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260,205 | [
"https://electronics.stackexchange.com/questions/260205",
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"https://electronics.stackexchange.com/users/58335/"
] | I want to use the HD44780 character LCD (commonly available in 16x2 characters, though I am using the 20x4 version) in an industrial application but since it will be on 24x7, I am just a bit worried about it lifespan expectancy. I hope it could last 5-10 years.
Have been searching all around, including the datashe... | My experience is that the 1602 type LCD display module will last a long time. What will not last a long time is the backlight if your module has one. In particular the ones I've used that have a white LED backlight last about 3 years before the LED brightness dims to the level as to render the display to about 10% of i... | There is no inherent wear-out mechanism except in the backlight LED. The types with zebra connectors are more sensitive to moisture and if there are PCB contamination problems then the part may not tolerate humidity well.
Minimize those problems by keeping them cool, dry, away from vibration and shock, and keep the ba... | https://electronics.stackexchange.com |
51,482 | [
"https://softwareengineering.stackexchange.com/questions/51482",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/4472/"
] | While attempting to make a list programming subjects/topics that were unclear to me, I was unable to come up with anything.
I know I can't be clear on everything. What steps can I take to get an accurate self-assessment of my knowledge and "know what I don't know"?
| I find the best way to find holes in your own knowledge is to try and <strong>explain the topic to someone else</strong>.
Find a classmate who admits they don't fully understand topic X, and attempt to explain topic X to them.
If you are successful (it clicks for you, it clicks for them), then you probably understand... | Try from the other direction: What do feel you know well?
Make that list. Write down the topic and a blurb describing what you know about it.
Go and look up what you should know for your class. If you missed something on your list, you are unclear on that topic. If your description about what you know about that to... | https://softwareengineering.stackexchange.com |
93,373 | [
"https://physics.stackexchange.com/questions/93373",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | It is well known that the speed of light $c$ can be interpreted as the speed limit for information propagation. Similarly, the Planck's constant $h$ is interpreted as the minimum quantum package of action/entropy. Is there a similar interpretation for the Newton's constant $G$?
| Any interpretation in some sense underlines the property that you find interesting.
Maybe Schwarzschild radius or Planck's mass could be used to give a satisfactory interpretation of G. Otherwise it's just a coupling const. like the fine structure const.
| I do not know of any such "limit" interpretation of $G$. The universal gravitational constant $G$ is defined by the Law of universal gravity:
Magnitude of the mutual attractive force two bodies exert on each other is given by
$$
F = G\frac{m_1 m_2}{r_{12}^2},
$$
where $m_1$, $m_2$ are masses of the two bodies and $r_{... | https://physics.stackexchange.com |
33,381 | [
"https://scicomp.stackexchange.com/questions/33381",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/17294/"
] | We've recently ported our Python/Fortran simulation code to a new supercomputer. <em>Some</em> (not all) of the tests (simulations) that we've run on the new platform yield results that are significantly different from those we got on the "old" cluster. We see <span class="math-container">${\cal O}(1)$</span> numerical... | If <span class="math-container">$A$</span> is of full column rank and <span class="math-container">$A^{T}A$</span> is non-singular and well-conditioned, then you can compute the pseudoinverse as:
<span class="math-container">$ A^{\dagger}=(A^{T}A)^{-1}A^{T} $</span>.
This will be faster than computing a QR or SVD f... | You can "frontend" the SVD of a tall/skinny matrix using a QR decomposition, then just SVD the remaining small/square matrix R. Here's a snippet of matlab code that computes the pseudoinverse based on this idea:
<pre><code>clear all
close all
% Make input.
I = 10000;
J = 20;
A = rand(I,J);
% Pseudoinverse B := pinv(... | https://scicomp.stackexchange.com |
26,484 | [
"https://scicomp.stackexchange.com/questions/26484",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/3761/"
] | I was thinking about the following problem:
Suppose there is a positive semidefinite matrix $X$ of size $n$ (for example, a kernel). Suppose $X$ can be approximated as a low rank matrix, $X\approx GG^T$.
Is there a way to find the $k$-largest/smallest values of each row of $X$ without computing it explicitly and goi... | 1) You have misinterpreted the order the fft2 output elements are stored. This is a very common mistake, since it is very easy to get confused. Thankfully, there is an easy way to avoid such bugs. Arrange the Fourier space vectors the "natural way"
<code>% Fourier space vectors
kx = 2*pi/Lx*[-Nx/2:Nx/2-1]';
ky = 2*pi... | I just tried running this, and it seems to remove the oscillations, so I'll add this as an answer. I suggest you change your code as follows, before your linspace definition for coordinates, add and modify the lines to read:
<pre><code> x = linspace(0, Lx, Nx+1)'; x = x(1:Nx);
y = linspace(0, Ly, Ny+1)'; y = y(1:Ny);... | https://scicomp.stackexchange.com |
176,513 | [
"https://physics.stackexchange.com/questions/176513",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/77967/"
] | I'm trying to numerically integrate the motion of an object (say, a falling vertical cylinder). Here, there's a drag force: the wind "acting" on the body (presumably adding horizontal velocity) and the air itself slowing down the vertical motion.
Is it correct to calculate both forces with the drag equation, $F_D = \f... | Yes, the force points along the vector of the relative velocity between the object and the air.
Quadratic drag is an interesting phenomenon. You have to calculate the net velocity vector (which includes a horizontal and vertical component) and compute the force along that axis; when you then decompose it into horizont... | "The vertical drag is greater" Could this be "lift"?
The vertical and horizontal velocity components do indeed produce a higher net velocity vector, but the vertical and horizontal kinetic energy components also have a Velocity squared function.
Interestingly, if you dropped an unpowered object from a tower in a 2 ... | https://physics.stackexchange.com |
2,532 | [
"https://physics.stackexchange.com/questions/2532",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/66/"
] | I know that string theory is still under heavy development, and as such it still can't make predictions (or not that many predictions anyways).
On the other hand, it is clear from the number of years this theory has been under development and from the large number of theoretical physicists studying it, that it is cons... | Some random points in support of ST, with no attempt to be systematic or comprehensive. I will not get into a long discussion, if someone does not find this convincing I'd advice them not to work on the subject. I also don't have the time to elaborate or justify the claims below, just take them at face value, or maybe ... | The main motivation is that string theory incorporates gravitation and gauge theories in a unique framework, avoiding the problems of General Relativity and Quantum Field Theory.
