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452,569 | [
"https://physics.stackexchange.com/questions/452569",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/210967/"
] | All the places that I've seen an answer to this question simply state that it's because there is a stronger gravitational pull on the near side of the moon, facing the earth. But I'm wondering how this gravitational pull actually manages to shift the centre of gravity of the moon, and how does it tie into the idea that... | The near side of the moon experiences more gravity <em>because</em> it is closer to Earth. The force of gravity from the Earth acting on the moon has an inverse relationship to the distance between the two bodies. So the part of the moon that is closer to Earth experiences greater gravity than the far side of the moon.... | A simple way to shoe the difference is to consider two particles of equal mass <span class="math-container">$m$</span> located along the same radius vector at distances <span class="math-container">$r_1$</span> and <span class="math-container">$r_2$</span> from the centre of the Earth.
The position of the centre of ... | https://physics.stackexchange.com |
55,418 | [
"https://chemistry.stackexchange.com/questions/55418",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/23171/"
] | Higher value of <em>a</em> means higher atttraction force between molecules. Attraction force causes the pressure to be less than expected. Now the actual pressure becomes $P + \frac{n^2a}{V^2}$ .
Which means if <em>a</em> increases the neat pressure increases too. But isn't it the other way around?<br>
(I assume here ... | You understand the chemistry: intermolecular attraction forces cause the pressure to be less than expected. The problem here is with the math. Though unintuitive at first sight, a positive $a$ leads to a <em>negative</em> correction to pressure. Let's look at a numerical example.
<blockquote>
Assume that the pressur... | The formula is good because it is correct in most of the regions and the parameters make sense. It is attractive because it both describes behavior of gas and approximate behavior of a liquid.
This formula has a problem in a region that corresponds to phase transition (boiling of a liquid). To account for that region ... | https://chemistry.stackexchange.com |
11,861 | [
"https://electronics.stackexchange.com/questions/11861",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1256/"
] | How do I easily measure how far apart two objects are in EAGLE 5.11.0 Light? Is the easiest way to record the coordinates and subtract?
| Use the <code>mark</code> command or the Mark button:
<img src="https://i.stack.imgur.com/fUixu.png" alt="screenshot of mark button with freehanded red circle!!!1!">
Then click the location you want to measure from. Unfortunately, the mark command doesn't accept coordinates; you have to click the location manually (... | Kevin's answer does not solve all situations and is not precise because the mark cross is aligned to the grid. For some mill layers I use circles or arcs for screws, which are out of grid. The position (managed by property position) can be real number (corners of hexagon for instance). It is difficult to find the dista... | https://electronics.stackexchange.com |
24,071 | [
"https://dsp.stackexchange.com/questions/24071",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/16213/"
] | I have a function with an equation:
$$C = 1.6925\left( e^{-0.136t}-e^{-1.192t}\right) $$
Where $C$ is real and $t$ represents time in hours. Beneath is the representation of my function.
<img src="https://i.stack.imgur.com/sHk7j.jpg" alt="Represents a pharmaceutical drug concentration increase and decay in the body ... | First, since $t>0$ in your case, you can write your function as
\begin{equation}
C(t)=1.6925\left(\exp^{-0.136t}- \exp^{-1.192t} \right) u(t)
\end{equation}
where $u(t)$ is a unit-step function. Then, denote the FT of $C(t)$ as $C(F)$, which is given by
\begin{equation}
C(f)=1.6925\left(\frac{1}{0.136+2\pi jf}- \fr... | How did you arrive at sampling frequency of 1000 Hz? Ideally speaking, you should find the Fourier transform of the given function analytically. This can be done using the FT tables for exponentials. Then you should find the highest frequency beyond which the FT is almost zero i.e less than the smallest number repre... | https://dsp.stackexchange.com |
2,584,857 | [
"https://math.stackexchange.com/questions/2584857",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/517254/"
] | Let $n \in \mathbb{N}$, and assume $n≥1$. Suppose you are at a party with $n$ people (including yourself). At the end of the party, define a person’s parity as <em>odd</em> if they have shaken hands with an odd number of people, and <em>even</em>, if they have shaken hands with an even number of people. Prove that the ... | Find some $\delta\in(0,1/2)$ such that $|f(x)|<\epsilon$ for all $x\in[1-\delta,1]$. Then by choosing $N$ large enough such that $(1-\delta)^{n}<\epsilon$ for all $n\geq N$, then
\begin{align*}
|f_{n}(x)|=|f(x)x^{n}|\leq\max_{x\in[0,1-\delta]}|f(x)x^{n}|+\max_{x\in[1-\delta,1]}|f(x)x^{n}|\leq M(1-\delta)^{n}+\ep... | Take $\varepsilon>0$. Let $M=\max|f|$. Since $f$ is continuous at $1$, there is a $\delta>0$ such that $1-\delta<x\leqslant1\implies\bigl|f(x)\bigr|<\varepsilon$. If $n$ is big enough, then $|x^n|<\frac\varepsilon M$ when $x\in[0,\delta]$. Therefore, if $n$ is big enough, then$$(\forall x\in[0,1]):\bigl|... | https://math.stackexchange.com |
237,090 | [
"https://softwareengineering.stackexchange.com/questions/237090",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/128175/"
] | I'm tasked with changing some procedural Java code into Object Oriented re-usable module. It's an XML generator utility which uses velocity for XML generation. There are also business rule enrichments, all of which is configurable in Database tables. I have already removed huge if-else statements for rules and made the... | Answers to your points:
<blockquote>
How can I be sure that the users of my utility call initialize before they call generateXML? Should I create some Wrapper that internally creates a lightweight object and then initializes it without the user knowing it?
</blockquote>
No. That would essentially be the same thing... | Why not make the whole constructor-building into a class and pass only that class into the constructor? Then you can even abstract it as interface, so the XML generation doesn't even depend on DB and can accept any data.
| https://softwareengineering.stackexchange.com |
55,179 | [
"https://security.stackexchange.com/questions/55179",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/-1/"
] | Are there any known instances of malicious security breeches exploiting the Heartbleed vulnerability? Or is there at present only a known vulnerability, albeit a very serious one?
| Every fix is a business decision. The business needs to make the call. You, as the one with the knowledge, need to properly inform and guide the business through the matrix of needs and costs. Optimally, there are policies and procedures in place to identify and incorporate fixes over time based on cost and priority, b... | One big problem about fixing something when being told not to do so is that you might be wrong in some point:
<ul>
<li>perhaps it's not a real bug / hole;</li>
<li>perhaps it is but some other layer of the application prevents it from leaking</li>
<li>perhaps it is a bug, it might lead to leaks, but your app isn't in ... | https://security.stackexchange.com |
583,299 | [
"https://physics.stackexchange.com/questions/583299",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/220004/"
] | I'm pretty sure that, if all of a sudden gravity just disappeared (someone just set <span class="math-container">$G=0$</span> by turning a magical knob) we would notice immediately, starting to float in the air and a bunch of other things. Same thing if <span class="math-container">$\alpha =0$</span>, I guess contact f... | I'm assuming you just want a general idea - I'll leave others to describe changes to the CKM matrix and Majorana equation...
If the strong force were to disappear, as Vadim hints, atomic nuclei would fall apart, since that force holds the neutrons and protons together. In fact, it would be worse than that; the strong f... | The neutrino is unaffected by strong or electromagnetic forces. So if these forces were “turned off” for all matter we can predict it would behave like a cloud of neutrinos with mass. All atoms would immediately break apart with a release of huge amounts of binding energy and you would simply be left with galaxy-sized ... | https://physics.stackexchange.com |
611,642 | [
"https://physics.stackexchange.com/questions/611642",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/285636/"
] | I just started to learn general theory of relativity by Hartle's gravity textbook. In a section on gravitational wave I encountered following statement 'Gravitational waves are hard to detect due to weak coupling of matter' and refers to this equation <span class="math-container">$$\frac{F_{grav}}{F_{elec}}\approx10^{-... | First, gravitational waves that we do have available for observations are, thankfully, not that much intense. Their sources are rather powerful (like, radiating few solar masses for half a second for a stellar black hole binary), but they are also far away and the inverse squares law kicks in pretty well. A billion lig... | I can try to tell you why gravitational waves are (experimentally) hard to detect.
If you want to detect them, you do so nowadays in Laser Physics experiments (e. g. at LIGO in the US or at Virgo in Europe). For this, huge mirrors are used. If know gravitational waves are in the interferometers, the amount by which the... | https://physics.stackexchange.com |
126,627 | [
"https://softwareengineering.stackexchange.com/questions/126627",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/36834/"
] | For the project my team and me are working on we often find that we need large pieces of scaffolding code. Creating domain objects with correct values, setting up mocks for repositories, dealing with the cache,... are all things that occur commonly throughout the tests. A lof of times we're working with the same basic ... | All the possibilities summed up in the answers:
<strong>Use the Builder pattern</strong> (Bedwyr Humphreys, DXM and Pascal Mestdach)
Advantages:
<ul>
<li>No code duplication in tests</li>
<li>Can combine different builders for complex tests</li>
<li>Clean interface</li>
<li>Big object graphs from builders can influe... | Setting up for all tests can be a good idea, particularly if you do a deploy. Instead of using mocks we create, deploy and populate a test database and then point the test at the instance.
Not exactly the way you should do it as per the manual, but it works, even more so for us because we use our deployment code to do ... | https://softwareengineering.stackexchange.com |
317,459 | [
"https://dba.stackexchange.com/questions/317459",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/260704/"
] | I have a database with the following tables: <code>items</code>, <code>categories</code>, and <code>category_items</code>. The (simplified, fields omitted) schema is as follows:
<pre><code>CREATE TABLE IF NOT EXISTS items (
id SERIAL primary key not null,
partNo text unique not null
);
CREATE TABLE IF NOT EXIS... | There are two/three problems with the design of the 3rd table:
<pre><code>CREATE TABLE IF NOT EXISTS category_items (
category_id SERIAL PRIMARY KEY,
partno TEXT NOT NULL,
FOREIGN KEY (partno) REFERENCES items(partno),
FOREIGN KEY (category_id) REFERENCES categories(id)
);
</code></pre>
<ul>
<li><code>c... | I have figured it's a quite simple fix, I am just feeling a bit silly for missing it. Since in <code>category_items</code>, <code>category_id</code> is the PRIMARY KEY, it will default to being UNIQUE. I need a separate ID for <code>category_items</code> like so:
<pre><code>CREATE TABLE IF NOT EXISTS category_items (
... | https://dba.stackexchange.com |
141,459 | [
"https://cs.stackexchange.com/questions/141459",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/138758/"
] | There is a problem that I am working on. I have shown that the problem is NP Hard, but I haven't been able to show that it is in NP. But the problem is also known to be in EXP. My gut feeling is that the problem is PSPACE-complete. I am leaving aside PSPACE-hardness for now. Even if I have to prove that the problem is ... | It's OK for the certificate to be exponentially long only if (1) the space consumption of the verifier is polynomial in the size of the problem instance (it is <em>not</em> allowed to use space polynomial in the size of the certificate) and (2) the verifier only accesses the certificate in a read-once fashion: once it ... | Lets say you have some certificate of length <span class="math-container">$s>>poly(n)$</span>, and you are only allowed to store at most <span class="math-container">$poly(n)$</span> memory. Assuming you are capable of verifying "chunks" from the certificate of size <span class="math-container">$poly(n... | https://cs.stackexchange.com |
392,017 | [
"https://softwareengineering.stackexchange.com/questions/392017",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/321831/"
] | I'm currently taking over a project that has a common pattern of interfaces like this:
<pre><code>public interface EmailService {
void sendInvitationEmail(Payload payload);
void sendNotificationEmailToAdmin(Payload payload);
void sendPasswordResetEmailToUser(User user);
void sendValidationEmailToNewUser(User u... | I'd be inclined to split the responsibilities into two: creating and sending emails, loosely coupled with an <code>Email</code> interface.
