Q}$. Prove that
$\mathbb{Q}(r+s\sqrt{t})=\mathbb{Q}(\sqrt{t})$.
</blockquote>
Ok. So I've fallen a little behind in my algebra class, and I'm a bit confused on how to approach this problem. I know that $\mathbb{Q}(\sqrt{t})=\{a+b\sqrt{t}\mid a,b\in\mathbb{Q}\}$. So I'm assuming th... | Suppose $A \subset S$ is complete. To prove that $A$ is closed, it suffices to prove that if $(x_n)$ is a sequence of points of $A$ which converges to $x \in S$, then $x \in A$. So let $x_n$ be such a sequence. Since $x_n$ converges in $S$, it is a Cauchy sequence in $S$. Therefore $(x_n)$ is also a Cauchy sequence in ... | We just need to prove every limit point of <span class="math-container">$Y$</span> is in <span class="math-container">$Y$</span>. Consider any limit point <span class="math-container">$p$</span> of <span class="math-container">$Y$</span>. For every positive integer <span class="math-container">$n$</span>, there is a po... | https://math.stackexchange.com |
3,030,168 | [
"https://math.stackexchange.com/questions/3030168",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/571762/"
] | <blockquote>
Prove that <span class="math-container">$a = d$</span> implies <span class="math-container">$a^b = d^b$</span>, where <span class="math-container">$a, d$</span> are arbitrary
nonnegative integers and <span class="math-container">$b$</span> is any positive integer.
</blockquote>
If I could use division... | You're overthinking it. We proceed by induction on <span class="math-container">$b$</span>. The case <span class="math-container">$b=1$</span> is trivial, so assume it works when <span class="math-container">$b=k$</span>. Then <span class="math-container">$a^{k+1}=a^ka=d^kd=d^{k+1}$</span> completes the inductive step.... | There must be something I don't understand. Are you sure you have asked the question you intended?
The equals sign in the assumption <span class="math-container">$a=d$</span> means that "<span class="math-container">$a$</span>" and "<span class="math-container">$d$</span>" are essentially just different names for the ... | https://math.stackexchange.com |
116,252 | [
"https://math.stackexchange.com/questions/116252",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/22687/"
] | As the topic, how to prove by $\epsilon$-$\delta $ approach $\lim_{(x,y)\rightarrow (0,0)}\frac {x^n-y^n}{|x|+|y|}$ exists for $n\in \mathbb{N}$ and $n>1$
| Let $\epsilon>0$. There is an $\delta>0$ such that $\xi^n\leq \epsilon\xi$ for all $\xi\in[0,\delta)$. Then if $(x,y)\in(-\delta,\delta)\times(-\delta,\delta)$ and $(x,y)\neq0$, we have $$\left|\frac{x^n-y^n}{|x|+|y|}\right|\leq\frac{|x|^n+|y|^n}{|x|+|y|}\leq\frac{\epsilon(|x|+|y|)}{|x|+|y|}=\epsilon.$$ We win.
... | <strong>Hint 2:</strong> Working from what you have (as per your comment on user22705's answer), observe that $$\begin{eqnarray}(|x|+|y|)^2&=&x^2+y^2+2|x||y|\\
&\leq& x^2+y^2+2x^2+2y^2\\
&=&3(x^2+y^2)\end{eqnarray}$$
| https://math.stackexchange.com |
81,905 | [
"https://softwareengineering.stackexchange.com/questions/81905",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/6559/"
] | Some companies selling software or libraries simply put their licensing model on their web page and be done with it. (Many also contain a disclaimer that there are volume discounts and special arrangements possible.)
Other companies (most notably those placing themselves in the "enterprise" market) don't disclose thei... | It's quite simple.
<ol>
<li>It initiates contact between a potential customer and sales.</li>
<li>They can then vary their price as they please based on any criteria you care to mention, without affecting the price expectations of other potential future clients.</li>
</ol>
| They want prospective clients to make contact with sales people. The prices in these cases are so criminally open ended as well that they don't want other customers to know that they gave a STEEP discount to Oracle where they screwed IBM.
Developer aversion to these types of pricing models is typically because it is ... | https://softwareengineering.stackexchange.com |
1,005,168 | [
"https://math.stackexchange.com/questions/1005168",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/140640/"
] | Let $G$ be a group and let $Z(G)$ be the center of $G$.<br>
We know that $Z(G) \unlhd G$, but does that mean that $Z(G)$ is the largest normal subgroup of $G$?
| <blockquote>
I don't know what limits to use.
</blockquote>
Note that $x=w/u$, $y=u$, $z=\sqrt{v}$ with $0\leqslant x,y,z\leqslant1$ hence the domain of integration is $$0\leqslant w/u,u,\sqrt{v}\leqslant1,$$ or, equivalently, $$0\leqslant w\leqslant u\leqslant1,\qquad0\leqslant v\leqslant1.$$
<blockquote>
Find t... | Notice that:
$$f_{WVU}(w,v,u)=|\boldsymbol{J(h)}|f_{XYZ}(h(x,t,z))=|\boldsymbol{J(h)}|f_X\left(\dfrac{w}{u}\right)\chi_{[0,1]}(w)f_Y(u)\chi_{[w,1]}(u)f_Z(\sqrt{v})\chi_{[0,1]}(v).$$
| https://math.stackexchange.com |
62,122 | [
"https://dba.stackexchange.com/questions/62122",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/36417/"
] | <img src="https://i.stack.imgur.com/EOM0x.jpg" alt="enter image description here">
Hi All, During the 11g installation on Win 2012, I am not able to select the available disks which are already stamped using ASM. Any idea what could be the reason? I have tried to select using keyboard space as well but doesn't work ou... | On the first "use" command after login, MySQL scans database, tables and columns name for auto completion. If you have many db, tables it could take a while.