Besides this basic fact, I would say that a great theoretical success of the theory is black hole physics. For the first time we have a quan... | https://physics.stackexchange.com |
2,089,273 | [
"https://math.stackexchange.com/questions/2089273",
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] | We have a structure: $\mathbb Q=\langle \mathbb Q,\,+,\,-,\,*,\,0,\,1 \rangle$
Question: Does $\mathbb Q$ contain a substructure which is not a field?
I have in my notes that there is such a substructure and it is $\mathbb Z$ because $\mathbb Z \subseteq \mathbb Q$
But I don't think that I fully understand it.
We... | I don't know what "structure" is supposed to mean. But I can easily explain to you why $\mathbb Z$ is not a field.
It is, as you state, because the multiplicative inverse axiom fails. For $\mathbb Z$ to be a field, it must be true that for all $x \ne 0$ in $\mathbb Z$, then exists a $y \in \mathbb Z$ so that $x*y = y... | The answer to your question depends on what kind of substructure you're looking for. (That might have been explained in class but didn't get to your notes.)
There is no subset of $\mathbb{Q}$ that is itself a field with the usual addition and multiplication.
$\mathbb{Z}$ is a subring of $\mathbb{Q}$ when you think of... | https://math.stackexchange.com |
308,018 | [
"https://physics.stackexchange.com/questions/308018",
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] | Apparently the formula that expresses the possible frequencies in a closed pipes is the following:
$$f = (2n+1)\frac{v}{4L}$$
Where $n=0, 1, 2, 3, ...$, $v=$ the speed of sound and $L=\frac{\lambda}{4}$ (divided by 4, for some unknown reason)
On the flipside you have the following formula for open pipes:
$$f = n\fr... | I will only consider taut, inextensible ropes. This represents an approximation regime where tension is much less than the Young's modulus of the rope material times the cross-sectional area of the rope. (As we will see this condition is enough to guarantee the conclusion for straight segments of the rope as long as th... | The answer to that question in one word is <strong>symmetry</strong>.
Indeed, let us assume that the two ends of the rope A and B have co-ordinates $-d$ and $d$ along an x-axis. The rope is supposed to be homogeneous, in static equilibrium. It does not matter whether it has a positive mass or not, whether it is extens... | https://physics.stackexchange.com |
683,813 | [
"https://physics.stackexchange.com/questions/683813",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | I found in a book the Maxwell equations written in a form different that other books and wikipedia,
<span class="math-container">\begin{align}
\nabla\cdot E &=\frac{\rho}{\epsilon_0}\\
\nabla\cdot B &=0\\
\nabla \times E &=\frac{\partial B}{\partial t}\\
\nabla \times B &=-\frac{1}{c^2}\frac{\partial E}... | These equations are wrong. Among other things, they do not obey charge conservation, since according to them
<span class="math-container">$$
\begin{align*}
\vec{\nabla} \cdot \left(\vec{\nabla} \times \vec{B}\right) &=-\frac{1}{c^2}\vec{\nabla} \cdot \left( \frac{\partial \vec{E}}{\partial t}\right) +\frac{1}{\eps... | They seem to have multiplied each of <span class="math-container">$B,\,J$</span> by <span class="math-container">$-1$</span>.
| https://physics.stackexchange.com |
87,035 | [
"https://physics.stackexchange.com/questions/87035",
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"https://physics.stackexchange.com/users/34162/"
] | Would it be possible to develop oculars that would enhance the vibrancy of color? I know there are many digital filters to improve vibrancy, but are there physical devices able to produce the same effect? Would it ever be physically possible to produce a device small enough to be worn like a contact lens?
This is quet... | I'll assume that "enhance the vibrancy of colour" means something like turning up the saturation in a photo editing application. I think it's highly unlikely that this could be accomplished using analogue optics, because it's a highly nonlinear operation. This is because we need to block or let through light in three d... | Well, it would seem that you are interested in creating some false color perspective; for some reason you don't explain.
The very familiar "color triangle", whether the original 1932 version or the later 1960s revision, is the very best experimentally derived representation of the complete range of hues that are disti... | https://physics.stackexchange.com |
222,514 | [
"https://electronics.stackexchange.com/questions/222514",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/102777/"
] | If i solder together enough binary adders, binary subtractors is it possible for it to work like a modern (very very slow) CPU (Such as one found in a graphics calculator).
| Yes! One can build such a real slow processor with discreet logic put together. Or implement it in an FPGA.
(Assuming this may not have an immediate application and just for thought! Apologies if it is too lengthy. Just ideation!) Here are some basic steps one can consider-
<ol>
<li>Develop an instruction-set first.... | In addition to combinational logic (which can form adders and subtractors), you'll need sequential logic (which allows the computer to have memory).
Yes, with enough components you could build a CPU.
Note that graphics calculator's CPUs can run at over 15 MHz. It is unlikely you could build a useful CPU that fast fro... | https://electronics.stackexchange.com |
233,057 | [
"https://softwareengineering.stackexchange.com/questions/233057",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/100991/"
] | <h1>Use Case</h1>
What are the use cases for creating a <strong>one-to-one</strong> relationship where the parent points to the child compared to a child pointing to the parent? If there is no difference, is one preferred over the other?
<h2>Example</h2>
<pre><code>+---------+ +-------+ +--------+ +---... | It can effect the representation of your structure if you marshal it to XML or JSON. For example, do you want "parent" to be the top element or object, or do you want "child" to be the top element or object?
A lot of times it depends on how the application uses the data. If the primary users of a system are children, ... | In terms of database design is quite more logical to have the child store the relationship back to the parent. Primarily, because keeping the information for each child in the parent's is inflexible (assuming you use fields for child's IDs), like in your first example, since you cannot dynamically allocate more than a ... | https://softwareengineering.stackexchange.com |
205,425 | [
"https://softwareengineering.stackexchange.com/questions/205425",
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"https://softwareengineering.stackexchange.com/users/57138/"
] | I have a bunch of calls to a method that may or may not need to be made depending on whether certain features are enabled or not. As such, I've wrapped these calls in <code>if</code> blocks checking the enabled statuses.