Then the <code>EmailService</code> takes the simple form you intuitively want and the implementation is only dependent on the transportation infrastructure.
<pre><code>public inte... | In my opinion is the EmailService implementation is way to broad, it will be a great idea to split it into more specific implementations (like you did). the interface-segregation principle states:
<blockquote>
ISP splits interfaces that are very large into smaller and more
specific ones so that clients will only... | https://softwareengineering.stackexchange.com |
24,464 | [
"https://softwareengineering.stackexchange.com/questions/24464",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/6987/"
] | My question here is relative to jobs for programmers.
Why does employer still contract programmers if today we have a lot of good commercial system avaliable on the market?
I want to be very clear at this point, this question is relative only to a system, more specially to ERP systems. Maybe this question looks a li... | Do you realize how expensive some of those higher-end commercial systems can cost to buy in the first place? If companies are spending hundreds of thousands if not millions of dollars, don't you think they would want someone to help them get the most out of this big purchase?
Paying for the customization is why the c... | <h2>Off the Shelf Vs. Custom</h2>
Having been partially involved on a complex ERP project I would say its simple:
<strong>Off the shelf</strong>
Prositive:
<ul>
<li>Maybe Cheaper Initially.</li>
<li>Well tested, stable.</li>
<li>Excellent documentation.</li>
</ul>
Negative:
<ul>
<li>Generic functionality.</li>
<... | https://softwareengineering.stackexchange.com |
72,664 | [
"https://physics.stackexchange.com/questions/72664",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/27546/"
] | Is there a proof that time is a 4th dimension?
If it is, then why not measure it in units of the previous three?
Logical right?
How many seconds is a temporal meter?
| Sure, it'd be $1/c$ seconds, which is exactly $1/299792458\text{ s}$. Although, really, there's no point because time is defined as a multiple of $c$, anyways.
As for proof that time is the fourth dimension, there's no 'proof' like any scientific theory (there's just evidence) and unlike mathematics, but one fairly la... | <blockquote>
How many seconds is a temporal meter?
</blockquote>
Approximately 3.33564095 nanoseconds
| https://physics.stackexchange.com |
345,077 | [
"https://electronics.stackexchange.com/questions/345077",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/171933/"
] | I need to specify the construction of a 4-layer PCB with transmission lines on the outer layers and planes on the inner layers. I need to control impedance and propagation speed. The target prepreg thickness is around 0.2mm (7-8mil). I can achieve that with a single ply of 7628 or with two plies of 2113 or 1080.
Most ... | <blockquote>
What are the advantages and disadvantages of one versus two plies?
</blockquote>
For controlled impedance, you get the best performance with zero plies. That is, if you are concerned about a repeatable RF performance between certain layers in a multilayer PCB layup, you should arrange for the impedance ... | Having spoken to PCB manufacturers here in the US and one in Europe specifically about this issue, I learned the following:
<ol>
<li>PCB manufacturers control the final thickness of the finished boards as well as the dielectric layers formed using prepreg compression and resin flow. The finished thickness is important... | https://electronics.stackexchange.com |
140,530 | [
"https://electronics.stackexchange.com/questions/140530",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/30449/"
] | Ohmmeters don't appear to make LEDs conduct which gives overestimates in the resistance measured (tested with a R1//(R2+LED) parallel circuit). So what is the voltage they apply to the circuit, assuming it is conventional? I assume it depends on the range selected (I seriously doubt it will apply 1V to a mOhm branch), ... | If it's a DVM I'd think along these lines: -
Smallest resolution in ohms is probably 0.1 ohms and smallest resolution in volts might be 1mV. This leads to the conclusion that the current used in the lowest ohm range is probably: -
\$\dfrac{1mV}{0.1\Omega}\$ = 10mA.
Given that the lowest ohm range will probably go-ov... | The obvious answer is to measure it with another meter.
Other than that, this can vary by meter but is usually around a volt or two. By default, most meters put out enough voltage to turn on ordinary silicon diodes. Some have a special low voltage mode meant to specifically avoid turning on silicon diodes, but the a... | https://electronics.stackexchange.com |
130,929 | [
"https://softwareengineering.stackexchange.com/questions/130929",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/830/"
] | We just deployed a large software that affects the way the user work-day looks like in many aspects. It changes a lot of things in the way they interact between eachothers.
The developers of the team are taking rounds and spending one day at the customer's site to understand better what is a typical day for our user... | What not to do:
<ul>
<li>Forget to tell those you are observing who you are and why you are
there. They will assume you are there for some bad reason like
determining if they should get fired if you don't explain.</li>
<li>Tell jokes. You don't know their corporate culture and what is
appropriate in the IT world is of... | I would shadow the user throughout their day. Sitting with the user and observing how they use the system and what their workflow really is. Ask questions about any aspect of their process that you don't understand by observing. Its a good way to learn what users are really doing.
| https://softwareengineering.stackexchange.com |
709,508 | [
"https://physics.stackexchange.com/questions/709508",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/157259/"
] | I have always presumed that gravity was 100% curvature. But, after thinking a bit I found a contradiction of understanding.
If gravity is only curvature, then all particles should behave as light does, and flow along the lines of curvature. However, light is massless and the expectation is that <em>even when light is... | <blockquote>
So the question is: what is, at a high, non-symbolic, conceptual level, Gravity in terms of components:
Curvature (applies to massive and massless objects)
??? (Force) applies to massive objects
And, finally, why should the (Curvature) and the (??? Force) be considered the same thing and not something co-i... | The spatial part of the trajectory is sharply curved, but the trajectory in spacetime is much less.
If you throw a rock and it takes one second to rise and hit the ground, the parabola is sharply curved. The distance it travels is a few meters and the maximum height is a meter or so.
If you include time, the separation... | https://physics.stackexchange.com |
380,513 | [
"https://mathoverflow.net/questions/380513",
"https://mathoverflow.net",
"https://mathoverflow.net/users/53155/"
] | Let <span class="math-container">$E$</span> be a Banach space. Let <span class="math-container">$F$</span> be the collection of all <span class="math-container">$f\in E^*$</span> such that <span class="math-container">$\left<f,e_n\right>\to 0$</span>, for every normalized basic sequence <span class="math-containe... | The answer is negative in every non reflexive space. If <span class="math-container">$X$</span> is non reflexive, there is a normalized basic sequence <span class="math-container">$(z_n)$</span> in X s.t. <span class="math-container">$(z_1 - z_n)_{n=2}^\infty$</span> and <span class="math-container">$(z_1 + z_n)_{n=2}^... | This answer is supplementary to the one of Bill Johnson, to fill in some details.
A sequence <span class="math-container">$\{e_n\}$</span> in a Banach space <span class="math-container">$E$</span> is called a basic sequence of type P* if (among other equivalent definitions) <span class="math-container">$0<\inf\|e_n... | https://mathoverflow.net |
51,275 | [
"https://electronics.stackexchange.com/questions/51275",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | So I'm reading "Elements of Computing Systems" trying to really understand how everything works underneath (Any other book/article suggestions that would help would be amazing) Since eventually I want to implement this basic stuff on a breadboard and maybe someday get a 4-bit computer or something similar going (but th... | There are flip-flops and there are flip-flops.
The RTL (resistor-transistor logic) schematic you show is a simple bistable multivibrator that is either set or reset by pulses on the E1 and E2 inputs. For exmaple, pulsing E1 high will cause A1 to go low and A2 to go high.
"Elements of Computing Systems" is talking abo... | Think of the "t' above as the clock NUMBER. i.e. after 3,453 clocks the output will be in a "1" state. so therefore 't+1" = clock number 3454.
That statement for the output basically says the output after a given clock is the same as what was presented on the input after the previous clock.
It's a confusing mix up ... | https://electronics.stackexchange.com |
574,396 | [
"https://electronics.stackexchange.com/questions/574396",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/52303/"
] | I have an old PCB with an edge connector and I am looking for a way to create a socket for it. I have a 3D printer so the housing is not an issue but where I am stuck is the contacts.
The edge connector has 25 fingers. Each finger is 3mm wide and 6mm long. The finger spacing is 5mm. The fingers are on both sides of the... | <h2>Large-Scale Result</h2>
Assuming you already know the value for the current in <span class="math-container">\$R_{_\text{E}}\$</span> (which, by the way, you do <em><strong>not</strong></em>) and also assuming the BJTs are matched (and in a simulator they probably <em><strong>are</strong></em>) then the collector vo... | The approximate one-sided (unsymmetric) gain is <strong>Au=0.5(gm*Rc)</strong>, assuming input at the most left (T1) and output at the most right transistor (T2).
For collector currents of 50µA the transconductance is <strong>gm=50µA/26mV=1.92 mA/V.</strong>
Hence the gain is <strong>Au=0.5(1.92*100)=96</strong> and th... | https://electronics.stackexchange.com |
334,264 | [
"https://physics.stackexchange.com/questions/334264",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/156653/"
] | In a system where a cylinder is erect and partly submerged (Floating and in Equilibrium) in water does the density of air change the ratio of the cylinder submerged.
A broader question does buoyant force always equal the weight of fluid dispersed.
| The integral form of Faraday's law says that $\oint_C {\bf E} \cdot d{\bf l} = -\frac{d\Phi}{dt}$, where $\Phi$ is the magnetic flux through an open surface bounded by the curve $C$. Let the surface be a cross-section of the cylinder parallel to the end caps. A superconductor is a perfect conductor so it cannot conta... | The cylinder is a perfect conductor.
Lenz's law says that when there is a change of flux inside a coil, this will set up an e.m.f. to resist that change. But the moment an e.m.f. is generated, this will create a current in the coil that resists the change in flux.
When the resistance is zero, any change in the flux w... | https://physics.stackexchange.com |
779 | [
"https://mechanics.stackexchange.com/questions/779",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/489/"
] | I have a standard click torque wrench. I was told I should set it to zero when not using it in order to keep the accuracy high. Is this true?
Secondly, I have not been doing this since I purchased the wrench a few years ago, how much of a problem is that?
| Yes you should store it at zero, it weakens the spring. I would have it checked/calibrated to make sure it is still accurate.
| My Craftsman torque wrench cannot be put back in the box unless it's at 20%. Granted, the plural (or even singular) of anecdote is not data, but I have always heard 20-25% of the max torque it's rated for.
| https://mechanics.stackexchange.com |
367,866 | [
"https://physics.stackexchange.com/questions/367866",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | Streamlines by definition are field lines corresponding to the velocity field.
when bringing the equation of streamlines we apply the condition that says that the velocity is collinear with the streamline.
what defines the streamline from the first place? Isn't it the velocity field? I mean the velocity field alone h... | A streamline is the path of one particle. Yes, it is defined by the velocity field, which essentially just a description of the motion (velocities) of <em>all</em> particles at <em>all</em> points. Pick one of those particles and follow it from start to end, and you have a streamline.
Streamlines are nothing but a vis... | The value of using the stream function is that it reduces the number of dependent variables you have to deal with (the two velocity components) to one, while, at the same time reducing the number of equations required by one (eliminating the continuity equation). I would say that's a pretty big advantage.
| https://physics.stackexchange.com |
670,841 | [
"https://physics.stackexchange.com/questions/670841",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/292877/"
] | From special relativity we know that,<br>
<span class="math-container">$$ m = \frac{m_0}{\sqrt {1-\frac {v^2}{c^2}}} $$</span>
where,
<span class="math-container">$m$</span>, <span class="math-container">$m_{0}$</span> and <span class="math-container">$v$</span> are the relativistic mass, rest mass of the object and sp... | The point of relativity is that all inertial frames are equivalent, which means that the mass of an object does not increase in its own rest frame. Suppose C was moving at almost the speed of light compared with A. When C fires its engines, it hardly seems to accelerate at all from A's perspective, in spite of the huge... | The resolution to your apparent contradiction may be along these lines, the mathematical details are likely to be quite complicated.
when viewed from <span class="math-container">$A$</span>s reference frame, the distance between the spaceships increases. Without any effects from relativity it would be <span class="math... | https://physics.stackexchange.com |
86,270 | [
"https://cs.stackexchange.com/questions/86270",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/80805/"
] | i have read about data hazards and then came across that mips architecture doesn't allow WAR AND WAW hazards can someone please help me understand it? the reason is not given in the book the MIPS pipeline is divided into :
1.IF(instruction fetch) 2.ID(decode the instruction) 3.EX(execute instruction) 4.MEM(write or re... | <blockquote>
in case I2 Takes less number of clock cycles than I1 for completion then can I2 access the register file going to WB phase directly in case it has nothing to do in the phase of MEM will this give rise to a hazard?