To avoid that, launch your client with the -A option (or --no-auto-rehash)
<pre><code>mysql -uroot -p -A
</code></pre>
You could also add the <strong>disable_a... | In my case, the "Reading table information" was taking an unreasonable amount of time. When I ran <code>mysql -e 'show processlist'</code> I discovered that the process that was "hanging" was "Waiting for table metadata lock". This made some sort of sense as I had a long-running query of the form <code>create table fro... | https://dba.stackexchange.com |
713,548 | [
"https://physics.stackexchange.com/questions/713548",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/323530/"
] | Pretty much what it says in the title.
For example, in the ‘particle in an infinite square potential well’ problem, we represent the wave function using sinusoids. As these are zero valued at the bounds.
However, could we also choose a different waveform? A square wave, for example. Or any waveform that fulfils that cr... | Sinuosoids (and the very closely related exponential function) are eigenfunctions of the derivative operator.
That means if you take the derivative of a sinusoid, the output is another sinusoid of the same frequency.
So if you have an equation that equates sums of derivatives of a function to the function, you are like... | As another answer says, you can use the principles of Fourier decomposition to construct a square wave or any other function you like from a superposition of sinusoids —— or, for that matter, from any other "complete basis" of functions.
However, the physics of the Schrödinger equation is that its eigenvalues... | https://physics.stackexchange.com |
2,719,738 | [
"https://math.stackexchange.com/questions/2719738",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/548198/"
] | Suppose $f$ and $g$ are continuously differentiable functions such that $f(x) = g'(x)$ and $g(x) = f'(x)$ and that any product of $f, f', g$ and $g'$ is commutative for all $x ∈ R$. Show that $ f^2 − g^2 = C $ for some real constant C
I have actually no clue how to solve this, and would be really greatfull for all the... | Define a new function $\gamma(x) = f^2(x) - g^2(x)$, then the derivative is:
$$ \frac{\mathrm{d}\gamma}{\mathrm{d}x} = 2 f(x) \frac{\mathrm{d}f}{\mathrm{d}x} - 2 g(x) \frac{\mathrm{d}g}{\mathrm{d}x} = 2 \Big(\underbrace{\frac{\mathrm{d}g}{\mathrm{d}x}}_{=f(x)}\frac{\mathrm{d}f}{\mathrm{d}x} - \underbrace{\frac{\mathr... | The expected answer was already given but, after studying ordinary differential equations, you will get the following solution:
From the assumptions we conclude that
$$f''=g'=f$$
and thus
\begin{aligned}f&=c_1e^x+c_2e^{-x},\\ g&=f'=c_1e^x-c_2e^{-x}.
\end{aligned}
As a result,
\begin{aligned}f^2-g^2&=(f+g)(... | https://math.stackexchange.com |
243,152 | [
"https://mathoverflow.net/questions/243152",
"https://mathoverflow.net",
"https://mathoverflow.net/users/94407/"
] | Is there an ordered 4-tuple of rational numbers $(a,b,c,d)$ such that $(b,d)\ne(0,0)$ and $2a^2+3b^2+30c^2+45d^2=2$?
The former (deleted) question was just about cases $(a,b,c,d)\ne(1,0,0,0)$ but it was quite silly :( I apologize and I think now it makes sense. I guess there is a canonical proof of nonexistence or an ... | Actually infinitely many, and a parametrization of all rational solutions is e.g.
$a:=\frac{3B^2+30C^2+45D^2-2E^2}{3B^2+30C^2+45D^2+2E^2}$
$b:=\frac{4BE}{3B^2+30C^2+45D^2+2E^2}$
$c:=\frac{4CE}{3B^2+30C^2+45D^2+2E^2}$
$d:=\frac{4DE}{3B^2+30C^2+45D^2+2E^2}$.