The arguments to the method in each of these calls use some long variable names, so I've broken th... | Usually when something feels awkward like that, it's because you need to refactor your objects to more logically allocate the responsibilities. If you have a bunch of these, my personal preference would be to put them in a list, and call them like this:
<pre><code>for feature in enabledFeatures:
feature.process()... | You may not have a choice here: if evaluating the <code>ReallyLongFeatureZSettingAName</code> property when <code>FeatureSettings.FeatureZIsEnalbed</code> equals <code>false</code> results in throwing an exception, the idea of passing the "guarding" <code>FeatureSettings.FeatureZIsEnalbed</code> to <code>TheMethodImCal... | https://softwareengineering.stackexchange.com |
82,195 | [
"https://security.stackexchange.com/questions/82195",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/67785/"
] | I have a Thompson TG585v7 router/firewall whose firewall is configured to <code>FORWARD</code> several ports to a computer <code>X54</code> within the LAN.
These ports are in the range <code>1024 through to 2500</code>
That <code>X54</code> computer is now gone and so there is nothing "listening" on those final de... | For a <code>SYN</code> scan of the sort you are performing, <code>nmap</code> defines an "open" TCP port as one where a <code>SYN</code> packet sent by <code>nmap</code> elicits an <code>ACK</code> packet from the target system. Assuming that the firewall is configured sensibly, and that the TCP/IP stack is programmed... | <ol>
<li>Yes. Although there are situations where an ostensibly open port may not mean that you can communicate with it in a meaningful way. </li>
<li>Not necessarily, like you just said, the firewall is waiting to forward those ports. Unless you have changed the firewall to no longer be waiting for data forward, it wo... | https://security.stackexchange.com |
188,787 | [
"https://security.stackexchange.com/questions/188787",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/164764/"
] | I have a web app. Existing users can invite new users by sending a mail throw the web app.
If the user fails 4 consecutive times I block the acount for 5 minutes.
Currently there is no important information in the application.
The problem with the current policy is:
<ol>
<li>If a malicious user B want to block the... | You have to protect for the greater threat. You have 2 scenarios:
<ol>
<li>Malicious user/troll trying to deny service to a fellow user. This is a relatively common concern but is rare to see in practice</li>
<li>Attackers brute forcing accounts: Although your site may not have any data useful for an attacker the cred... | As asked, I'll make up my own answer.
<blockquote>
If a malicious user B want to block the user A he could try to log with A username's 4 times every 5 minutes. Then A couldn't log to the app.
</blockquote>
That's the issue when locking accounts: you don't know if user is actually legitimate until they passed the l... | https://security.stackexchange.com |
156,771 | [
"https://softwareengineering.stackexchange.com/questions/156771",
"https://softwareengineering.stackexchange.com",
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] | I have been using an agile methodology (SCRUM) for about three years now and I see certain advantages to it, especially in the short-term feedback at many levels (from customers having early access to implemented features, from testers that can test features as soon as they are implemented, from other developers that c... | <blockquote>
On the other hand, developing some complex feature in small increments, with daily commits and continuously rethinking the code when it gets unstructured is not allowing me to produce really good design.
</blockquote>
Then don't do that.
Not everything fits into the nice agile box. Often times a produ... | It is very possible to implement in small increments and end up with well-structured maintainable code. In theory, it's very simple: if you ensure that the code is well-structured after each change, it will always be well-structured. Your code is becoming poorly structured because you are continuing to add code when ... | https://softwareengineering.stackexchange.com |
130,896 | [
"https://security.stackexchange.com/questions/130896",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/118432/"
] | Recently, I have discovered a security flaw in a business website. This website has a password-protected "Partners Area", and like many websites it provides a form to reset the user's password.
When a user asks for a password reset for his nickname, a new password is sent to their email address and that password becom... | Your question is: <em>Are security flaws acceptable if no much harm can derive from them?</em>
The answer is <strong>yes</strong>, if decided by business while understanding the consequences.
What you are doing is called a risk assessment. For each risk you must highlight the consequences for your company when it is ... | Yes. This is a problem - a big problem.
Lately I found a design flaw in a business' webshop that allowed me to insert innocent notes in other visitors' charts.
Seems innocent, and only annoying, until I looked further and found that I was also able to insert Javascript code (XSS) into those notes. So in other words, I... | https://security.stackexchange.com |
302,309 | [
"https://physics.stackexchange.com/questions/302309",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/55856/"
] | Assume a truck of mass 1 ton braking from 60mph to 0 on a road surface.
From the reference frame of the road, the following energy is transferred to the brakes: 1 ton * 60mph^2 / 2 = 1800 ton mph.
From the reference frame of the truck, the following energy is transferred to the brakes: 1 ton * 60mph^2 / 2 = 1800 ton ... | The energy transferred to the break is given by the friction force between brakes and tire (or rather the part of the brake attached to the tire), times the relative velocity of tire and breaks, integrated over the total time the break is acting (this is, it is force times distance, as usual).
Clearly, the <em>relati... | The question seems to be a special case of the following question: A particle of mass $M$ traveling at speed $v$ and a second particle of mass $m$ traveling at speed $v+V$ undergo a totally inelastic collision. Calculate the change in kinetic energy. Show that it is independent of $v$. (In the special case of the qu... | https://physics.stackexchange.com |
69,111 | [
"https://stats.stackexchange.com/questions/69111",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/17308/"
] | I've been recently learning about mixed effects models (e.g. via Fitzmaurice, Laird, and Ware 's book <em>Applied Longitudinal Analysis</em>) as well as Bayesian hierarchical models (e.g. via Gelman and Hill's book <em>Data Analysis Using Regression and Multilevel/Hierarchical Models</em>)
One curious thing I've noti... | Yes it is. I don't know the commands in <code>R</code> but in <code>SAS PROC MIXED</code> you can have variables at either level in the MODEL statement and you can include interactions. e.g., a split plot design
<pre><code>proc mixed;
class A B Block;
model Y = A B A*B;
random Block A*Block;
run;
</code></pr... | If we define levels differently, mixed models may not be able to do what Bayesian models can. The other alternative is structural equation modeling.
For e.g When variables A,B drive C. Variables A,B,C,D, drive E.