</blockquote>
I2 reads the register R1 at its ID phase. Therefore, if implemented directly... | The actually executed codes are:
<pre><code>lw $R1, 0($R2)
nop
add $R1, $R2, $R3
</code></pre>
Therefore the space diagram should be:
<pre><code>|IF |ID |EX |MEM|WB | | |
| | |IF |ID |EX |MEM|WB |
</code></pre>
With forwarding from MEM of I1 to EX of I2, the hazard would be eliminated
| https://cs.stackexchange.com |
43,439 | [
"https://datascience.stackexchange.com/questions/43439",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/65273/"
] | I am searching for a way to create a new column in my data. I have tried using iterows() but found it extremely time consuming in my dataset containing 40 lakh rows. So here is what I want.
Consider I have 2 columns:
Event ID, TeamID ,I want to find the no. of unique TeamID under each EventID as a new column. In other ... | You can try something like this to get a new dataframe that has pairs of (EventID, TeamCount):
<pre><code>event_id_team_count = data.groupby('EventID').agg({'TeamID': lambda x: x.nunique()})
event_id_team_count.rename(columns={"TeamID": "TeamCount"}, inplace=True)
</code></pre>
If you want to have this new column in ... | <ol>
<li>Create a dictionary with the unique count of TeamID with respective to EventID</li>
</ol>
<pre><code>uCountDict = dict(data.groupby("EventID").TeamID.count())
uCountDict
</code></pre>
Sample output
{'A': 4,
'C': 3,
'D': 2,
'F': 1
}
<ol start="2">
<li>Now create a new column with unique count with respect... | https://datascience.stackexchange.com |
193,022 | [
"https://physics.stackexchange.com/questions/193022",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/14087/"
] | How can we construct the Pauli matrices starting from $$\sigma_i=\begin{bmatrix}
a & b\\
c& d
\end{bmatrix}$$ by using the conditions $$\sigma^2_i=1,$$$$\left [ \sigma_x,\sigma_y \right ]=2i\sigma_z,$$ and so on?
| Since each $\sigma_i$ is a scalar multiple of a Lie bracket of other finite matrices, each $\sigma_i$ must be traceless. So straight away we know:
$$\sigma_i=\left(\begin{array}{cc}a&b\\c&-a\end{array}\right)\tag{1}$$
and $\sigma_i^2=\mathrm{id}$ then yields $a^2 + b\,c=1$.
The eigenvalues of any matrix of t... | <strong>SECTION A :</strong> <em>Angular Momentum in Quantum Mechanics - The minimum non-zero case $\:j=1/2\:$</em>
The angular momentum in Quantum Mechanics has the following properties :
<hr>
<strong>THEOREM :</strong>
The components of the dimensionless orbital angular momentum of a particle $\:\mathbf{L}=\ma... | https://physics.stackexchange.com |
212,876 | [
"https://stats.stackexchange.com/questions/212876",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/115814/"
] | I work at a call center in a department where we receive two grades of calls: A and B. 15% of our calls are grade A, and 85% are grade B. Only two people work in my specific department, me and my co-worker Dale.
The call center directs calls such that one call is sent to me, the next call is sent to Dale, the call aft... | Yes, based on the information provided, you can think of your calls as independent from Dale's calls. Just think- say you just got an A call. Now the phone is ringing and it is Dale's turn. How does the fact that you just got an A call give you any information about whether the call on Dale's line is A or B? It doesn't... | There's two interpretations for this. The first is that each call is truly random, in that there's a 15% chance you get an $A$ call and 85% chance you get a B call. In this case the calls you recieve are independent from Dave's in that if you condition on the number of $A$'s Dale recieved, this still doesn't change the... | https://stats.stackexchange.com |
599,255 | [
"https://physics.stackexchange.com/questions/599255",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/276140/"
] | I was trying to prove that the Ricci scalar <span class="math-container">$R$</span> is not invariant under conformal transformations and when we talk about conformal transformations we have the relation:
<span class="math-container">$$ \hat g_{\mu\nu} = \Omega(x) \eta_{\mu\nu}$$</span>
Is this always the case or can we... | The presence of Minkowski metric tensor <span class="math-container">$ \eta_{\mu \nu}$</span> means, that you are considering the particular class of the metrics, related to the <span class="math-container">$\eta_{\mu \nu}$</span> by conformal factor <span class="math-container">$\Omega(x)$</span>. In general case, one... | The metric <span class="math-container">$\eta_{\mu\nu}$</span> is just one flat metric, if you use spherical coordinates <span class="math-container">$(u^0,u^1,u^2,u^3) = (t,r,\theta,\phi)$</span> in Minkowski space you have:
<span class="math-container">$$\text{d}s^2 = \hat{g}_{\mu\nu} \text{d}u^\mu \text{d}u^\nu = -\... | https://physics.stackexchange.com |
96 | [
"https://ai.stackexchange.com/questions/96",
"https://ai.stackexchange.com",
"https://ai.stackexchange.com/users/5/"
] | What is the definition of a deep neural network? Why are they so popular or important?
| A deep neural network (DNN) is nothing but a neural network which has multiple layers, where <em>multiple</em> can be subjective.
IMHO, any network which has 6 or 7 or more layers is considered deep. So, the above would form a very basic definition of a deep network.
| Deep networks have two main differences with 'normal' networks.
The first is that computational power and training datasets have grown immensely, meaning that it's practical to run larger networks and statistically valid (that is, we have enough training examples that we won't just run into over-fitting problems with ... | https://ai.stackexchange.com |
4,263,178 | [
"https://math.stackexchange.com/questions/4263178",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/556883/"
] | I am currently reading some lecture notes where the calculation of
<span class="math-container">\begin{align}
\int_{-\infty}^{\infty} \frac{x\sin(x)}{x^2+1}\ \mathrm{d}x
\end{align}</span>
using residues is explained. The existence of <span class="math-container">$\lim_{R\to \infty}\int_0^{\infty} \frac{x\sin(x)}{x^2+1... | Note that the derivative of <span class="math-container">$x \mapsto \frac{x}{x^2+1}$</span> is pointwise equal to <span class="math-container">$\frac{1-x^2}{(1+x^2)^2}$</span>, hence by integration by parts <span class="math-container">$$ \int_0^\infty \frac{x}{x^2+1}\sin(x)dx = -\cos(x)\frac{x}{x^2+1}\Big|_{x=0}^{x=+\... | You can easily compute the antiderivative writing
<span class="math-container">$$\frac{x}{x^2+1}=\frac{x}{(x+i)(x-i)}=\frac{1}{2 (x+i)}+\frac{1}{2 (x-i)}$$</span> So, you face two integrals looking like
<span class="math-container">$$I(k)=\int \frac{\sin(x)}{x+k}\,dx$$</span> Make <span class="math-container">$x+k=y$</... | https://math.stackexchange.com |
82,969 | [
"https://softwareengineering.stackexchange.com/questions/82969",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | So I have a website I would like to make that would essentially be selling files. For the sake of discussion let's say that these files are like the raw text of a book. If somebody buys a file from my site, there really isn't anything preventing them from sharing that unlimited amounts of times with their neighbor or w... | The music industry is a perfect example. Instead of embracing reality, they tried to fight it by imposing restrictions on their end users. The restrictions got so bad that many of their end users said something rude and started looking for pirate alternatives.
You can't stop people pirating stuff.
However, if you mak... | You can relatively easily include customer-specific watermarks in the files, so when the file lands on a bulletin board, you know which user to sue. Teach your users about that and it will keep at least some of them from distributing your content.
| https://softwareengineering.stackexchange.com |
100,619 | [
"https://electronics.stackexchange.com/questions/100619",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/4767/"
] | I have a transformer that has the following specifications:
<ul>
<li>Primary: 220V</li>
<li>Secondary: 12+12V</li>
<li>Rating: 5A</li>
</ul>
Does this mean the transformer has two 2.5A windings? Or is each winding capable of delivering 5A as long as the total rating is not exceeded?
If I use it as a 24V transformer,... | <blockquote>
Primary: 220V Secondary: 12+12V Rating: 5A
</blockquote>
This notation generally means that there are two secondaries, each rated at 12V and 5A. It could also mean a center-tapped secondary that's rated at 24V @ 5A overall.
<blockquote>
If I use it as a 24V transformer, is the total current 2.5A?
</b... | Just to add a bit of extra info to Dave Tweed's answer: -
<blockquote>
What happens (besides heating) if the transformer's current rating is
exceeded?
</blockquote>
It gets warmer under heavier load conditions and this is due to copper losses (\$I^2 R\$) in the windings. But, a side effect of this is that it migh... | https://electronics.stackexchange.com |
212,069 | [
"https://electronics.stackexchange.com/questions/212069",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/91522/"
] | How long does it take to load a new configuration on a FPGA? can a FPGA be re-programmed on the fly while a computer program with offloads to the FPGA is running?
| In my experience, it's usually one or two seconds or at least 100's of milliseconds.
It depends on how big is the FPGA and what interface (serial, parallel, etc) you use to program it. The time remains relatively constant as FPGA technology improves because as the FPGAs get bigger, they also add new higher-speed prog... | <blockquote>
can a FPGA be re-programmed on the fly while a computer program with offloads to the FPGA is running?
</blockquote>
That is called <em>partial reconfiguration</em>, and is possible, under rare circumstances, namely, that you use the right tools (with pricey licenses), and partition your FPGA design acc... | https://electronics.stackexchange.com |
444,889 | [
"https://electronics.stackexchange.com/questions/444889",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/224970/"
] | Having some trouble understanding the concept of voltage.
Suppose an initially neutrally charged wire is touched only to the positive terminal of a 9V battery, but not the negative terminal. The positive terminal of the battery has an accumulation of positive charges, and the wire has no accumulation of charge. Since ... | You have a 9V battery => You have a device which generates an electric field between its terminals.
You connect a metal wire to the +terminal => the field draws free electrons from the wire towards the +terminal until the 3 forces find a balance. They are:
<ul>
<li>the attraction from the metal atoms of the wire</li... | It's all relative. So relative to a third reference (Conductor C), conductor A might be positive and conductor B might be neutral (aka equal to conductor C). But to conductor A (i.e. if you use conductor A as your reference) then Conductor B and C are negative (while conductor A is neutral). So if you label some conduc... | https://electronics.stackexchange.com |
3,247,744 | [
"https://math.stackexchange.com/questions/3247744",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/678956/"
] | I already tried it with a binomial distribution, but are uncertain how to apply that here.
Another approach would be <span class="math-container">$1- \frac{something }{6^5}$</span> where the "something" is the total number of possibilities to have at least two times where the dice facing a <span class="math-container"... | The probability of a given roll giving one of those numbers is <span class="math-container">$\frac{1}{3}$</span>. Note that the probability of this not happening at all is <span class="math-container">$\left( \frac{2}{3} \right) ^5$</span>, and the probability of it happening once is <span class="math-container">$5 \le... | As regards your second approach then "something" is equal to
<span class="math-container">$$\underbrace{4^5}_{\text{no 5 or 6}}+\underbrace{5\cdot 4^4\cdot 2}_{\text{exactly one 5 or 6}}.$$</span>
| https://math.stackexchange.com |
156,668 | [
"https://softwareengineering.stackexchange.com/questions/156668",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/47485/"
] | I know that Senior Developer doesn't use only one language and only one platform or IDE.