| First, one doesn't normally call $(a,b,c,d)$ a "pair" of rational numbers. In any case, first check that your equation has a solution with $(b,d)\ne0$ in $\mathbb R$ (which it clearly does) and in $\mathbb Q_p$ for every $p$. For the latter, it suffices (I think) to check $p=2,3,5$, since your form is non-singular for ... | https://mathoverflow.net |
2,958,643 | [
"https://math.stackexchange.com/questions/2958643",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/19661/"
] | Let
<span class="math-container">$$a_n = \frac{\left(1+\sqrt{4n^2+1}\right)^n+\left(1-\sqrt{4n^2+1}\right)^n}{2^n}=2^{1-n} \sum _{k=0}^{\lfloor n/2\rfloor} \binom{n}{2 k} \left(4 n^2+1\right)^k,$$</span>
then we have
<span class="math-container">$$a_1=1,\quad a_2=9,\quad a_3=28,\quad a_4=577,\quad a_5=3251,\quad a_6=10... | I'll give two approaches: In either case, let
<span class="math-container">$$
b_{m,n}=\left(\dfrac{1+\sqrt{4m+1}}{2}\right)^n+\left(\dfrac{1-\sqrt{4m+1}}{2}\right)^n
$$</span>
thus <span class="math-container">$a_n=b_{n^2,n}$</span>. We will prove <span class="math-container">$b_{m,n}\in\mathbb{Z}$</span> for all <sp... | Fix some integer <span class="math-container">$n$</span> and consider the Galois conjugated algebraic integers
<span class="math-container">$s,t$</span> equal to
<span class="math-container">$$
\frac 12\Big(\ 1\pm\sqrt{4n^2+1}\ \Big)
$$</span>
in the appropiate quadratic field over <span class="math-container">$\Bbb Q$... | https://math.stackexchange.com |
49,886 | [
"https://mechanics.stackexchange.com/questions/49886",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/33887/"
] | Hi I have a 2008 Audi A5 3.2L V6 with about 80k miles. Every once in a while the car wont start. The dash lights work fine along with all the electronic parts of the vehicle. The vehicle doesn't crank at all but the lights come on and when I open the door the dash reads: " Ignition is on ". Its like the car thinks its ... | Follow a logical procedure, going from easiest to hardest/more time consuming thing:
-check for error codes in the ECU
-check if starter motor gets 12V from the solenoid/relais
-check if solenoid gets signal impulse from ECU
As most intermittent problems it usually is something "about to fail" or some sensor/conne... | I have been experiencing a similar situation. Same model and year as OP. No obvious reason for when or why it would occur, no pattern that I could discern, it would just randomly not start whether with the key in the insert position or using the start/stop button. I would have to try multiple times, but after a few att... | https://mechanics.stackexchange.com |
2,930,430 | [
"https://math.stackexchange.com/questions/2930430",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/484902/"
] | I've got a quick question about a proof I saw. The statement was:
<span class="math-container">$$\frac{1}{2} x^T
\begin{bmatrix}1 & 2 \\
2 & 5 \end{bmatrix} x - \frac{3 - \sqrt{8}}{2} x^T x = \frac{1}{2} x^T \begin{bmatrix}\sqrt{8} - 2 & 2 \\
2 & 2 + \sqrt{8} \end{bmatrix} x $$</span>
Now, I see that ... | By definition the principal argument <span class="math-container">$\operatorname{Arg}(z)$</span> in usually defined in the interval <span class="math-container">$(-\pi,\pi]$</span> therefore
<span class="math-container">$$\operatorname{Arg}(8i)=\pi/2$$</span>
If we do not refer to the principal value therefore we ca... | It's <span class="math-container">$\dfrac{\pi}{2}$</span>. Just find the point <span class="math-container">$8i$</span> in the complex plane.
| https://math.stackexchange.com |
171,805 | [
"https://electronics.stackexchange.com/questions/171805",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/65265/"
] | Lets say I have a circuit which involves an OpAmp and a comparator. They're both single supply running from a noisy USB power supply.
Each component has local bypass capacitors, a big and a small one (10µF and 0.1µF, here simplified as one capacitor).
<img src="https://i.stack.imgur.com/xkMlZ.png" alt="enter image de... | The obvious solution is to use a linear Low-Drop Out regulator (LDO) to feed both the Vdd opins on the op-amps and comparitors as well as any reference voltages needed.
You will continue to power your load directly from the Vusb supply but the op-amps & comparitors should be nicely insulated from noise on the USB ... | It's good idea with following consideration (if you are trying it on PCB)
<ol>
<li>Bypass capacitor nearer to VDD/VCC pins.</li>
<li>Ferrite bead (or inductor in your case) nearer to VDD/VCC i.e supply pins.</li>
</ol>
| https://electronics.stackexchange.com |
460,709 | [
"https://electronics.stackexchange.com/questions/460709",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | Hi I'm an electrical engineer but have not seen this problem before. I'mn trying to measure/calculate the resistance of a liquid.
<strong>Background:</strong>
I'm working on an electronic device that can come in contact with a liquid. Unintentional, can be avoided but is not considered a big deal. It's easy to clean ... | Resistivity is measured in (Ω⋅m). But you should think of the single distance measurement as "area over distance". Area over distance is m^2/m, which reduces to m. So resistivity goes up linearly with distance, and down linearly with cross-sectional area.
So if your tap water is 264µS/cm ~= 3800Ω.cm, then there is 380... | Hmm inside a liquid charge don't move as electrons but as ions. The resistance of the liquid changes with change in the applied voltage.What i try to say is that the resistance may not be ohmic.
| https://electronics.stackexchange.com |
2,172,132 | [
"https://math.stackexchange.com/questions/2172132",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/253787/"
] | I don't really understand why the absolute value of a complex number is defined as its magnitude.
The absolute value for a real number, I think has two sensible interpretations: the magnitude of this number from the origin or the positive value of this number.