You have equation : E = oA + pB + qC + rD + z ;<br>
C = mA + nB + k ; <br> <br>where ... | https://stats.stackexchange.com |
56,591 | [
"https://electronics.stackexchange.com/questions/56591",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/18472/"
] | I have an input sensor with a signal level from 2.3 to 3.5 volts that I want to sample with an ADC. I want to be able to shift this range for the ADC from 0 to 3.5 volts to take full advantage of the ADC dynamic range. I used a summing op amp with an LM741 but it seems to be stuck at 2.3 VDC output all the time.
So ... | The solution ends up being very, very dependent on the exact model of your car and the physical distribution of the outlets within the vehicle.
You'll need a service manual for your car that has a complete wiring diagram. Check first before you buy one, as many only have block diagrams or step-by-step electrical test... | I've done this to my last 3 cars. All of them are Ford Escape Hybrids (2008, 2010 and 2012). The for the first car I was in Circuit City in late 2007 to get Bluetooth installed (the 2008 model didn't have SYNC) and I asked the installer to switch the outlet. He asked his boss if it was possible and said sure, for an ... | https://electronics.stackexchange.com |
1,414 | [
"https://mechanics.stackexchange.com/questions/1414",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/511/"
] | Still working on the 2000 Honda CRV. Trying to get the lock assembly out of the door so I can work on it, but I'm having trouble disconnecting it from the outside door handle.
part #8 plugs into the handle assembly, but I can't see how to disconnect it. Is there a special trick to getting this disconnected, or should... | Turns out part 8 is not designed to be easily removed from the handle assembly. I ended up removing the exterior handle assembly from the door, and unscrewing part 8 from the lift arm of the lock assembly.
| Pry it with a small screwdriver, it's just a snug fit. This first picture is what that rod is held in with
<img src="https://i.stack.imgur.com/q7mwc.jpg" alt="enter image description here">
Some latches like the one below have a retaining clip that hooks onto the rod, but your's isn't one of them.
<img src="https://... | https://mechanics.stackexchange.com |
139,256 | [
"https://physics.stackexchange.com/questions/139256",
"https://physics.stackexchange.com",
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] | I need someone to help me understand this equation:
$ \Delta p = qEt$ where $q$ is the charge, $E$ is the electric field and $t$ is in seconds. I thought that we were supposed to write momentum in this form: $p = mv$
| The electric field strength can be represented by the equation $$E=F/q$$ where $E$ is the electric field strength in N/C, $F$ is the force in Newtons, and $q$ is the charge in Coulombs. If we take the equation that you provided: $$\Delta p=qEt$$, and substitute $F/q$ in for $E$, then $$\Delta p=q\frac Fq t$$ which sim... | The equation simply says that the variation of momentum is equal to the force impulse. For a constant electric field $E$, we have that the force is $F=qE$. Then, we have
$$\Delta p=m\Delta v=mat=Ft=qEt$$
| https://physics.stackexchange.com |
32,622 | [
"https://physics.stackexchange.com/questions/32622",
"https://physics.stackexchange.com",
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] | Leonard Suskind gives the following formulation of the energy-momentum tensor in his Stanford lectures on GR (#10, I believe):
$$T_{\mu \nu}=\partial_{\mu}\phi \partial_{\nu}\phi-\frac{1}{2}g_{\mu \nu}\partial_{\sigma}\phi \partial^{\sigma}\phi$$
In an intro to GR book I find this formulation of the same:
$$T^{\mu \... | <strong>0. Caveat Lector:</strong> This was done before I drank my morning coffee, so there may be some errors in the reasoning (well, the physical reasoning, the mathematics should be kosher).
<strong>1. Perfect Fluid.</strong> So we have two stress-energy tensors here. One is the stress energy tensor for a perfect f... | Keep in mind that the stress-energy tensor is described by the matter and energy fields. Each model of matter or field will have different expressions for this tensor
the first one is for a scalar field $\phi$ under the usual $E^2 - c^2 P^2 = m^2 c^4$ relativistic identity defined by the Klein-Gordon equation, the sec... | https://physics.stackexchange.com |
231,723 | [
"https://dba.stackexchange.com/questions/231723",
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"https://dba.stackexchange.com/users/174256/"
] | I have a site where a users can comment on posts or reply to a comment. The user can also like replies or comments. Replies are not nested, so a reply doesn't have a reply. However, there is another field called <code>reply_to</code> within the reply table. Here's my current schema:
<pre><code>Comment
id
user (foreign... | Start with getting all the required counts:
<pre><code>SELECT
post_id,
meta_value AS required_count
FROM
this_table
WHERE
meta_key = 'requirement'
</code></pre>
Then derive another row set, which is the <em>actual</em> counts per <code>post_id</code>:
<pre><code>SELECT
post_id,
COUNT(*) AS actual_count
F... | Perhaps this is what you want:
<pre><code>INSERT INTO this_table
( post_id, meta_key, meta_value )
SELECT ??var_post_id, 'complete_date', NOW())
FROM this_table
WHERE post_id = var_post_id
AND meta_key = 'requirement'
AND ( SELECT COUNT(*)
FROM... | https://dba.stackexchange.com |
2,555,418 | [
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"https://math.stackexchange.com",
"https://math.stackexchange.com/users/405754/"
] | My answer is in general no, because n-term (as n tends to infinity) should go to zero, but here I can choose my n-th term to be $a_2$. Is my reasoning right, if yes, then can someone rigorously write my line of reasoning. Also can someone give me an example which shows the answer is no?
In case question is not clear, ... | No. Take for example $a_n=\dfrac{(-1)^n}{n}$. Then $\sum_{n\geq 1}a_n=-\ln(2)$,
$\sum_{n=1}^{\infty} a_{2n}=+\infty$ and $\sum_{n=0}^{\infty} a_{2n+1}=-\infty$.
P.S. Note that if $\sum_{n=1}^{\infty}a_n$ is conditionally convergent then
$$\lim_{N\to +\infty}\sum_{n=1}^{N} a_{2n}+\lim_{N\to +\infty}\sum_{n=0}^{N} a_{2n... | Counterexample: $\sum_{n=1}^\infty \frac{(-1)^n}{n}$.
| https://math.stackexchange.com |
138,598 | [
"https://dba.stackexchange.com/questions/138598",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/37064/"
] | This is something I am just interested in knowing if it is possible.