Can you advise how to mix different styles of programming to make efficient code?
For example, <strong>best</strong> mixing is <strong>Perl + Objective-C</strong>.
<code>$ObjectiveCLongNameOfVariablesAndMethods</code> are worst... | Keep to the conventions of the language being used.
When using Objective C, keep Objective C conventions in those parts of the code. When using Perl keep to Perl conventions... etc.. etc... etc...
This keeps things more compartmentalized - when you move to a different language it is easier to see that you have moved ... | Base your styles and conventions on the language being used.
You may love "{'s" everywhere in your code. You always use a series of "[" and "{" and "(" in the most verbose form. You believe they should be on their own line. Then one day your team is assigned a large development task that requires python. If you don't... | https://softwareengineering.stackexchange.com |
96,583 | [
"https://electronics.stackexchange.com/questions/96583",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/35616/"
] | I'm trying to create a circuit with two loads in parallel ( essentially piggy backing one circuit on the power supply of the other ). Circuit 1, the main circuit requires ~900ma at 12v. Circuit 2, requires ~70ma at 5v. To step down I'm using a buck regulator that provides 300mA at 5v. The main supply is 12v DC rated fo... | You said you measured the 1.3 Amps <em>across</em> Vin and GND. This is NOT the way to measure the current capability of a power supply - it does give you the short circuit current, but that is usually not a useful value. If the existing power supply claims to be 12 volt and 900 mA, you should believe that current ra... | This is not a complete answer but meant to clear up a couple of misconceptions that appear in your question.
<ol>
<li>If the load on your 5 V converter is 70 mA, the converter will only produce 70 mA. The 300 mA is a maximum rating that doesn't affect how much current is drawn from the 12 V supply.</li>
<li>If you red... | https://electronics.stackexchange.com |
2,626,387 | [
"https://math.stackexchange.com/questions/2626387",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/525257/"
] | How can I calculate the following limit:
$$\lim \limits_{n \to \infty}(n-\sum_{k=1}^n\cos{\frac{\sqrt{k}}{n})}$$
A hint or direction would be appreciated (please not a solution for now, I would post mine once I get it).
I have tried to use 3rd order of taylor but I couldn't get through with the algebra.
Thank you
| Let us write $z_1,z_2,z_3$ in their polar representation:
$$z_k=e^{i\theta_k},\ k=1,2,3$$
for some angles $\theta_k$. Now, since $$z_1+z_2+z_3=0\Leftrightarrow e^{i\theta_1}+e^{i\theta_2}+e^{i\theta_3}=0\Leftrightarrow1+e^{i(\theta_2-\theta_1)}+e^{i(\theta_3-\theta_1)}=0$$
or,
$$e^{i(\theta_2-\theta_1)}+e^{i(\theta_3-\... | Hint: If you divide the three points by $z_1$ you have three different points which satisfy the same conditions. One of these points is $1$ and that simplifies the analysis easily. Find those three points and then multiply by an arbitrary $z_1$ of modulus $1$ to get the general solution.
Note: Multiplying/dividing is... | https://math.stackexchange.com |
126,389 | [
"https://security.stackexchange.com/questions/126389",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/113774/"
] | I recently forgot to turn off proxy and connect through a premium account,
will the owner of proxy server be able to use the cookies and access the account?
| Yes.
As mentionned by u2702, anything sent over HTTP via the proxy can be clearly read by the owner of the proxy.
In your particular case, since the login page (ONLY) was over HTTPS (and I suppose that by that, you mean that the other pages were over HTTP after the login), your password could not be compromised. How... | Anything that went over HTTP through a proxy was available to proxy controller.
HTTPS you should be okay, depending on the CAs that your browser trusts and assuming that you didn't click "yes" on trusting an untrusted certificate.
| https://security.stackexchange.com |
66,502 | [
"https://softwareengineering.stackexchange.com/questions/66502",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/17494/"
] | In a typical software development environment, <strong>project closures</strong> mark the end of a project.
<ol>
<li>Project records are completed and archived, </li>
<li>resources released, </li>
<li>issues and lessons are documented, and </li>
<li>a formal dinner/party held for celebration. </li>
</ol>
Last step i... | <blockquote>
For a group that works on multiple simultaneous projects, how do project closures fit in?
</blockquote>
First, "multiple simultaneous projects" is considered a really bad idea. The point of scrum is to sprint and be done. Switching projects to start another sprint is disruptive. Doing two projects at... | I usually see agile methods like scrum practices within a more structured project management framework. This isn't a contradiction at all. Agile works for delivery, its goal is to deliver the right software faster. It helps with the interactions between the developers and stake holders. It can be used as part of a fixe... | https://softwareengineering.stackexchange.com |
5,678 | [
"https://mathoverflow.net/questions/5678",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1837/"
] | Let $\ell$ be a positive integer greater than 1. The problem is to find a set of $n$ real positive numbers $x_i$ and $n+1$ numbers $y_i$ such that
$$\sum_{i=1}^n x_i^k= \sum_{i=1}^{n+1} y_i^k$$
for $k=\ell,\cdots,2\ell-1$. These $2n+1$ numbers need to be upper/lower bounded by a constant independent of $\ell$ [thus $x_... | Actually Darsh gave an almost full solution. Let me fill in the minor technical details.
1) We need the following quantitative form of the inverse function theorem. Suppose that $F:\mathbb R^n\to \mathbb R^n$. Assume also that $\|DF(X)^{-1}\|\le C_1$, that $\max_{Y\in B(X, \delta)}\|D^2F(Y)\|\le C_2$, and that $C_1C_... | Maybe the following is useful: first pick arbitrary distinct positive numbers $y\_1,\ldots,y\_n$. Note that $(y\_1,\ldots,y\_n,y\_1,\ldots,y\_n,0)$ is a solution to your system for all $l$; however, the last component is zero, so it doesn't fit your constraints. To remedy this, fix $l=n$ and define $F:\mathbb{R}^{n+1}\... | https://mathoverflow.net |
402,615 | [
"https://stats.stackexchange.com/questions/402615",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/244508/"
] | I have been recently asked in an interview a question that: How to set up an event with probability of one seventh from coin tossing?
I couldn't find the correct answer and still don't know the correct answer yet.
| What about you toss 3 coins giving the possible events
<span class="math-container">$$
{TTT,TTH,THT,HTT,HHT,HTH,THH,HHH}
$$</span>
Let event B = not all heads
and event A = All tails
then
<span class="math-container">$$
P(A|B) = \frac{P(B|A)P(A)}{P(B)}=\frac{1*1/8}{7/8}=1/7
$$</span>
| I assume they mean fair coins, o/w the answer would be trivial. And, I humbly think that this is a <em>brain teaser</em> problem and the hidden question is: write <span class="math-container">$1/7$</span> in binary, i.e. <span class="math-container">$0.0010010...$</span>.
For example, an event with probability <span c... | https://stats.stackexchange.com |
427 | [
"https://physics.stackexchange.com/questions/427",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/17/"
] | General relativity tells us that what we perceive as gravity is curvature of space-time.
On the other hand (as I understand it) gravity can be understood as a force between objects which are exchanging (hypothetical) virtual particles called gravitons, similar to the way electromagnetic forces are due to objects exch... | Well, consider this: the same thing happens with electromagnetic forces. We can describe them as particles responding to the presence of electric and magnetic fields, or we can describe them as resulting from the exchange of virtual photons. Those views seem similarly incompatible, but nevertheless both theories (class... | Here is just a small remark. It is possible to give a strict mathematical proof about the equivalence of these two pictures.
If you just start with the three (semi-experimental) facts: Lorentz invariance, <span class="math-container">$1/r$</span> long-range tail of gravitational force and its one-way action (attraction... | https://physics.stackexchange.com |
82,196 | [
"https://physics.stackexchange.com/questions/82196",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/26191/"
] | To my understanding the work done on an object is defined mathematically as:
$$W = \vec{F}\cdot\vec{S}=|\vec{F}||\vec{S}|cos\theta$$
This, I understand. My problem is that I don't understand that if the angle $\theta$ is 90 degrees how can the work done by $\vec{F}$ on the object is zero. For example; say you have a pa... | Because it's not any work, but the work done by a force that produces a displacement.
In the scenario you describe, somehow that force is not doing any work on the particle. This could be because the particle is restricted by another force to not go perpendicular and then the sum of forces in the perpendicular direct... | I like to think about it in the context of the Lorentz Force, i.e. the force on a charged particle by an electric and a magnetic field. The first time you check by yourself that the magnetic force does no work, it is puzzling.
$$\vec F = \vec F_{electric} + \vec F_{magnetic} = (q\vec E) + (q\vec v \times \vec B) $$
T... | https://physics.stackexchange.com |
212,593 | [
"https://physics.stackexchange.com/questions/212593",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/89952/"
] | The spacetime interval $(\Delta s)^2 = (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 - c^2(\Delta t)^2$ is invariant under the Lorentz transformation and this isn't the case for the Galilean transformation. As the title might suggest, I have tried to prove that the spacetime interval is not invariant under Galilean transf... | Recall that to <em>disprove</em> something, you only need one counterexample. So I'd simply advise: don't bother with the symbols: choose a simple example. Think of the events at $X_1=(t,\,x,\,y,\,z)=(0,0,0,0)$ and $X_2=(t,\,x,\,y,\,z)=(1,0,0,0)$. The proper time between them is 1. Now transform to co-ordinates boosted... | You just correctly showed that a Galileian "transformation" where $v_x=v_y=v_z=0$ "preserves" the interval.
You were supposed to find two Galilean frames and two events where the two frames compute different intervals. You didn't even pick two frames since you let $v_x=v_y=v_z=0$.
| https://physics.stackexchange.com |
35,360 | [
"https://mechanics.stackexchange.com/questions/35360",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/21721/"
] | I have a 2006 Nissan Sentra and replaced both front rotors n brake pads not less than 6mo. Ago. My passenger side was making grinding noise so I took a look at my brakes cause it sounded like metal on metal. When I took my brakes off seen they were gone n my rotor looked worn yet on the drivers side both looked fine. C... | I've seen this happen when the pads aren't aligned properly, sometimes from a missing shim or retaining spring. Basically the pad and rotor are in constant low grade contact and things wear really quickly as a result.
| It's possible that you have a caliper that is stuck or simply not working or a bubble in the brake line/fluid. Bleed the brake line. If the fluid is brown, keep bleeding until it runs clear. If you see bubbles (or the fluid stops coming out for a few seconds) wait until you see all the normal brake fluid come out.
Don... | https://mechanics.stackexchange.com |
331,331 | [
"https://physics.stackexchange.com/questions/331331",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/155239/"
] | I have been studying theoretical mechanics and just now I came cross a formula
called "Lagrange classical relation", that is, if we let $q_1$, $q_2$,$\cdot $$ \cdot $$\cdot $, $q _ m$, $t$ be the $generalized$ $coordinates$ of $x$, then we have
$${\partial\dot{ x}\over\partial \dot{q _ k}}={\partial x\over\partial q... | In Lagrangian mechanics we use independent generalized coordinates and express every cartesian coordinate using these generalized coordinates:
$$\begin{cases} x_{1} \equiv x_{1}(q_{1}(t),.., q_{n}(t), t) \\ ...\\ x_{N} \equiv x_{N}(q_{1}(t),.., q_{n}(t), t)
\end{cases}$$
As you can see every $x_{n}$ is a composite f... | Well, I'd like to give my personal idea:<br/>
Since we have $$\dot{x}(t)=\sum_{i=1}^m[({\partial \phi\over \partial q _ k})\circ g](t)\cdot\dot{q_i}(t)+({\partial \phi\over \partial {t}})\circ g(t), \forall t\in \mathbb{R},$$
Then if we define the following maps:
$$ \mu:\mathbb{R}^{2m+1}\to \mathbb{R},(y_1,y_2,\cdo... | https://physics.stackexchange.com |
654,512 | [
"https://electronics.stackexchange.com/questions/654512",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/333236/"
] | I've an old UPS for my computer which draws 50 W on average and less than 150 W at full load. With the the built-in battery I only have about 10 minutes of backup time.