When extrapolating this to complex numbers, why is the ... | In general, we invent definitions and notation because we intend to make use of them somewhere. For example, the term "absolute value" and the corresponding notation $|-|$ exist because we regularly have occasion to refer to it in e.g. the definitions of variance of a random variable, limit of a sequence, and other con... | "The positive value of the number" is the <em>effect</em> of taking the absolute value of a real number, <em>not the definition of absolute value</em>. The <strong>actual</strong> definition of absolute value is a number's distance from zero. This is why the absolute value of a complex number is a positive real number,... | https://math.stackexchange.com |
101,630 | [
"https://mathoverflow.net/questions/101630",
"https://mathoverflow.net",
"https://mathoverflow.net/users/24978/"
] | Hi Folks,
I just came across a few lines where a (sheaf-)cohomology group of a scheme is treated as a sheaf. I've never seen this in Hartshorne.
Could you give any reference for this?
Thanks
Steven
| I guess you have seen sheaf cohomology as being the right derived functor of the global section functor, taking a sheaf $\mathcal{F}$ on a space $X$ to the abelian group $\Gamma(X,\mathcal{F})$. Suppose $X$ is a $k$-scheme, where $k$ is any field, with structural morphism $f:X\to\mathrm{Spec}(k)$. Then you can consider... | Just as an addition:
In many settings you can think about the higher direct image of sheaves as the $\mathcal{O}_X$-module associated to the cohomology group.
Proposition 8.5 Hartshorne:
Let $X$ be a noetherian scheme, and let $f:X \rightarrow Y$ be a morphism of $X$ to an affine Scheme $Y=Spec\; A$. For any quasi-c... | https://mathoverflow.net |
3,914,423 | [
"https://math.stackexchange.com/questions/3914423",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/794439/"
] | Consider this question:
<blockquote>
In how many ways can <span class="math-container">$5$</span> tourists be placed in <span class="math-container">$3$</span> different hotels, such that there is at least one tourist in each hotel?
</blockquote>
To start working on this, I removed the lower bound on the number of tour... | This is not correct. Without the lower bound you can assign one hotel to one by one the tourists. So, if you line up the tourists in a line and record the hotel you will get: <span class="math-container">$3$</span> possibilities for each one, giving you <span class="math-container">$3\times 3\times \cdots \times 3=3^5.... | The number 150 was very logically solved by Phicar. For fun, I wrote a Python that confirms it.
<pre><code>from random import seed
from random import randint
seed(1)
Number_of_Tourists = 5
Number_of_Hotels = 3
class Permutation():
def __init__(self):
self.make_permutation()
def make_permutation(self):... | https://math.stackexchange.com |
78,265 | [
"https://dba.stackexchange.com/questions/78265",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/33041/"
] | With this command I can generate 16384 random integers between 1 AND 200,000.
<pre><code>SELECT generate_series (1,16384),(random()*200000)::int AS id
</code></pre>
I want to generate 10 sets of such integers. Each set must have an integer identifier, something like that:
<blockquote>
1 | 135
1 | 1023
..... | Would this be what you want?
<pre><code>SELECT
n, generate_series (1,16384), (random()*200000)::int AS id
FROM
generate_series (1,10) AS x(n) ;
</code></pre>
or the similar:
<pre><code>SELECT
n, i, (random()*200000)::int AS id
FROM
generate_series (1,10) AS x(n)
CROSS JOIN
generate_serie... | You can do something like this:
<pre><code>SELECT ((generate_series-1)/16384)::int+1 as series, (random()*200000)::int as rand
from generate_series(1,10*16384);
</code></pre>
This does the sampling with replacement. If it needs to be done without replacement, that is quite a bit hard.
| https://dba.stackexchange.com |
2,757 | [
"https://mathoverflow.net/questions/2757",
"https://mathoverflow.net",
"https://mathoverflow.net/users/317/"
] | For positive integers $n$ and $L$, denote by $SL_n(Z,L)$ the level $L$ congruence subgroup of $SL_n(Z)$, i.e. the kernel of the homomorphism $SL_n(Z)\rightarrow SL_n(Z/LZ)$.
For $n$ at least $3$, it is known that $SL_n(Z,L)$ is normally generated (as a subgroup of $SL_n(Z)$) by Lth powers of elementary matrices. Inde... | Hi Andy,
I don't know if you are still interested in this, but I just found the reference:
MR0049937 (14,250d)
Grosswald, Emil
On the parabolic generators of the principal congruence subgroups of the modular group.
Amer. J. Math. 74, (1952). 435--443.
It is based on the previous work of H.Frasch (1933) who gave an e... | Kulkarni (American J of Math, 113, 6, 1053-1133) gives a method to compute nice fundamental domains for the action of subgroups on $SL_2(\mathbf{Z})$ on the upper half-plane.
"Nice" means that in particular that the subgroup is a free product of the subgroups generated by the edge-pairing transformations. In the case ... | https://mathoverflow.net |
551,757 | [
"https://physics.stackexchange.com/questions/551757",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/127670/"
] | First, an introduction.
Consider the surface of the Earth (whose mass is <span class="math-container">$M$</span>): the geometry of the spacetime nearby can be described to a first approximation by the Schwarzschild Metric.
If we wish to compute the 4-acceleration of an observer which is stationary with respect to the... | <blockquote>
Now, to my question: is there an intuitive way to explain how this result for the acceleration comes about?