Could I write an SQL query that could return the text of itself as a variable?
Where I might use this would be on things like reports that I might want to return a variable that saves the actual query that ran to generate the report, or as a debuggi... | There is no way that a query can output its own text, that I am aware of, but you can certainly capture it using sys.dm_exec_requests.
You can try this:
<pre><code>-- Query to Run
SELECT 100 / 10
-- Query Text Capture
DECLARE @Query NVARCHAR( MAX )
SET @Query = ( SELECT text /*, query_plan*/
FROM sys.dm_exec_req... | Thanks Alex
I was able to use what you had written to make a query that will do what I want.
This should let me implement my own preprocessor logic.
<pre><code>if(1 = 1)
BEGIN
DECLARE @Query NVARCHAR( MAX )
SET @Query = ( SELECT text /*, query_plan*/
FROM sys.dm_exec_requests AS er
CROSS APPLY sy... | https://dba.stackexchange.com |
99,612 | [
"https://electronics.stackexchange.com/questions/99612",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/37087/"
] | I've connected a scope probe directly to the ground clip of the scope. I then observe the signal on the scope and it's reading 0, as expected. I set my trigger to be 1V above the 0V reading it currently has, put it to single, set the timebase to 100ns/div. At this point, i plug a standalone usb thumb-drive into the ... | When we talk about a digital representation of a signal it is implied that we can store this representation in memory, which requires that the amount of information (bits) is finite.
An analog signal has an unbounded amount of information, both in its level and in its variation in time. To make the amount of informati... | A discrete time signal is just a sequence of numbers. They could be real numbers, mathematically.
If they're in a computer, they need to be represented somehow, and that representation means that they can't be <strong><em>infinitely</em></strong> precise, however they <em>can</em> be <strong><em>arbitrarily</em></str... | https://electronics.stackexchange.com |
121,313 | [
"https://softwareengineering.stackexchange.com/questions/121313",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/28565/"
] | I was looking on the internet for common interview questions. I came upon one that was about finding the occurrences of certain characters in an array. The solution written right below it was in my opinion very elegant. But then another thought came to my mind that, this solution is way better than what came to my mind... | I don't think it's so terrible, as long as you <em>understand</em> the solution and are able to explain it and adapt it to new situations. And you worry that you weren't as "elegant"? Now you've seen a better example of "elegance" and you can <em>learn</em> from this how to be more elegant.
In general, I think it's pr... | I'll ask you a question, Do you usually work of your own knowledge or do you query the web to expand your knowledge and solve a problem better than you could on your own? Or perhaps you reference a book.
"Borrowing" knowledge as you put it is nothing more that doing research in order to improve on your best solution.... | https://softwareengineering.stackexchange.com |
753,622 | [
"https://physics.stackexchange.com/questions/753622",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/351968/"
] | In newtonian mechanics, if a body is experiences an acceleration that is perpendicular to the direction of motion at all times, it moves in a circle and the magnitude of it's velocity does not change. How does this phenomenon look like with relativistic velocities?
Suppose that a body moves with constant velocity <spa... | I think it's worth taking a moment to clarify some things. The phase space probability density <span class="math-container">$\rho:X\rightarrow \mathbb R$</span> (where <span class="math-container">$X$</span> is the phase space, typically something like <span class="math-container">$\mathbb R^{6N}$</span>) is defined su... | You need to be careful. If I understand correctly, your system has the Hamiltonian (normalising mass):
<span class="math-container">$$
H = \sum_i\frac{p_i^2}{2}
$$</span>
so the support of your ensemble is actually a cylinder i.e. isomorphic to <span class="math-container">$\mathbb S^{dN-1}\times\mathbb R^{dN}$</span>,... | https://physics.stackexchange.com |
138,770 | [
"https://physics.stackexchange.com/questions/138770",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/59523/"
] | I was reading Griffiths' <em>Introduction to Electrodynamics</em>, specifically Section 9.2.2 on plane waves. I can see that if we want a transverse wave traveling in the <span class="math-container">$z$</span> direction that we are only going to want our waves to have <span class="math-container">$x$</span> and <span ... | Let's take a slightly more general case: Consider a wave with wave vector <span class="math-container">$\vec k=(k_x,k_y,k_z)$</span>, with the electric field given by <span class="math-container">$$\vec E=\vec E_0\ e^{i(\vec k \cdot \vec r-\omega t)} $$</span>
where <span class="math-container">$\vec r=(x,y,z)$</span>.... | In this answer, I'll start with a real expression for $E$, because I think the exposition is clearer. There is no loss of generality in doing that, because the real expression will always be equivalent to the real part of the complex version of $E$, for some appropriate choice of the origin. Thus, my starting point i... | https://physics.stackexchange.com |
67,647 | [
"https://physics.stackexchange.com/questions/67647",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/25631/"
] | To my understanding, matter and energy are one and the same. Shifting from $E$ to $M$ in Einstein's famous equation requires only a large negative acceleration. If $M$ really is $E/c^2$, does that make matter the solid state of energy? I've read a lot about positron-electron collisions at high energies creating larg... | Energy and matter are not the same. Matter is a type of thing, whereas energy is a <em>property</em> of a thing, like velocity or volume. So your premise is flawed. In particular:
<ul>
<li>there's no such thing as "a solid state of energy" - hopefully it makes sense that a property of something does not have states</l... | The thing about energy becoming particles is not entirely true. Quantum mechanics explains that particles themselves are waves. The energy that forms mass, however, is not a part of the particles themselves. For subatomic particles such as electrons and quarks, their mass is caused by their interaction with the Higgs... | https://physics.stackexchange.com |
517,278 | [
"https://physics.stackexchange.com/questions/517278",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75502/"
] | I read that electron can exhibit particle and wave like property, but in particle form it has mass then when in wave form... Where did it mass go?
| For waves, "mass" is just finite frequency at zero wave number. The free particle dispersion relation (with <span class="math-container">$\hbar = c = 1$</span>) is:
<span class="math-container">$$ \omega = \sqrt{\omega_0^2 + ||\vec k||^2}$$</span>
so at zero wave number <span class="math-container">$\omega = \omega_0... | Your intuition about what "mass" is is what's causing your problem. If you try and take mathematical descriptions of the world too literally you will hit a dead end pretty fast. In this example you're right in thinking that given your usual understanding of what mass is it seems strange that a wave would have such a pr... | https://physics.stackexchange.com |
84,902 | [
"https://mathoverflow.net/questions/84902",
"https://mathoverflow.net",
"https://mathoverflow.net/users/14454/"
] | Can someone point out the gap in this argument. Consider a simply-connected Lie group with the (-)-connection. This connection is flat and so the sectional curvatures are zero. Then, by the Cartan-Hadamard theorem and simple-connectedness, the Lie group must be diffeomorphic to ${\Bbb R}^n$. However, I don't think that... | As Emerton pointed out, you need to be careful about the connection. Cartan-Hadamard theorem is a statement involving the curvature of the Levi-Civita connection determined by some metric.