I am thinking about getting a solar panel (around 150/200 W) together with a MPPT/PWM controller (around 10/20 A) so that I can charge the UPS battery ... | In commercial smartmeter, the microcontroller and ADC are not isolated from mains, so voltage sensing is done with a simple voltage divider.
In your case I would absolutely not recommend this option because it requires the whole circuit to be at mains potential, which is quite dangerous if you work on it. It also makes... | One solution is not to care which line is phase and which is neutral. Pick one of the two incoming wires, and call it ground for the purposes of your design.
Don't make any connection between your circuit and the protective Earth wire. Don't allow anyone to touch any part of the circuit while it is plugged in.
If the... | https://electronics.stackexchange.com |
256,511 | [
"https://softwareengineering.stackexchange.com/questions/256511",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/149492/"
] | I have the suspicion that many bug-fixes carried out by our developers sooner or later cause another bug, simply because the product is too complex.
I'd like to improve the quality of bug-fixes, i.e. make sure bug-fixes do not produce additional errors in the code. For that, I'd like to be able to measure how the qua... | Ideally you will have as many useful unit tests as possible, testing every combination of inputs to each class.
Then when fixing a bug, check the unit test that should have caught it. Maybe there is an edge condition or combination of inputs not previously encountered (add a new unit test). Maybe an existing test erro... | Are your developers working under time pressure? Do they have quiet working conditions? Do they have the best debugging tools the money can buy? Do you have testers?...
There are too many factors which can make bug solving a task which creates more bugs than it solves. Too many to be enumerated here. If you notice tha... | https://softwareengineering.stackexchange.com |
127,801 | [
"https://physics.stackexchange.com/questions/127801",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/44895/"
] | I am actually working with Green-Schwarz anomaly cancellation mechanism in which I have came across a strange formula which relates trace in the adjoint representation (Tr) to trace in fundamental representation (tr).For the special case of $SO(n)$, the relation is
$$Tr(e^{iF})= \frac{1}{2}(tre^{iF})^2-\frac{1}{2}(tr... | Good luck. To check the cancellation for particular groups like $E_8\times E_8$ and $SO(32)$, you will indeed have to get through similar group-theoretical tasks. Similar trace formula for the traces of $E_8$ transformations are especially yummy, including the factor of $1/30$.
The orthogonal case is easier even if on... | $\newcommand{\tr}{\mathrm{tr}}$For $\mathrm{SO}(N)$, the adjoint representation can be seen as the antisymmetric part of the tensor product of the fundamental representation with itself.
In general, we have the following property for such an antisymmetric representation:
<blockquote>
Given a representation $(V,\rho... | https://physics.stackexchange.com |
181,788 | [
"https://mathoverflow.net/questions/181788",
"https://mathoverflow.net",
"https://mathoverflow.net/users/22019/"
] | <b>Edit</b> After Andreas Blass answer below and comments below the original post I have changed it to accommodate posters' remarks. I hope it is clear and makes more sense now.
Let $\mathrm{PA}$ be the first-order Peano Arithmetic with full induction schema. Let $\mathrm{Con(PA)}$ be the standard $\Pi_1$ consistency ... | The witness coding a proof of 0=1 in a nonstandard model is likely to be very specific; depending on your encoding, most nonstandard numbers may not code proofs at all. And even if all numbers encode proofs, many nonstandard numbers will encode proofs of true formulas, or of other false formulas.
The encoding of proo... | Your two questions should probably be answered together, because "coding a proof" makes sense in any model of PA, whereas "coding" and "proof" alone require us to go outside the model, decoding a number as a (possibly nonstandardly long) string of symbols. But "$x$ codes a PA-proof" is expressed, thanks to Gödel, as a... | https://mathoverflow.net |
12,109 | [
"https://mathoverflow.net/questions/12109",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3333/"
] | In <i>The Geometry of Schemes</i> by Eisenbud and Harris, Exercise I-32 asks one to show that a scheme $X$ is reduced if and only if every local ring $\mathcal{O}_{X,p}$ is reduced for closed points $p \in X$. However, this does not seem to work in general, since $X$ may not have enough closed points. What additional... | There do exist schemes without a closed point, yes. (Liu, exercises 3.3.26/27)
But under some very reasonable additional conditions - I think quasi-compactness will be sufficient, if you are happy with using Zorn's lemma - the result holds. Use/prove the existence of a closed point, and the fact that localizing a red... | Brunoh:
1) If $X$ is a quasi-compact scheme such that $\mathscr O_{X,x}$ is reduced for every closed point $x$, then $X$ is reduced. Indeed, let $y\in X$. The scheme $\overline{\{y\}}$ is a closed subscheme of $X$, hence is quasi-compact, and non-empty because it contains $y$. It thus has a closed point $x$, which is... | https://mathoverflow.net |
103,124 | [
"https://physics.stackexchange.com/questions/103124",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/42329/"
] | I learnt that the formula for refractive index when light travels from rarer to denser medium is
$$\frac{\sin i }{ \sin r}$$ where
$i =$ angle of incidence, $r =$ angle of refraction.
Is the same formula used for calculating refractive index when light travels from denser to rarer medium? Or is it
$$\frac{\sin r }... | It is important to note that the equation you mention gives the index of refraction of one medium <em>with respect to</em> another. If light travels from one medium, with refractive index <span class="math-container">$n_i$</span> and incident angle <span class="math-container">$i$</span>, to another medium, with refrac... | The formula for refractive index when light is traveling from denser to lighter medium is
<span class="math-container">$$\frac{\sin\theta_r}{\sin \theta_i}$$</span>
where <span class="math-container">$\theta_r$</span> and <span class="math-container">$\theta_i$</span> are the angles of refraction and incidence respecti... | https://physics.stackexchange.com |
302,965 | [
"https://physics.stackexchange.com/questions/302965",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/112190/"
] | The electrostatic potential energy of a point charge $q$ at potential $V$ is $$U_E=q V \tag{1}$$
The electrostatic potential energy of a capacitor that has been charged with charge $q$ at potential $V$ is $$U_E=\frac{1}{2}q V \tag{2}$$
<hr>
The magnetic energy of a single loop of (constant) current $i$ in a (unifo... | <blockquote>
My question is: why when these factors $\frac{1}{2}$ appear exactly?
</blockquote>
In the case of the point charge, the electric potential $V(\mathbf{r})$ does not depend on the charge $q$ of the test particle. Assuming zero potential at infinity, the potential is <em>defined</em> as the work done per ... | Regarding the capacitor: it starts at charge "0" with no E field, so the 1st charge requires no energy. Half way through charging, the field is E_final/2. The last little bit of charge, dQ, is at the full field so is (dQ)E_final. Basically, it's a ramp-up, and the average of a linear ramp is 1/2 the final 'height'.
| https://physics.stackexchange.com |
38,810 | [
"https://softwareengineering.stackexchange.com/questions/38810",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/1306/"
] | Is there such a thing as too much uniformity? Where I work we of course have standards including naming conventions, architectures, frameworks to leverage etc. However lately there has been a lot of critiquing of things I would consider more style.
For example writing <code>if</code> statements in multiple lines v... | <strong>Uniformity</strong> is not a problem (it's good) but <strong>rigidity or inflexibility</strong> can be. If in striving for uniformity you become dogmatic then the harm you are doing to the team may be greater than the good that comes from the (possibly) resulting uniformity.
It's best just to set basic style ... | When potentially dozens of people are working on a project over the years of its lifespan, it sometimes gets confusing when you have to jump styles. Imagine reading a book where different chapters are written by different authors who only <em>somewhat</em> maintain writing style. It's possible, but it's annoying.
Most... | https://softwareengineering.stackexchange.com |
314,780 | [
"https://softwareengineering.stackexchange.com/questions/314780",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/23355/"
] | When should class diagrams, data flow diagrams, and flow charts be made? After making classes or before making classes?
Should data flow diagrams and flow charts be made all the time in all the projects or it depends on some factors? Which factors would they be?
If the developers are short of time, what out of data ... | This depends a lot on the project methodology your are using (e.g. the Rational Unified Process versus Scrum), and how much you value process documentation in comparison to code.
In some contexts it is important that all requirements and design decisions are traceable: why did we choose this alternative, who decided i... | I use Petri’s net elements and annotations to create JavaScript programs that use the Acrobat/JavaScript API for PDF form applications. The method begins with creating a diagram to establish the input-output relations of net elements (plus a few annotations), continues with specifying other annotations in two forms and... | https://softwareengineering.stackexchange.com |
95,674 | [
"https://dba.stackexchange.com/questions/95674",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/61689/"
] | Basically, I have a dataset that is a list of internal location identifiers attached to an ID (so each 'set' of geographical points has its own ID). So an 'id' column and a 'location' column exist in the table.
I need a way to find an ID which contains two different locations, that is:
<pre>
ID | location
-----------... | <pre><code>select id
from the_table
where location in ('a', 'd')
group by id
having count(distinct location) = 2;
</code></pre>
| Shouldn't get it more simple than this:
<pre><code>SELECT ID FROM tbl GROUP BY ID HAVING '{a,c}' <@ array_agg(location)
</code></pre>
| https://dba.stackexchange.com |
130,066 | [
"https://math.stackexchange.com/questions/130066",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/24930/"
] | Let the real sequence ${x_n}$ be given by,
$$\sum_{j=1}^{2n} \frac {1}{j} - \sum_{j=1}^{n} \frac {1}{j}. $$
Show that $0<x_{n}<x_{n+1}$ and that $x_{n}<1$ for all $n$. Deduce that $x_{n}$ converges, giving your reason.
I seem to think this has something to do with $\sum_{j=1}^{2n} \frac {1}{j} - \sum_{j=... | First note that the sequence $(x_n)$ is bounded above. This follows from your observation that $\sum_{j=1}^{n} \frac {1}{j+n}$. Here we have $n$ terms, all of them clearly less than $1/n$, so their sum is less than $1$.
Next you want to show that the sequence $(x_n)$ is increasing. Calculate $x_{n+1}-x_n$, and show i... | $\sum^n 1/j \approx log(n)$ and that's all you need.
| https://math.stackexchange.com |
562,819 | [
"https://physics.stackexchange.com/questions/562819",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/263433/"
] | Suppose I have two arbitrary electric fields (vector fields), <span class="math-container">$\mathbf{E}_1 (\mathbf{r})$</span> and <span class="math-container">$\mathbf{E}_2 (\mathbf{r})$</span>, which are a function of position <span class="math-container">$\mathbf{r}$</span> (the <span class="math-container">$e^{i\ome... | A way to define the wave vector of an arbitrary field is in terms of the expectation value. First, consider an electric field that is described by an angular spectrum <span class="math-container">$H(\mathbf{k})$</span>. Then one electric field is given by
<span class="math-container">$$ E(\mathbf{r}) = \int H(\mathbf{k... | As you correctly wrote, the superposition of waves is
<span class="math-container">$$\mathbf{E}(\mathbf{r}) = \mathbf{E}_1(\mathbf{r}) + \mathbf{E}_2(\mathbf{r}).$$</span> This is true for <em>any</em> form of electric field (not encessarily plane waves) and in no way translates in a superposition rule for wave vectors... | https://physics.stackexchange.com |
7,689 | [
"https://dba.stackexchange.com/questions/7689",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1726/"
] | From what I understand about index fragmentation, this should not be possible. The cases I have found in my databases are non-clustered.