</blockquote>
Yes. This was actually Einstein's starting point for general relativity, formulated from the equivalence principle in 1907, which he found by thinking of the twin paradox. The accele... | The general idea that a static observer experiences a proper acceleration is just the equivalence principle, of course. You can easily show this to yourself by downloading an accelerometer app to your phone, and placing it on a table. You will see that the app registers an acceleration of around <span class="math-conta... | https://physics.stackexchange.com |
34,989 | [
"https://physics.stackexchange.com/questions/34989",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/11364/"
] | What could be the most efficient fan blade design? There are three main factors for a good fan: one is speed at which air is circulated; second,the volume of air it can circulate; and the third is providing maximum work for minimum power. Combining these three which would be the most efficient fan blade design.
| Just as the most efficient wings are long, narrow, and run at slow speed, propellers that waste the least energy are long, narrow, and turn at slow speed.
Given all that, the helix angle of the blade (as a function of radius) should be adjusted so that it makes a good angle of attack against the air moving past it. No... | And the cost of the material and manufacture.
Each of this differ depending on the application. The most efficent shape for a wind turbine is not the most efficent for a jet engine.
There is an overall most 'efficient' in terms of maximum amount of energy transferred to/from the air-flow, but it would only be valid f... | https://physics.stackexchange.com |
78,621 | [
"https://mathoverflow.net/questions/78621",
"https://mathoverflow.net",
"https://mathoverflow.net/users/940/"
] | Let $G$ be a complex reductive group, and $K$ a maximal compact subgroup (such that $K_{\mathbb{C}}=G$). By the polar decomposition theorem one has that, as manifolds, $G\cong T^*K$. The inherited symplectic structure is compatible with the complex structure, making $G$ into a Kähler manifold.
On the other hand $G$ ... | Isn't the answer no in the very simplest case? If $K$ is the circle group, then the Kähler structure on the cotangent bundle makes it metrically a cylinder $R \times S^{1}$. I believe this cylinder cannot be isometrically embedded in $C^n$ (apply the maximum modulus principal to the derivative of the map).
| Let me give a simple argument until we think a better answer. Using Peter-Weyl you can choose an embedding of $G \subset \mathbb{A}^n$ such that $K$ is Lagrangian (using real representations for example), since $G = K_\mathbb{C} \simeq T^* K$ you obtain that $K$ is also Lagrangian in this manifold. Now you can use Wein... | https://mathoverflow.net |
224,565 | [
"https://stats.stackexchange.com/questions/224565",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/10117/"
] | In many beginner ML lectures / tutorials, it's advised to remove those features that uniquely identify the example. For example, if predicting user behavior, a numeric <code>user_id</code> column should be removed. The stated reason is that a powerful classifier would use that column to fit perfectly on the training se... | The predictive value of an ID field will vary considerable from dataset to dataset, so in some cases it's probably ok to leave in, and in others not. One case where it could have high predictive value (and should be taken out) is where you're trying to predict the age of something, and the ID is assigned according to a... | "Certainly, any continuous column (with enough resolution) has the power to uniquely identify the example." - that's not true for a predictor that is treated as continuous. For instance, if you generate Y and X at random using uniform distribution, then all of the values of X will most likely be distinct. However, whe... | https://stats.stackexchange.com |
263,082 | [
"https://softwareengineering.stackexchange.com/questions/263082",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/111862/"
] | Working on an ecommerce project whereby a PHP application (back-end & non-customer facing) is currently responsible for processing an order from checkout stage through to generating profit/loss reports, processing the order and also performing various algorithms on behalf of a data science team.
The algorithmic co... | If the front end is made responsible for the 'large payload' for the processing by the Python back-end then you have a high degree of implementation coupling between the two systems that means maintenance, change management, or refactoring becomes more complex as both sides of the communication require significant inte... | I would try to avoid any solution which requires sharing a database between the front end and a back-end service, because my experience is that shared databases cause a lot more coupling that is much harder to detangle than a complex exchange format does.
I presume the data is initially gathered by the front end and t... | https://softwareengineering.stackexchange.com |
4,317,431 | [
"https://math.stackexchange.com/questions/4317431",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/583624/"
] | I have a 3-by-3 matrix,
A=<span class="math-container">$\left [ \begin{matrix}
1 & 2 & 3 \\
1 & 0 & 1 \\
1 & 1 & -1\\
\end{matrix} \right]$</span>
the known terms are (-6, 2, -5), at the right of "=" symbol.
(1) I've calculated the determinant,
(2) I've used Cramer's ... | The determinant of the matrix representing <span class="math-container">$x$</span> is, expanding down the middle column (which you definitely can do, no row operations needed!):
<span class="math-container">$$\det\begin{pmatrix}-6&2&3\\2&0&1\\-5&1&-1\end{pmatrix}=(-2)\cdot\det\begin{pmatrix}2&am... | The determinant of<span class="math-container">$$A_x=\begin{bmatrix}-6&2&3\\2&0&1\\-5&1&-1\end{bmatrix}$$</span>is <span class="math-container">$6$</span>, which is equal to <span class="math-container">$\det(A)$</span>. Therefore, <span class="math-container">$\frac{\det(A_x)}{\det(A)}=1$</span... | https://math.stackexchange.com |
246,527 | [
"https://dba.stackexchange.com/questions/246527",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/188667/"
] | I am intending to do an update (Oracle SQL) for any customer records that includes an ampersand in their name (eg: Joe Bloggs & Co.) to replace this ampersand with the actual word 'and' (eg: Joe Bloggs and Co.).