If $G$ is a Lie group equipped with a <strong>bi-invariant</strong> metric $h$, then this metric induces a metric $\langle-,-... | Your connection is not Riemannian; it has torsion, so cannot be the Levi-Civita connection of any Riemannian metric. The Cartan-Hadamard theorem isn't even true in Lorentzian geometry, and so you wouldn't expect it for a flat connection which isn't torsion free.
| https://mathoverflow.net |
112,733 | [
"https://mathoverflow.net/questions/112733",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1682/"
] | If $\kappa$ is an inaccessible cardinal then the tree property at $\kappa$ is equivalent to weak compactness of $\kappa$, which implies that $\square(\kappa)$ fails---that is, that every coherent sequence of clubs of length $\kappa$ can be threaded.
I am wondering about other implications involving square and the tree... | The answers to the second and third questions are no and yes, respectively. I don't know the answer to the first question.
For the second question, let $\lambda$ be regular and let $\kappa > \lambda$ be weakly compact. Then forcing with $\mathrm{Coll}(\lambda, <\kappa$) yields a model in which $\kappa = \lambda^... | To complete the accepted answer to my question (which addresses parts 2 and 3) perhaps I should mention here that the answer to part 1 is no: If $\delta$ is a supercompact cardinal and $\kappa$ is the least inaccessible cardinal above $\delta$ then $\square(\kappa)$ fails but $\kappa$ is not weakly compact.
| https://mathoverflow.net |
38,523 | [
"https://security.stackexchange.com/questions/38523",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/27988/"
] | I have the problem that I usually use 4 passwords that I use quite often. I use the first two strong passwords for very important services (e.g. Email, PayPal,..), and the other two not so strong for not so important services. The problem comes when I forget the password of something that I do not recall how important ... | <blockquote>
I have the problem that I usually use 4 passwords that I use quite often.
</blockquote>
All of your other trouble stems from this. If you're concerned about security (and you should be) then <strong>stop it</strong>.
<blockquote>
Is this a serious security concern for me?
</blockquote>
Most definit... | I'd say "not very much" since wrong passwords are almost never stored: unless you <em>failed</em> to obtain login, the password that was <em>right</em> is usually a much juicier bit of information to grab.
It is recommended not to save <em>wrong</em> passwords in logs etc., since they might disclose the <em>real</em> ... | https://security.stackexchange.com |
142,220 | [
"https://electronics.stackexchange.com/questions/142220",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/30449/"
] | <strong>Context:</strong> One of my colleague is arguing I can't use one of my baseline equipment for a long lifetime (15years) product because it is not an "industry standard" and might become obsolete and unsupported during that timescale.
<strong>Question:</strong>
So when should we consider a particular equipment... | Solving the first part gave me 216.667 us. I would double check your math there.
$$100000 \cdot 1.3 = 130000$$
$$\frac{130000}{600 \cdot 10^6} = 2.167 \cdot 10^{-4}$$
Using this gives you the correct solution.
| You've got a mistake in the first equation: I get a CPU time of \$2.2 \cdot 10^{--4} s\$, or ~200 us.
The second equation can be reworked to \$I = \dfrac{f \cdot T_{CPU}}{CPI}\$
| https://electronics.stackexchange.com |
101,974 | [
"https://softwareengineering.stackexchange.com/questions/101974",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/20636/"
] | I'm about to extend a system containing two separate systems. Or domains, if we see the system as a domain level.
<strong>Today</strong>
One domain is used internally. The other is public, which means it is more exposed to whatever can happen "out there". Services of some kind (few options apply) perform operations b... | Let's think of this from the perspective of potentially splitting up one database into two, in order to highlight the differences.
The main <em>disadvantages</em> of a split are:
<ul>
<li>Inability to use DRI on common columns. Hardly a deal-breaker but you do need to start designing your application(s) around the po... | If it will remain 2 systems then changes to the implementation of one of them should not effect the other. That requires a clear separation and to do that I would:
<ol>
<li>Only allow access to each database by the system that owns it.</li>
<li>Access the other system through clearly defined interfaces.</li>
</ol>
| https://softwareengineering.stackexchange.com |
1,014,250 | [
"https://math.stackexchange.com/questions/1014250",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/128422/"
] | Let $\alpha$ be the probability that a geometric random variable $X$ with parameter p is an even number
a) Find $\alpha$ using the identity $\alpha=\sum_{i=1}^{\infty}P[X=2i]$
b)Find $\alpha$ by conditioning on wether $X=1$ or $X>1$
My attempt for a):
$$\alpha=\sum_{i=1}^{\infty}P[X=2i]=\sum_{i=1}^{\infty}p(1-p... | We have
$$\eqalign{
P(\hbox{$X$ is even})
&=P(\hbox{$X$ is even}\mid X=1)P(X=1)+P(\hbox{$X$ is even}\mid X>1)P(X>1)\cr
&=P(\hbox{$X$ is even}\mid X>1)P(X>1)\cr}$$
since obviously the first term on the RHS is zero. Now the probability that $X$ is even, given that the first trial was a failure,... | Let $\alpha$ be the required probability. In order for $X$ to be even, we must have a failure on the first trial, and have the number of trials after the first be odd. The probability of that, given that the first trial was a failure, is $1-\alpha$. Thus
$$\alpha=(1-p)(1-\alpha).$$
Solve for $\alpha$.
| https://math.stackexchange.com |
234,322 | [
"https://mathoverflow.net/questions/234322",
"https://mathoverflow.net",
"https://mathoverflow.net/users/66236/"
] | Let's consider a separable Hilbert space $(\mathcal H, \langle\cdot, \cdot\rangle_{\mathcal H})$ with Norm $||\cdot||_{\mathcal H} := \langle\cdot, \cdot\rangle^{1/2}_{\mathcal H},$ orthonomal basis $(e_j)$ of $\mathcal H$ and let $s\colon \mathcal H \rightarrow \mathcal H$ be a Hilbert Schmidt operator, denoted by $s ... | The answer is No, assuming of course that for you $s$ acts on $\mathcal{S}_\mathcal{H}$ by left-multiplication. There is no need to assume that $\mathcal{S}_\mathcal{H}$ is separable, since it actually is, with an explicit countable orthonormal basis given by the elementary operators $e_{ij}$ that act as $e_{ij}(e_k) =... | No it's not.