Example:
<pre><code>ALTER TABLE [dbo].[ClaimLineInstitutional] ADD CONSTRAINT [PK_ClaimLineInsitutional]
PRIMARY KEY NONCLUSTERED
(
[ClaimLineInstitutionalID] ASC
)WITH (PAD... | Updates on data already there causes rows to be moved and forward pointers added
In this test, we can get 65% fragmentation on 115k densely packed rows
<pre><code>CREATE TABLE #FragTest (
FragTestID int NOT NULL IDENTITY PRIMARY KEY,
SomeString varchar(4100) NULL
);
INSERT #FragTest (SomeString) VALUES (... | Logical fragmentation occurs when the logically next page is different from the physically next page.
In the case of the leaf level of an index with a monotonically increasing key this can happen if extent allocations for the index become interleaved with the extent allocations for other objects.
Even without this ... | https://dba.stackexchange.com |
559,541 | [
"https://physics.stackexchange.com/questions/559541",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/232634/"
] | I am confused about the first law of thermodynamics when applied to an isothermal process for an ideal gas. In my textbook it says that for any process involving an ideal gas:<br />
<span class="math-container">$dU=dQ=nC_V∆T$</span><br />
Then doesn’t this imply that since temperature doesn’t change, there is not heat ... | The ideal gas law says that for a fixed number of molecules in a gas
<span class="math-container">$$\frac{PV}{T}=\text{constant}.$$</span>
If the process is isothermal, as you specify, then <span class="math-container">$T$</span> is constant and we can write
<span class="math-container">$${PV}=\text{constant}.$$</span>... | <blockquote>
<span class="math-container">$dU=dQ=nC_V∆T$</span>
</blockquote>
Does your book really state that <span class="math-container">$Q=nC_{V}\Delta T$</span> for an isothermal process involving an ideal gas? Because, as far as I know, that would apply to an isochoric (constant volume) process.
On the other hand... | https://physics.stackexchange.com |
432,045 | [
"https://softwareengineering.stackexchange.com/questions/432045",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/230788/"
] | If you wish to perform the same action using different parameters, you can either make differently named functions:
<pre><code>public Apple findAppleById(long id){
return repo.findById(id);
}
public Apple findAppleByCultivar(String cultivar){
return repo.findByCultivar(cultivar);
}
</code></pre>
Or you can over... | Identifiers should not repeat information that is already indicated by the types. So <code>findAppleByString()</code> and <code>findAppleByInteger()</code> would be redundant. But in your case the function names add the information that the integer represents an ID and the string represents a cultivar name, which is no... | I would say, if overloading is available, you only include the argument in the name if you have to use different arguments of the same type (like first name and last name).
For other cases the argument immediately follows the method name anyway so it will read pretty fluently. Also IntelliSense (or whatever they call i... | https://softwareengineering.stackexchange.com |
517,859 | [
"https://physics.stackexchange.com/questions/517859",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/190163/"
] | Why does the area under Wien's displacement graph give Stefan-Boltzmann law for a black body?
I couldn't find any proof of this. (I could just find this expression). I am not aware of the function of Wien's displacement graph as well (I just know that it is between Intensity and wavelength emitted by a black body).
... | Since the question is a little terse, it is difficult to interpret. I think what must be happening is that the phrase 'Wien's displacement graph' is being used to mean the graph of <span class="math-container">$\rho(\omega)$</span> as a function of frequency <span class="math-container">$\omega$</span>, where <span cla... | Actually this question has two answers modern and classic,viz.
1- Deriving the Stefan-Boltzmann law and the Wien's displacement law from the modern Planck radiation law or
2-Deriving both laws from the classic Wien,s radiation law as Wien himself established by introducing his law u(f,T) =const. f **3 .exp (-hf/kT) ,... | https://physics.stackexchange.com |
66,704 | [
"https://physics.stackexchange.com/questions/66704",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/24900/"
] | Something I can never understand is that where the cosmic background radiation spreads?
If I know well, the cosmic background radiation is actually the light of the Big Bang. If it happened <em>exactly</em> in the same time, it must have spread into the theoretic center of the universe. Which would mean that it alread... | The CMB doesn't come from one place; it comes from everywhere. It also doesn't go in one direction; it goes in every direction. And it didn't happen all at once, but it happened at roughly the same time everywhere. In particular, it's not the light of the Big Bang, but the light of a time roughly 378,000 years <em>a... | The big bang is completely centerless.
The right way to picture where the CMB is coming "from" is to imagine that, long ago, the universe was as hot as the surface of the sun. This means that the universe was filled with a super-hot plasma that looked much like the surface of the sun today. Then, after enough expa... | https://physics.stackexchange.com |
216,082 | [
"https://electronics.stackexchange.com/questions/216082",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7523/"
] | I want to use a microcontroller and A/D converter to do some high-frequency (~100 kHz) long-term (minimum of five second buffer, looping until triggered) data logging. It looks like a good way to do this is with an SD card. I know there are different ways of accessing an SD card, including directly through SPI. I also ... | You may not be able to do this with a PIC33, and almost certainly not just any PIC33. Some flash cards 'go away' for long periods of time (tens of milliseconds or more) despite the high throughput this latency can kill you with a small microcontroller because you'll run out of buffer RAM.
If you allow buffering for 2... | I have done this before, but I don't remember the all details. I used Fat filesytem and there was some kind of different approach, I used to transfer a block of data 512 bytes. But I can tell you what you need for sure: a circular buffer, mine was 16k bytes. When you sample in ISR you write into a buffer then you incre... | https://electronics.stackexchange.com |
36,714 | [
"https://mathoverflow.net/questions/36714",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7732/"
] | Is there a standard notation for a graph (on a given set of vertices) without any edges?
| There are many ways to define a <em>graph</em>, but a pretty standard one is a pair $(V,E)$ where $V$ is a finite set of points and $E \subset \binom{V}{2}$. So, what you are looking for is $(V, \emptyset)$; which would be pretty widely understood.
| I don't think there is standard notation for this. If you've already fixed a notation for complement (say a superscript c) then you could use $K_n^c$. But I don't think standard notation exists for this.
| https://mathoverflow.net |
97,780 | [
"https://electronics.stackexchange.com/questions/97780",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/30642/"
] | Recently I was try to rectify the output of an “electronic transformer” using an ordinary rectifier diode 1N4007. The output of this device is bursts of frequency around 50kHz, with an envelope of 100Hz and RMS 15Volt measured by scope.
Under these conditions, why does the diode become extremely hot even with a pur... | Every diode needs some time to recover its reverse resistance after voltage polarity changes. During the recovery time there is high reverse current through the diode. This reverse current makes the diode to produce some heat.
The higher the frequency is, the more time is spent in the recovery state and so the more hea... | You can use fast rectifier diodes for slow AC waveforms. Just make sure that the reverse voltage and current rating is suitable and that any heat-sinking requirements are implemented.
Slow diodes won't work very well as the frequency rises because the diode's reverse recovery time is usually quite long - this makes th... | https://electronics.stackexchange.com |
273,683 | [
"https://softwareengineering.stackexchange.com/questions/273683",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/168518/"
] | Currently I am interning at a company as a "full stack" developer (Application developer on the job title) and I realize that I am having difficulties coping with frontend tasks. This is especially true when I am tasked with implementing a new frontend feature and I can see myself struggling to get the hang of frontend... | How did you start to be a backend developer? It must've felt very similar back then. Yet you managed it. I'm sure you'll do the same for frontend.
Here's how I'd suggest your learning:
<ol>
<li>Get to know html first. That should be very easy and quick. </li>
<li>Learn CSS. Not master it. Get familiar with <strong>m... | The short answer is to read a good book on Angular, read it again, and then practice coding, lots of it. That said, if you've never worked with UI, it can be an interesting challenge, because you might be missing some fundamental conceptual information to help you put it all together.
What follows assumes that you kno... | https://softwareengineering.stackexchange.com |
294,598 | [
"https://physics.stackexchange.com/questions/294598",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/136326/"
] | I was reading Zee's book in Group Theory, chapter VIII.2 (The Conformal Algebra) and I'm stuck in something probably easy:
In p.516, he states that under a scale transformation, $x'^{\mu} = \lambda x^{\mu}$, the metric changes as:
$g'_{\rho\sigma}(x') = g'_{\rho\sigma}(\lambda x) = \lambda^2g_{\mu\nu}(x)$
However, t... | I think he means something more mundane i.e <span class="math-container">$g_{\mu \nu} dx^{\mu}dx^{\nu} \rightarrow g_{\mu \nu} d (\lambda x^{\mu})d( \lambda x^{\nu}) = g_{\mu \nu} \lambda^2 dx^{\mu}dx^{\nu} $</span>. Then we can define new components <span class="math-container">$g_{\mu \nu}' =g_{\mu \nu} \lambda^2 $</... | There is nothing wrong with your logic.
I believe that you have found a typographical error in Zee's book.
Congratulations!
| https://physics.stackexchange.com |
382,947 | [
"https://mathoverflow.net/questions/382947",
"https://mathoverflow.net",
"https://mathoverflow.net/users/137640/"
] | Suppose <span class="math-container">$\Omega$</span> is a bounded domain in <span class="math-container">$\mathbb R^3$</span> with Lipchitz boundary <span class="math-container">$\partial\Omega$</span>, and <span class="math-container">$u\in H_0^1(\Omega)\cap C(\Omega)$</span>. Is <span class="math-container">$u$</span... | Not necessarily- let <span class="math-container">$\Omega = B_1 \cap \{x_3 > 0\}.$</span> Then <span class="math-container">$u(x) := (1-|x|^2)\frac{x_3}{|x|}$</span> is in <span class="math-container">$H^1_0(\Omega) \cap C^{\infty}(\Omega),$</span>
but <span class="math-container">$u$</span> is discontinuous at the ... | The answer to the follow-up question is negative too. For consider the half-ball <span class="math-container">$\Omega=\{x\,;\,x_3>0,\,|x|<1\}$</span>. Choose a number <span class="math-container">$\alpha\in(1,\frac32)$</span>, and a function <span class="math-container">$\phi\in C^\infty({\mathbb R}^3)$</span> su... | https://mathoverflow.net |
55,029 | [
"https://math.stackexchange.com/questions/55029",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/13589/"
] | Assume that $K$ is a complete field under a discrete valuation with Dedekind ring $A$ and maximal ideal $\mathfrak p$ and $A\diagup\mathfrak p$ is perfect. Let $e$ be a positive integer not divisible by $E$. Let $E$ be a finite extension of $K$, $\pi_0$ a prime element in $\mathfrak p$, and $\beta$ an element of $E$ su... | In general, we have $ef=n$, where $f$ is the residue class field extension degree, and $e$ is the ramification, and $n$ is the degree. Here, the hypothesis $|\beta|^e=|\pi_0|$ does not suggest (nor imply) that $E/K$ is totally ramified, nor that the subextension $K(\beta)/K$. If you <em>add</em> the hypothesis that $E/... | I checked: this is a Lemma on p. 53 of Lang's <em>Algebraic Number Theory</em>. The proof begins:
"We can write $\beta^e = \pi_0 u$ with $u$ a unit in $B$ [the integral closure of $A$ in $E$]. Since the extension is totally ramified..."
<b>Edit</b>: What I wrote in a previous version was wrong; I hadn't read carefu... | https://math.stackexchange.com |
148,093 | [
"https://math.stackexchange.com/questions/148093",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1650/"
] | Let $k$ be a field. Assume that you already know that the category $\mathrm{Alg}(k)$ of $k$-algebras (everything here is commutative and unital) has a coproduct $\sqcup$. But you don't know that this actually comes from the tensor product of vector spaces over $k$. You just know the universal property of $A \sqcup B$ (... | Here is a geometric argument that will prove something slightly weaker. I assume
that $k$ is algebraically closed. I will use letters $A,B, C$ to denote $k$-algebras, and $X,Y,Z$ to denote corresponding algebraic sets.