See script below:
<pre><code>UPDATE acuheader
SET apar_name = REPLACE (apar_name, '&', 'and')
w... | My choice for a test would be a simple <code>LIKE</code>:
<pre><code>SELECT id
FROM acuheader
WHERE apar_name LIKE '%&%'
AND client = 'W5'
AND apar_id = 'x';
</code></pre>
| I don't see a reason to run a costly SELECT statement before the UPDATE.
<pre class="lang-sql prettyprint-override"><code>UPDATE acuheader
SET apar_name = REPLACE (apar_name, '&', 'and')
where client = 'W5'
AND apar_id = 'x'
and instr(apar_name, '&') > 0 --<< only update rows that need it.
</c... | https://dba.stackexchange.com |
4,636 | [
"https://security.stackexchange.com/questions/4636",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/2212/"
] | I have several e-mail accounts configured in Thunderbird. I just wanted to move an e-mail from one of my e-mail accounts [A] Trash folder to another accounts [B] Inbox folder. Because the moved e-mail has been lost, Thunderbird doesn't shows it, but here's the catch: Another email appeared in the Inbox of the [B].
I f... | <strong>Logically deleting is very common</strong> in many application that handle huge amounts of data for performance reasons. This includes other email programs for example Microsoft Outlook and even database servers for example MySQL.
Even <strong>files</strong>, that you delete from your hard disk, are not actual... | There are options related to email deletion in Thunderbird.
It can happen that it is set in your client to only mark the message as deleted, but do not really delete it or not immediately. These are part of the standard IMAP protocoll what you use to connect to gmail.
You should double check how yours are set up.
| https://security.stackexchange.com |
220,993 | [
"https://electronics.stackexchange.com/questions/220993",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/102553/"
] | <br/>
I made a simple LED circuit for a hobby project. It uses a cellphone charger rated at 5V. <br />
There are 2 LED's rated at 700mA at 2.4 V in series.
The calculated resistance for my current limiting resistor is 0.5 Ohm.
This is a very small value, but is this negligible ? <br/>
I did some research on this pr... | It means that you're using a voltage source which is too close to the forward-drop voltage of the LED. The problem is that the values are never exact. You may have a really fresh battery which gives out a bit more voltage or the actual forward-drop of that particular LED may be a bit lower. In this case, you will burn ... | It looks OK, because the voltge dropping will be increasing while the LED's getting to be hot (and this not stabilized current will go lower). Don't forget about heat sinker! But in this case the accuracy of current value is not perfect, but the effeciency is good :)
On the other hand U must be shure, that your phone c... | https://electronics.stackexchange.com |
946,313 | [
"https://math.stackexchange.com/questions/946313",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/74199/"
] | Question: Show that the function $f(x):= x^3 -2x -5$ has a zero $r$ in the interval $I:= [2,2.2]$. If $x_1 :=2$ and if we define the sequence $(x_n)$ using Newton's procedure, show that $|x_{n+1} -r| \le (0.7)|x_n -r|^2$. Show that x_4 is accurate to within six decimal places.
I was able to the do the first and last p... | First note that you have made a slip in the recursion, it should be
$$x_{n+1}=\frac{2x_n^3+5}{3x_n^2-2}\ .$$
This gives
$$|x_{n+1}-r|=\Bigl|\,\frac{2x_n^3+5}{3x_n^2-2}-r\,\Bigr|
=\Bigl|\,\frac{2x_n^3-3rx_n^2+2r+5}{3x_n^2-2}\,\Bigr|\ .$$
Now the numerator can be factorised as
$$(x_n-r)^2(2x_n+r)\ ,$$
where we have use... | $f(x)$ is convex and increasing on the interval $I=[2,2.2]$, hence given that
$$ x_0=2,\quad x_{n+1} = x_n-\frac{f(x_n)}{f'(x_n)}$$
we have that $\{x_n\}_{n\in\mathbb{N}^*}$ is a decreasing sequence that converges towards the only root $\xi$ of $f$ in $I$.
Since in a neighbourhood of $\xi$ we have:
$$ f(x) = (x-\xi)f'(... | https://math.stackexchange.com |
118,177 | [
"https://mathoverflow.net/questions/118177",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1375/"
] | Let $A$ be a subset of ${\mathbb N}$ with positive upper-Banach density, and for each integer $k\geq3$, define $R_k=R_k(A)$ to be the smallest positive integer $r$ such that $A$ contains a length $k$ arithmetic progression
$$
\{a, a+r, a+2r, \dots, a+(k-1)r\}.
$$
Thus, the finiteness of $R_k$ is Szemeredi's theorem. ... | Let
$$
S=\mathbb N\setminus\bigcup_{n\ge 5}\bigcup_k\lbrace 2^n(2k+1),2^n(2k+1)+1,\ldots,2^n(2k+1)+(n-1)\rbrace.
$$
This has positive upper density (in fact positive density), because what you're removing has density $\sum_{n\ge 5}n/2^{n+1}<1$.