If $s:H\to H$ is a rank one projection, then
$s\otimes\mathrm{id}:H\otimes \overline H\to H\otimes \overline H$
is a projection of rank $\dim(H)$.
In particular, if $H$ is infinite dimensional, then
$s\otimes\mathrm{id}:H\otimes \overline H\to H\otimes \overline H$
is a projection of infinite rank, and t... | https://mathoverflow.net |
108,008 | [
"https://physics.stackexchange.com/questions/108008",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/34669/"
] | We know that in the quantum harmonic oscillator $H=a^\dagger a$, $a^\dagger$, $a$, $1$ will span a Lie algebra, where $a, a^\dagger$ are the annihilation and creation operators, and $H$ is the Hamiltonian operator.
$$[H,a^\dagger\ ]= a^\dagger$$
$$[H,a]=-a$$
$$[a,a^\dagger]=1$$
So these four operators, $H=a^\dagger a... | I apologize, this is my third correction to my answer. This question is very subtle
indeed. I hope this answer is the ultimate one!
First of all, if you want to take advantage of Lie's theorem
you mention (some time called third Lie theorem), the Lie algebra has to
be real, as it must be the Lie algebra of a real Lie ... | There is one more option. You can check that $aa$, $\{a,a^+\}$ and $a^+a^+$ form Lie algebra $sp(2)\sim sl(2)$. Then you can add $a^+$ and $a$ treating them as supergenerators. These are words that tell you to take anticommutators of $a$ and $a^+$ as I did in the first line.
Then you get a $5$-dimensional superalgebra... | https://physics.stackexchange.com |
9,764 | [
"https://mathoverflow.net/questions/9764",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1358/"
] | How do sheaves arise in studying solutions to ordinary differential equations?
<strong>EDIT:</strong> Is it possible to construct non-isomorphic sheaves on a domain $D \subset \mathbb{R}^n$ using solution sets to differential equations?
<strong>EDIT:</strong> Is the sheaf of vector spaces arising from the solution se... | Let $U$ be an open subset of $\mathbb R^n$, and let $X$ be a vector field on $U$. You can construct a sheaf $\mathcal F$ of solutions of the ODE $Xf=0$ by letting $\mathcal F(U)$, for each open subset $V\subseteq U$, be the vector space of all $C^\infty$ functions $f$ on $V$ such that $Xf=0$.
By changing the field $X$... | I will start commenting on Mariano's answer. I believe it is a perfect answer for the question
<blockquote>
How do sheaves arise in studying
solutions of differential equations ?
</blockquote>
but not for the question
<blockquote>
How do sheaves arise in studying
solutions to <strong>ordinary</strong> diff... | https://mathoverflow.net |
466 | [
"https://quant.stackexchange.com/questions/466",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/89/"
] | What is an efficient method of pricing callable range accruals on rate spreads? As an example:
A cancellable 30 year swap which pays 6M Libor every 6M multiplied by the number of days the spread of 10-year and 2-year CMS rate is above 0, in exchange for a fixed or floating coupon.
Using LMM for this is dog slow, and ... | I know this may sound extreme, but in my experience for these kind of payoffs you do need a LMM and possibly with at least 8 factors. There is no shortcut unfortunately, even a 3 factor gaussian model, which you can use to price faster using trees, will not capture the possible dynamics of the curve implicit in an 8 fa... | I've priced similar animals with a naive N-factor method, adding a convexity adjustment for the swap rates. But I'm not sure this is very orthodox...
| https://quant.stackexchange.com |
231,507 | [
"https://mathoverflow.net/questions/231507",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4054/"
] | Let $X$ be a compact Kähler manifold of complex dimension $n$, and let
$\omega_1, \omega_2$ be Kähler classes on $X$. Denote the Lefschetz
operator of a Kähler class $\omega$ by $\Lambda_{\omega}$. Then
$$
\Lambda_{\omega_1} \omega_2 + \Lambda_{\omega_2} \omega_1 \geq 2n
$$
with equality if and only if $\omega_1 = \ome... | Here is a simple proof using Theorem 1.6.1 in Lazarsfeld book, which is the following:
<blockquote>
<strong>Theorem</strong> (Demailly)
If <span class="math-container">$H_1,\ldots,H_n$</span> are Kähler classes in a compact Kähler manifold of dimension <span class="math-container">$n$</span>, then the following inequal... | It is a consequence of the Khovanskii-Teissier inequality for Kähler classes (which was proved by Gromov and Demailly on Kähler manifolds, the algebraic case is also in Lazarsfeld's book):
$$\int_X \omega_1^{n-1}\wedge\omega_2 \geq \left(\int_X \omega_1^n\right)^{\frac{n-1}{n}}\left(\int_X\omega_2^n\right)^{... | https://mathoverflow.net |
2,841,085 | [
"https://math.stackexchange.com/questions/2841085",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <strong>Describe the region of unit sphere covered by normal Gauss map on the
paraboloid $z = x^2+y^2$.</strong>
I did this way: Consider the parametrization $X(u,v) = (u,v,u^2+v^2)$. Then $X_u = (1,0,2u)$ and $X_v = (0,1,2v)$.
Then $X_u \times X_v = (-2u,-2v,1)$ and $||X_u \times X_v|| = \sqrt{4(u^2+v^2)+1}$, so $N(... | Note that there is an ambiguity when talking about (normal) Gauss map, in particular when choosing the normal unit vector. Both your choice and the one given by the solution (which is just the negative of what you have) are both acceptable choices.