<ul>
<li>Show that the set of (closed) points of the product is the product of the sets of closed ... | I come also here to bore you...
ANyway, you know that the achievement is true iff $k$ is a field, but your points are true also for a general commutative rings $k$. THen you need some "Extra" points:
1)You have a functor $U: Alg_k\to Vect_k$ that map any monomorphism is a section,
2) Exist a bifuctor $B: Vect_k\ti... | https://math.stackexchange.com |
15,413 | [
"https://electronics.stackexchange.com/questions/15413",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2064/"
] | SMT resistor arrays are available in convex or concave form. What are the dis/advantages of either?
<img src="https://i.stack.imgur.com/J8Vlv.jpg" alt="enter image description here">
| Convex have five sided terminations for easier or better soldering. The space between terminations is better with convex (generally 0.1mm). Visual checking of soldering is easier with convex, as the solder is not sucked in and hidden from view. Convex is also supposed to self align better, due to the terminators all... | When manually probing the res network, concave is better, because the probe tip does not slip off or short to adjacent terminals as easily as it does for convex.
| https://electronics.stackexchange.com |
38,447 | [
"https://stats.stackexchange.com/questions/38447",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/14550/"
] | <blockquote>
A team has conducted a study in which an introductory class was
randomly divided into two groups. Group 1 was administered a dosage of
alcohol. Group 2 was given an equvialent dosage of marijuana. Fifteen
minutes after administration, both groups were asked to solve a
puzzle. The experimenter rec... | It depends on to whom you wish to generalize your final results. If your sole interest was just to see how these people react and you don't care about inference, they are your population. If you wish to use the results to somehow infer how other similar people may behave under influence, then they are samples. Most stu... | As @Michael said, this would be considered a sample. One additional question is "from what population"? That is harder to say, but this is a problem that bedevils many studies. Often researchers will assume that a sample like this is "almost random" or something like that. What is the population, though? All college st... | https://stats.stackexchange.com |
546,623 | [
"https://physics.stackexchange.com/questions/546623",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/252872/"
] | I have a point let's say <strong>A</strong>, and I'm trying to calculate its position under the effect of different forces in a way that its distance to a point <strong>B</strong> stays fixed as if they were attached by a string.
One initial approach I thought of is to calculate its position without the distance const... | To solve problems like this you take the following steps:
<ol>
<li><strong>Position Kinematics</strong> - Take the position of the particle and parameterized it such that it <em>always</em> obeys the constraint.
In this example, the position of point <strong>A</strong> described by a vector <span class="math-contain... | What you are basically trying to solve is totally the same thing as trying to find the equations of motion for a particle constrained to move on the surface of a sphere. The radius of the sphere is the string length (more like rigid rod since you want the distance to be constant) and its center is the position of the ... | https://physics.stackexchange.com |
9,468 | [
"https://physics.stackexchange.com/questions/9468",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/2599/"
] | I know:
<ol>
<li>Quantum Mechanics (Griffiths Level, currently doing Sakurai Level)</li>
<li>Mechanics (Newtonian+ Lagrangian/Hamiltonian but at level lower than Goldstein/Landau)</li>
<li>Classical Electrodynamics (Griffiths + electro/magnetostatics from Jackson)</li>
<li>Statistical Physics (Pathria)</li>
</ol>
I ... | You can try reading Zwiebach 'A first course in String theory' which is roughly at your level right now. Its very handwavy, but well thats the best you can hope for at this level.
Otherwise, to really learn the subject you will absolutely need
1) Grad level GR
2) Quantum II, + 2 semester long courses in QFT
And the... | I would say Special Relativity, then General Relativity, and finally QFT.
Books:
Special Relativity -- I would recommend Wheeler & Taylor and Woodhouse
General Relativity -- Woodhouse
QFT -- Zee and Aitchison & Hey
There's also an undergrad physics book [junior level] on String Theory by Zwieback that's hi... | https://physics.stackexchange.com |
132,620 | [
"https://physics.stackexchange.com/questions/132620",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/52718/"
] | The Law:
<ul>
<li>The size of a solid material that can be carried by a (water) stream is proportional to the sixth power of its velocity.</li>
</ul>
I have just discovered that I read this law long time ago (it has a name starting with N or P or something), and I was required to construct a convincing model that nat... | Suppose you have a spherical particle being pushed up a slope of angle $\theta$ by the current:
<img src="https://i.stack.imgur.com/KJV57.gif" alt="Sixth power law">
Assume that the system is dominated by inertial forces not viscous forces, in which case the force on the particle is equal to the momentum change per s... | If the velocity of a river is doubled, the transportation capacity of that river increases by 64 times. This is sixth power law.
| https://physics.stackexchange.com |
31,394 | [
"https://dsp.stackexchange.com/questions/31394",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/21048/"
] | How can you implement a $9\rm V$ battery with a phase of $45^\circ$? (As a black box with a DC Voltage of $9\rm V$ and a phase of $45^\circ$)
Please preface your answer with spoiler notation by typing the following two characters first ">!"
| OK, this is a slightly constructed situation, but as far as I can see, the following is the only thing that makes sense, kind of ...
<blockquote class="spoiler">
If $A$ is your DC voltage, then a phase of $45$ degrees means multiplying it with $e^{j\pi/4}$, i.e., you get $Ae^{j\pi/4}=\frac{A}{\sqrt{2}}(1+j)$. So sca... | <blockquote class="spoiler">
Take a sinusoidal oscillator circuit with two outputs that are always 45 degrees out of phase from each other feeding two DC coupled 9V amplifier circuits. Stop the oscillator (set f = 0) when one output (whichever one you designate is "real") of the two is at 90 degrees (of a sinewave ... | https://dsp.stackexchange.com |
45,600 | [
"https://dba.stackexchange.com/questions/45600",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/25572/"
] | I've noticed that when you set up a transactional replication, SQL Server will set identity range management to manual. What this means is that in my subscription database, when I try to insert a new record into a table whose PK is an identity column, it will give me an error and say that it tried to insert a PK of "1... | What I ended up doing was sticking with a pull-based transactional replication, and having my program update the subscriber identity values to be the same as those on the publication database immediately after synchronization (kinda what I wish the distribution agent did of its own accord). In pseudo-code it looked a ... | Assuming your Publisher is using an int identity that begins at 1, you could issue <code>DBCC CHECKIDENT('dbo.mytable', RESEED, -2147483648)</code>
at the subscriber. You can then use the range from -2147483648 to 0 to hold your "temporary deltas".
| https://dba.stackexchange.com |
96,089 | [
"https://softwareengineering.stackexchange.com/questions/96089",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/31418/"
] | Consider this scenario:
Stakeholder(s): Let's build a web application to manage user's financial data.
Scrum team: Ok, let's do it.
.
.
.
<strong>After 3 sprints</strong>
Stakeholder(s): Let's also implement a mailing system, so that when user's financial status is not good, (s)he would be warned.
Scrum team: Ok, ... | The very purpose of Agile methodology and sprint development is to support the new and changing requirements of the stakeholders. If this project were being managed in a waterfall way these kinds of request would threaten the success of the project.
If there is one thing that I learned, <strong>You can't fight scope ... | I think it's fine, as long as you're re-evaluating the new goals in light of the old ones.
I'd say that as soon as your stakeholder wants a mail server the team might do one of two things:
<ul>
<li>double check that a mail server is more important with the previously defined features in the backlog for the financial ... | https://softwareengineering.stackexchange.com |
623,964 | [
"https://physics.stackexchange.com/questions/623964",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/293064/"
] | Consider a system which is initially at a state <span class="math-container">$A$</span>. Then it is moved to state <span class="math-container">$B$</span> absorbing <span class="math-container">$Q_h$</span> amount of heat from a heat reservoir at <span class="math-container">$T_h$</span>. As the process is reversible s... | The entire gas does not heat up to Th all at once. First the boundary is at Th, and then the heat penetrates in further and further by (transient) heat conduction into the interior. So initially, the interior portion of the gas is still cold. It is like baking a turkey in the oven. First the outside heats up, and t... | In Clausius theorem for second law of thermodynamics, the temperature in the integrand is <strong>the temperature of the reservoir, not the system</strong>:
<span class="math-container">$$
\oint \frac{\delta Q}{T_{surr}}.
$$</span>
Therefore, there exists no problem about measuring the system temperature in an irreve... | https://physics.stackexchange.com |
80,751 | [
"https://softwareengineering.stackexchange.com/questions/80751",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/24488/"
] | We’re roughly midway through our transition from waterfall to agile using scrum; we’ve changed from large teams in technology/discipline silos to smaller cross-functional teams.
As expected, the change to agile doesn’t suit everyone. There are a handful of developers that are having a difficult time adjusting to agil... | I will say that there are very few software shops that are fortunate enough to have the rare distinction where Agile truly doesn't make sense as a methodology. If your entire team consists of truly exceptional software developers with a deep understanding of aspects of the business and longevity with the company and e... | my company attempted (and still attempting after years of trying) to do the same transition and so far personally, I haven't seen much success with it. During this transition, I did a whole lot of reading up on agile development and different ways/aspects/concerns/techniques and one thing I strongly agree with is that... | https://softwareengineering.stackexchange.com |
3,590 | [
"https://mechanics.stackexchange.com/questions/3590",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1848/"
] | The clamps that are attached to the car battery are corroded, I was told either of these liquids will work. Which one is better? Is there a how to guide on the exact steps I need to take? With my limited knowledge, I know...
Disconnect the battery (the order of the clamps matters I think?),
Clean the clamps and po... | What about a can of battery terminal cleaner? Should be available at any parts store (aerosol can). That plus a wire brush has always worked for me. As far as order of disconnection / connection, ground/black/negative is the first off and last on.
You could try cola or baking soda and water. They should work, bu... | Baking soda/water works fine to neutralize the acid. Big puffy or crusty chunks of white or greenish corrosion around the battery terminals are indicators that the metals have been exposed to the sulfuric acid in the battery. This happens because the seal between the lead terminals and the plastic battery case degrades... | https://mechanics.stackexchange.com |
166,612 | [
"https://chemistry.stackexchange.com/questions/166612",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/115142/"
] | In chemical kinetics, since we often have to deal with complex reactions, approximations are introduced in order to make the calculations easier. A widely used simplification is the steady state approximation, which can be applied when an intermediate is present in the reaction. This can be applied when the concentrati... | Let's look at your exact solution again.
<span class="math-container">$$
[\mathrm{B}] = \dfrac{k_1[\mathrm{A}]_0}{k_2-k_1} \left( e^{-k_1\ t} - e^{-k_2\ t} \right) \qquad
$$</span>
Let's think carefully about the criteria for the steady-state approximation, to well, approximate, this exact solution.
<ol>
<li><span cl... | Approximate solutions are equivalent to solutions are when
<span class="math-container">$k_2 \ggg k_1$</span>: this condition ensures that the intermediate reacts as soon as it is formed
<span class="math-container">$e^{-k_2\ t} = 0$</span>: for this to be true, this expression must be checked
<span class="math-contain... | https://chemistry.stackexchange.com |
392,430 | [
"https://physics.stackexchange.com/questions/392430",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75085/"
] | I am a little confused, I would like to prove that :
$$ F=U-TS $$
Using only the fact that :
$$ F=-k_b T ln(Z) $$
$$P(\sigma)=\frac{e^{-\beta} E(\sigma)}{Z}$$
$$S(E)=k_b ln(\Omega(E))$$
What I mean by using only stat mech is that I don't want to use the classical thermodynamic relation saying $S=-\frac{\partial F}... | There is a misunderstanding regarding entropy. Given a probability distribution $P(\sigma)$, the <strong>statistical entropy</strong> is defined as
$$S[P]=-k_B\sum_\sigma P(\sigma)\ln P(\sigma)$$
The extremum of this quantity with the only constrain that $\sum_\sigma P(\sigma)=1$ leads to the microcanonical ensemb... | For me the most satisfying "proof" is using Liouville's Theorem. Simplifying, using Poisson Brackets, and for a system in statistical equilibrium (recall that Liouville's theorem is nothing more than partial differential chain rule on H, a function of the phase space),
<span class="math-container">$$\frac{\pa... | https://physics.stackexchange.com |
271,656 | [
"https://dba.stackexchange.com/questions/271656",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/211152/"
] | I need to display my <code>emailType</code> in <code>DESC</code> order. Now it is a <code>varchar</code> field so I need it to be reverse alphabet order Z - A. When I run my query it is displayed in <code>ASC</code> order, and since I am using a <code>UNION</code> I can't add an <code>ORDER BY</code> clause.