If you want to find an arithmetic progression with length $2^{n+1}$, ... | It seems that a nice example is the set $A$ of positive integers which have an even number of 1's in their binary expansion, although I don't see a reasonable lower bound on $R_k(A)$ for now. A quick computation suggests that $R_2(A) = \dots = R_8(A) = 3$, $R_9(A) = R_{10}(A) = 9$, $R_{11}(A) = \dots = R_{20}(A) = 15$,... | https://mathoverflow.net |
152,178 | [
"https://cs.stackexchange.com/questions/152178",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/151357/"
] | <strong>The problem:</strong> in 2d, given a line and an unordered set of <span class="math-container">$N$</span> points with real coordinates, find the intersection between the line and the convex hull of the points.
Clearly, one can explicitly construct the convex hull and find the answer in <span class="math-contain... | What you're asking for reduces to finding the so-called bridges of the convex hull across this line, i.e. the two edges of the convex hull which have one vertex on both sides of the line. Kirkpatrick and Seidel [1] show how to do this in linear time. Their method amounts to using the two dimensional linear programming ... | <del>I think it can be done in O(N).</del>
WLOG, we assume the line is <span class="math-container">$x=0$</span>, and the intersection set is non empty. We can rotate the point set if the line is not <span class="math-container">$x=0$</span>. The intersection check can be done in O(n) so we can make such assumption.
So... | https://cs.stackexchange.com |
473 | [
"https://mathoverflow.net/questions/473",
"https://mathoverflow.net",
"https://mathoverflow.net/users/256/"
] | Maximal Biclique: A complete bipartite subgraph, that isn't a subgraph of another complete bipartite subgraph.
Given a bipartite graph $G=(V_{1}\cup V_{2}, E)$ where $|V_{1}|=|V_{2}|$ with probability $p$ of there being an edge from any $a\in V_{1}$ to any $b\in V_{2}$, what is the expected number of maximal bicliques... | The expected clique number (i.e. size of the maximum clique) in a random graph (all edge probabilities = 1/2) is around 2log_2(n) where n is the number of vertices. You can find the proof in Alon and Spencer's "The Probabilistic Method", chapter 4. My guess is that a similar method would apply in the bipartite case, wi... | One approach might be as follows (I will assume your initial graph had n vertices on each side):
Given a subset S of size s on one side, and a subset T of size t on the other side, what is the probability it is a maximal clique? We need two things to happen.
<ol>
<li>It must be a clique. This occurs with probabilit... | https://mathoverflow.net |
404,630 | [
"https://softwareengineering.stackexchange.com/questions/404630",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/356572/"
] | I'm writing a fairly large piece of logic, during which there are 6 points where things could go wrong and execution should stop after logging the error. The error is also stored in an object.
However, up to now I have been using a <code>public static final String</code> for this error string. As it is only used in a... | Declaring it separately means you can reference it in unit (or integration) tests. If you end up needing to change the contents of the string, you then only have to change it once (where it's defined), rather than making the same change in the other instances of the string.
There can be other benefits to centralizati... | A little late response here, but I'll summarise some of the other comments on autophage's answer and combine them with my own experience. Personally, I would not usually put these in a static constant field, although it largely depends on context. The main reasons for this are outlined as follows:
<h2 id="testing-ykas"... | https://softwareengineering.stackexchange.com |
112,135 | [
"https://datascience.stackexchange.com/questions/112135",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/137405/"
] | I am quite new to this neural network stuff, so please bear with me :)
<strong>TL;DR:</strong>
I want to train a neural network to predict a scalar score from 32 binary features. Training data is expensive to come by, there is a tradeoff between precision and amount of training samples. Which scenario will likely give ... | super-interesting question!
My approach to the problem would be not to do <strong>any preprocessing</strong> on the data. This is, feed all the experiments to the network with the target being the 0/1 variable corresponding to lose/win. For example, if you have a dataset like
<pre><code>| hand of cards | game outpu... | I would say that it's better to have more data, since noise in the data is reduced by the optimization algorithm when optimizing (and therefore cause no problem in the optimization phase), and you can start training your model with this noise fact in mind, and therefore take very heavy precaution on overfitting (checki... | https://datascience.stackexchange.com |
125,398 | [
"https://mathoverflow.net/questions/125398",
"https://mathoverflow.net",
"https://mathoverflow.net/users/37371/"
] | A friend of mine asked me the following question (which is motivated by an image processing problem of which I am unable to say more). Let $(f_n)_{n\geq 0}$ be an orthonormal sequence in $L^2([0,1])$, and define $F_n(x)=\int_0^x f_n(t)dt$. Is it true that $\frac{F_n}{\Vert F_n\Vert_2}\to 0$ weakly in $L^2$? Thanks in ... | No, there is no upper bound. For any $n$, if you take a sufficiently fine mesh on a torus or projective plane, deleting $n$ edges will still result in a graph with a $K_7$ or $K_5$ minor, respectively.
| There are two ways to read this question. (I'll just ignore the projective plane part.)
Zare's reading: Suppose that a graph $G$ embeds in the torus. Is there an upper bound on the number of edge crossings of $G$ when drawn in the plane?
The answer is "no". You can draw $K_7$ in the torus and then take many parall... | https://mathoverflow.net |
214,164 | [
"https://softwareengineering.stackexchange.com/questions/214164",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | I have been writing my website, front-end: html, JS, jquery and css, back-end: php mysql. However my php files only contain php and mysql code. Is this a really bad thing? In what situation should PHP files contain html/javascript?? Currently my php files are just there to receive request and response with array of inf... | I think that it a good practices to separate front-end to back-end.
I am supposing that you are using <em>AJAX</em> to communicate with the back-end, and it is the reason why you are not using HTML/JavaScript in your PHP files. If you have to create a dynamic web page without <em>AJAX</em>, you have to write some HTML... | Three questoins, three answers. YMMV.
<h3>1. Is this a really bad thing? (that you have no HTML or javascript in your PHP)</h3>
No, it isn't. It's just fine to have clear separation of concerns, especially for PHP files meant to be included by other PHP files, or core navigation PHP's.
What would be bad form is i... | https://softwareengineering.stackexchange.com |
161,033 | [
"https://electronics.stackexchange.com/questions/161033",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/70523/"
] | <img src="https://i.stack.imgur.com/vykS9.png" alt="enter image description here">
What pulse should I set to produce a waveform like in the graph?
| u can always try something like this:
PWL(0 0 1.0000ms 5V 1.0001ms 0V 2ms -5V 2.0001ms 0)
basically 0.0001ms rise and fall time
| Break the shape into simpler more realizable sub shapes. Apply the simpler sub shape to a generator. Apply the 2nd sub shape to a 2nd generator. Connect generators in series.
| https://electronics.stackexchange.com |
92,209 | [
"https://mathoverflow.net/questions/92209",
"https://mathoverflow.net",
"https://mathoverflow.net/users/11142/"
] | To check that a subgroup of $SL(n, \mathbb{Z})$ for $n>2$ is profinitely dense, one need only check that it surjects under all the projections mod $m\in \mathbb{Z}$ (which, while in appearance infinite, is usually a finite computation). What about $SL(2, \mathbb{Z})$ is there anything resembling a decision procedure... | This group is virtually free so subgroup separable so a fg subgroup is dense iff it is the whole thing. For non-fg subgroups an algorithm probably doesn't make sense.
| There is an algorithm to check if a subgroup of a free group is dense in the pro-nilpotebnt-topology (not every finitely generated subgroup is pro-nil-closed). It involves finding a rank of a certain matrix modulo arbitrary $p$ which in fact only need a finite number if checks (subgroup is $p$-dense iff the matrix has ... | https://mathoverflow.net |
137,545 | [
"https://electronics.stackexchange.com/questions/137545",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/57758/"
] | <ol>
<li>In a simple battery+resistor circuit with a fixed voltage, the resistance of a series resistor determines the current flowing through it.
But what happens if this resistor is placed between two ICs? (for eg a microcontroller and a motor driver IC - specifically an Arduino and an L293B). </li>
<li>Can the curr... | Many digital inputs are already high impedance, so will only consume in the micro -> milliamps range from a direct connection between the output of a digital device (microcontroller for instance) and the input of another device. Some devices like older transistor (not CMOS style) inputs will consume many times more cur... | By Ohm's law: \$I=\frac{V}{R}\$, the current flow in circuit always determined by the source voltage and the impedance of the circuit. So, even when you put the resistor between two IC, it should obey the Ohm's law. There should one IC used as a "driver" and one IC used as a "receiver", and the "driver" should have out... | https://electronics.stackexchange.com |
1,652,705 | [
"https://math.stackexchange.com/questions/1652705",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/265684/"
] | To start off, I am not looking for the answers to this question, only a how-to. I would like to figure out the solutions myself, but I don't know where to start with this one. The form described was not covered in the lecture and I have not been able to find it by searching, so I am reaching out so that maybe someone... | $e^z=6i$.
Let $z=x+iy$. Note that $e^z=e^x\cdot e^{iy}$
Thus
$$e^z=e^x\cdot e^{iy}=6e^{i\left(\frac{\pi}{2}+2k\pi\right)}$$
So $e^x=6$ and so $x=\ln{6}$.
So $y=\frac{\pi}{2}+2k\pi$
Therefore you have as your solutions $z=\ln{6}+i\left(\frac{\pi}{2}+2k\pi\right)$ for integer $k$.
| Suppose $z=x+iy$ and $x$ and $y$ are real. Then
$$
6i = 6(0 + i) = e^z = e^{x+iy} = e^x e^{iy} = e^x(\cos y + i\sin y).
$$
So $e^x = 6$ and $0+1i=\cos y + i\sin y$. Thus $\cos y=0$ and $\sin y=1$. So $y = \pi/2$ or $\pi/2+ 2\pi n$ for some integer $n$.
| https://math.stackexchange.com |
33,954 | [
"https://chemistry.stackexchange.com/questions/33954",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/17456/"
] | How to represent/ show an ionic bond visually?
For example in NaCl
| <ol>
<li>They're called "reversible" because the processes can run backwards without additional input of energy. There aren't really any truly reversible processes in the universe, though (some come very close, but the construct of "reversible" is an ideal, not a reality).</li>
<li>Entropy of a <em>system</em> can incr... | Second law of thermodynamics tells that:
<blockquote>
Energy tends to disperse from being localized if it is not hindered from doing so.
</blockquote>
Why does a hot cup of tea become cool? Because the higher vibrational energy of the hot mug & tea was localized only to the tea-mug system. When it is brought in... | https://chemistry.stackexchange.com |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.