What cha... | Instead of
<pre><code>'2020-04-30' = date_add(op.dataDate, INTERVAL 14 DAY);
</code></pre>
Use
<pre><code>op.dataDate = date_sub('2020-04-30', INTERVAL 14 DAY);
</code></pre>
Your first statement will be interpreted as "add 14 days to all <code>dataDate</code> and return when that is 2020-04-30." This will r... | The formulation is the main problem. After rewriting the query, the index you have can be used for the entire <code>WHERE</code> clause.
<pre><code>SELECT *
FROM op.prices
WHERE ticker = 'AAPL'
AND expDate >= '2020-04-30'
AND expDate < '2020-04-30' + INTERVAL 3 MONTH
AND dataDate = ... | https://dba.stackexchange.com |
2,466,343 | [
"https://math.stackexchange.com/questions/2466343",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/29038/"
] | I am looking for a characterization of the solutions of
$$a^2+b^2+c^2+d^2+2ab+2bc+2cd-2ca-2ad-2db=N^2$$ in positive integers.
| In case you typed the thing correctly, it is integrally equivalent to $x^2 + 4yz.$ Setting this to zero is easy, setting it to a square not too bad.
Alright, this is exactly the comment by Joffan, with $x = a+b-c-d$ and $y=b$ and $z=c.$
$$
\left(
\begin{array}{rrrr}
1 & 0 & 0 & 0 \\
1 & 1 & 0 &... | I suppose that you mean
$$
a^2 + b^2+c^2+d^2 + 2ab - 2ac - 2ad - 2bc - 2bd + 2cd =N^2.
$$
Since the left hand side is $(a+b-c-d)^2$, we are done.
| https://math.stackexchange.com |
206,825 | [
"https://math.stackexchange.com/questions/206825",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/43536/"
] | Let's say i have
N1 = -584
N2 = 110
Z = 0.64
How do i calculate from Z which value is it in range of N1..N2? Z is range from 0 to 1.
| If by $Z=0.64$ you want a number that $64\%$ of the way from $-584$ to $110,$ the expression is $-584 + 0.64(110-(-584))$
| We want to map numbers in the interval $[0,1]$ to numbers in your interval $[-584,110]$ by a function $fx)$ of the shape $f(x)=px+q$.
We want $f(0)=-584$, and $f(1)=110$, so $q=-584$ and $p=694$.
So our function is $694x-584$. Plug in $x=0.64$.
<strong>Remark:</strong> Exactly the same idea will work if our target ... | https://math.stackexchange.com |
37,851 | [
"https://cs.stackexchange.com/questions/37851",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/27250/"
] | Just need a little help understanding hardware interrupts.
As I understand (feel free to correct) a hardware interrupts occurs when hardware wants attention of the computer. In basic terms the hardware sends a message down the interrupt line which is then controlled by the PIC. The CPU receives the interrupt and carri... | In general, no, on modern platforms, not everything is a hardware interrupt -- though you could imagine a platform where it is.
On some platforms, hardware interrupts are used for all input events (including, yes, pressing a key on a keyboard or moving a mouse).
However, interrupts come with some performance implicat... | Not everything is a hardware interrupt. Hardware interrupts are mostly used to gather input from IO devices. Today, it is rather complex and quite different from how it used to work with the old 8259 PIC. Today, there's a combination of IO APIC which serves the whole CPU and local APIC which serves a specific core of t... | https://cs.stackexchange.com |
123,093 | [
"https://security.stackexchange.com/questions/123093",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/106190/"
] | Can you use transport mode with IPsec processing to provide confidentiality between two hosts in geographically separate private IP networks?
I have read somewhere that transport mode is the default mode to use to provide end to end confidentiality using IPsec processing which makes sense when the two end hosts have p... | As described, the disadvantage to allowing TKIP (also known as WPA) is that there is a known weakness. AES (used in WPA2) is more robust. Setting it to a mode that allows both will allow older devices that don't support WPA2 to connect in WPA mode, while devices that do support WPA2 will use that instead. Setting it ... | TKIP is vulnerable to an attack similar to the WEP "ChopChop" attack.
TKIP uses MIC for guaranteeing the integrity of an encrypted
frame. If more than two MIC failures are observed
in a 60 second window, both the Access Point (AP)
and client station shut down for 60 seconds. The newer
TKIP attack uses a mechanism sim... | https://security.stackexchange.com |
27,795 | [
"https://quant.stackexchange.com/questions/27795",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/-1/"
] | If I have a forecasted volatility of the log returns of say, 0.03, this is obviously transformed relative to the log I took of the returns. It strikes me that I should raise <code>e</code> to the power of the volatility I forecasted to in order to get back something "normal" looking. When I do this I get <cod... | It isn't strictly speaking possible to convert a log vol to a normal vol, although it may be possible to get a rough idea. I am assuming you only have the vol of log returns but not the actual time series here. If you had the original time series, then you would just calculate the standard deviation of the prices to ge... | If you have the vol of the log returns, that means you have the normal vol.
You can then use that vol in the the lognormal distribution formula to get the volatility of the time series of prices.
<span class="math-container">$$ \left[\exp(\sigma^2) - 1 \right]\exp(2\mu+\sigma^2)$$</span>
| https://quant.stackexchange.com |
1,582,395 | [
"https://math.stackexchange.com/questions/1582395",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/299853/"
] | $A=\{1,2,3,4,5,6,7,8,9\}$.<br>
If we omit those subsets of $A$ that have at least one of $(1,6)$ or $(2,5)$ or $(3,4)$ from all the subsets, then we'll get the answer. Can anyone tell how?
I've tried different ways, but no success. Its a multiple choice question and the choices are:
a) $32$<br>
b) $14$<br>
c) $108$<... | Use <em>inclusion/exclusion</em> principle:
<ul>
<li>Include the number of subsets containing at least $\color\red0$ out of $3$ pairs: $\binom{3}{\color\red0}\cdot2^{9-2\cdot\color\red0}=512$</li>
<li>Exclude the number of subsets containing at least $\color\red1$ out of $3$ pairs: $\binom{3}{\color\red1}\cdot2^{9-2\c... | $A=\{1,6\}\cup\{2,5\}\cup\{3,4\}\cup\{7\}\cup\{8\}\cup\{9\}$. The number of choices for subsets of $A$ satisfying the given constraint (no two elements sum to $7$) is $(2^2-1)^3\cdot2^3=216$.
This is not one of the choices, so there is something wrong in the statement of the problem.
| https://math.stackexchange.com |
23,149 | [
"https://quant.stackexchange.com/questions/23149",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/19351/"
] | Say an option with five years left before maturity has a value of $x$ today. Theoretically, under the B/S framework, what is its expected value in five years (upon maturity)? Do we assume it will simply grow in line with the five-year risk free rate? Can you please also provide any reference I can cite for this?
$E(v)... | OP is absolutely right in his approach and this is the underlying idea behind risk neutral valuation or even BS model. If Black-Scholes model assumptions hold, then a <strong>derivative payoff can always be replicated in such a way it would never provide return more than risk free interest rate</strong>, <strong>otherw... | The expected value of the option at maturity is simply $$\mathbb{E}[(S_T-K)^+]$$
Note that this is under the real world measure. In a B-S framework this value is given by
$$e^{rT}C(\alpha;S_0, K, \sigma, T)$$
Where $C(r; S_0, K, \sigma, T)$ is the B-S call option price. Hence the expected growth rate (using a simple... | https://quant.stackexchange.com |
314,326 | [
"https://electronics.stackexchange.com/questions/314326",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/134757/"
] | I understand as the clock frequency of a chip is increased, some issues arise. Probably, the most known issues are those related to the so-called "power wall", which alludes to the fact the thermal dissipation becomes an issue when the clock reaches a given threshold. However, there is something else I don't get: as th... | Higher capacitance inside the IC has several effects, among them:
1) Signal degradation. A sharp pulse going thru an RC filter will go out "less sharp". Namely, it if had a fast rise-time at the input of the RC, at its output the rise time will be slower. If it is slower, it may grow not fast enough so that the receiv... | Key formula for energy consumption:
$$SignalPower = Frequency * Capacitance * Voltage * Voltage$$
Finer resolution permits smaller FETs, thus the baseline FET will have less output current.
Finer resolution permits smaller FETS, which being smaller in all dimensions does require a shorter time for electrons to cros... | https://electronics.stackexchange.com |
124,127 | [
"https://security.stackexchange.com/questions/124127",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/92860/"
] | I understand how public key infrastructure works.
There is a private and public key, and someone may use the public key to encrypt data that can only be decrypted with the private key.
However there seems to be a flaw with this...
When you want someone, E.g Bob to send you a secret message, you send the key to him:... | Either
<ul>
<li>you give the public key to Bob when you physically meet him and mutually verify identities (as at a key-signing party), or</li>
<li>Bob verifies your public key through a trusted introducer (e.g. a Certification Authority)</li>
</ul>
This is the "Infrastructure" part of PKI.
| There are broadly two classes of methods: you deliver the public key in person (which assumes you yourself are immune from tampering in transit, of course), or you use a trustworthy intermediary to vouch for it, say, by signing a certificate — cryptographically or otherwise — or carrying it in a sealed and hopefully ta... | https://security.stackexchange.com |
13,533 | [
"https://mathoverflow.net/questions/13533",
"https://mathoverflow.net",
"https://mathoverflow.net/users/630/"
] | Suppose $C \subset \lbrace 0,1\rbrace^{n}$ is a binary code with distance $\delta * n$, for $1/2 < \delta < 1$. Can $|C|$ be arbitrarily large (if I allow n to be arbitrarily large)? Note that the Hadamard code gives you $\delta = 1/2$.
| No. If we take $\{-1/\sqrt n,1/\sqrt n\}^n$ instead of $\{0,1\}^n$, the problem reduces to asking if we can have many unit vectors $v_j$ with pairwise scalar products $-\gamma$ or less where $\gamma>0$ is a fixed number. But if we have $N$ such vectors, then the square of the norm of their sum is at most $N-\gamma N... | Gama doesn't have to be negative, in fact if delta is smaller than 1/2 gamma will be positive. It's known for Hadamard codes that arbitrarily large codes exist, and it seems intuitive that if the distance between vectors should be smaller then large codes should exist still, but I don't have a proof
| https://mathoverflow.net |
369,733 | [
"https://softwareengineering.stackexchange.com/questions/369733",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/170173/"
] | I'm on a new CRM dev team. And simply put, I haven't seen sprint execution such a mess in my whole professional career.
I have a deployment plan moving forward. I have an idea how I want continuous testing done in our test environment. However, I am torn on how often to push to test; because some sprints have alot o... | Let me answer the actual question which is:
<blockquote>
When it isn't right to add types to a well known namespace?
</blockquote>
The question should rather be asking: <em>when it's right</em> to do so because usually it's never right to add anything to well know namespaces. You only do this when you want to use a... | If you have enough code that you want to re-use, create a company namespace. You can organize diffrent code into different libraries as well so that you don't need to include all your company's shared code in every app.
An example of how I do it is a database class library that includes the oracle managed data access ... | https://softwareengineering.stackexchange.com |
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