For example, if you use the chart
$$ X(u, v) = (v, u, u^2+v^2),$$
yo... | The gradient of $z = x^{2}+y^{2}$ is the projection of the vector normal to the surface determined by $z$ over the plane $z=0$.
| https://math.stackexchange.com |
97,711 | [
"https://electronics.stackexchange.com/questions/97711",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16226/"
] | Just to give a little back ground on the project - I am currently building a buck converter linked up to 2 * 250W solar panels in parallel, then use an MPPT algorithum to track the max power. I will be using a TI Stellaris microcontroller to control the PWM, and will be using a synchronous buck topology with possibly ... | There are many sources of loss in a SMPS. Here are just two:
<h3>switching losses</h3>
Each time the "switch" (usually a MOSFET) changes from on to off, it spends some time in a state between. During this time, there is simultaneously significant current in the device, and significant voltage across it. As \$P=IE\$, ... | This is somewhat of a aside to what you asked, but if you are worried about every last bit of efficiency, don't connect the two solar panels together, especially if that leads to a multi-phase switcher. There will be differences between the two panels, and of course the insolation can vary too as shadows cross the two... | https://electronics.stackexchange.com |
49,800 | [
"https://electronics.stackexchange.com/questions/49800",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16399/"
] | I have the following schematics:
<img src="https://i.stack.imgur.com/7xrff.png" alt="enter image description here">
If I have a scope probe on VIN, everything works very well. VIN is an amplification of the input and the ADC reports it very well: good accuracy and no delay. But if I don't put the scope probe on VIN,... | The probe adds a path to the ground and it pulls VIN. Add a one-mega-ohm resistor between VIN and ground.
| Diode D6 means that the op-amp can only drive the ADC input high. On its own, the amplifier circuit can't pull VIN low.
When you connect the scope probe, you effectively add a resistor to ground, probably in the neighborhood of 1 - 10 Megohms. This pulls VIN low whenever the op-amp isn't driving it high.
| https://electronics.stackexchange.com |
309,577 | [
"https://mathoverflow.net/questions/309577",
"https://mathoverflow.net",
"https://mathoverflow.net/users/73942/"
] | I have a preprint X that is sitting in the ArXiv for which I am not sure if it is still worth publishing. It turns out the paper I wrote has considerable overlap with another preprint Y after one of its authors informed me about it through email. Consider the following:
<ol>
<li>Paper Y was posted in the ArXiv just a ... | I once wrote a paper with an undergraduate that I thought was very nice. After it was <strong>accepted</strong> for publication, we found a paper not only proving our results, but going a step further. We hadn't found it previously because, similar to your situation, they used different terminology. In our case, our... | In the few times in my career I have been in a similar situation, I have withdrawn my paper before publication, but gone on to modify it to be different enough from the other's (and my) prior work that it justifies publication. The lesson is: don't always view a paper as a complete, fixed, immutable work of scholarsh... | https://mathoverflow.net |
163,934 | [
"https://softwareengineering.stackexchange.com/questions/163934",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/44899/"
] | I just joined a small start-up as a software engineer after graduation. The start-up is 4 year old, and I am working with the CEO and the COO, even if there are some people abroad. Basically they both used to do almost everything. I am currently on some kind of training phase. I have at my disposition architecture, set... | Technically, I think a decent wiki platform is the best choice for most of this sort of documentation. Easy to get at, easy to fill in, good search and version history are all great features for this task. Exactly which platform isn't important -- I'd run with whatever is in place first.
The best advice I've heard on... | Well, I think the real issue is that you want your installation document to be kept up-to-date. That is nothing you can really solve by improving the design of the document. Someone has to be responsible for this, for example, the developers of the system whenever they change something which influences the installation... | https://softwareengineering.stackexchange.com |
264,727 | [
"https://physics.stackexchange.com/questions/264727",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/103630/"
] | According to Wikipedia the definition of motion is:
<blockquote>
In physics, motion is a change in position of an object with respect to time. Motion is typically described in terms of displacement, distance, velocity, acceleration, time and speed.
</blockquote>
The definition of uniform motion is that the object i... | <blockquote>
The definition of uniform motion is that the object is supposed to cover equal distances in equal intervals of time.
</blockquote>
Well, it <em>isn't</em> defined from velocity. As you clearly write it here yourself. That is your own interpretation. You could just as well have said that "<em>that means ... | In uniform velocity, changes occur uniformly is the cause of acceleration but in constant velocity no changes occur, then the acceleration is zero.
| https://physics.stackexchange.com |
573,257 | [
"https://math.stackexchange.com/questions/573257",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/70868/"
] | Prove that if $f$ is integrable on $[a,b]$ then so is $|f|$.
I can prove the converse of this is false, I also try using the definition of integrable function $f$, but I don't know what to do after that
| Integrability means that certain sums involving value differences $|f(x)-f(x')|$ are small. Given that $\bigl||y|-|y'|\bigr|\leq|y-y'|$ the same sums with $|f|$ instead of $f$ tend to be even smaller.
| One suggestion: Show that if $f$ and $g$ are integrable, then so is $\max(f, g)$. Then you can apply this lemma to $|f| = \max(f, -f)$.
| https://math.stackexchange.com |
47,806 | [
"https://mathoverflow.net/questions/47806",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4903/"
] | Is there an explicit basis for the algebraic numbers as a vector space over the rationals?
| Every computable field which is an <em>algebraic</em> extension of the rationals $\mathbb{Q}$ has a computable basis (as a vector space over $\mathbb{Q}$). The idea is to build up this basis by recursion: let $F_0 = \mathbb{Q}$, with basis $B_0=$ {$1$}, and, given a basis for $F_s$ over $\mathbb{Q}$, find the least e... | Let me offer a formulation of your question, using ideas of
computable model theory, which make it both interesting and
nontrivial. Given that there is a computable presentation
of the field $\mathbb{A}$ of algebraic numbers, meaning
the algebraic closure of $\mathbb{Q}$, the natural
questions would seem to be:
<ul>
<... | https://mathoverflow.net |
510,659 | [
"https://physics.stackexchange.com/questions/510659",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/42568/"
] | I just did the following experiment:
Using a metal Whitman's chocolate box, I placed my phone it it, closed the lid then called it from another phone. To my surprise, it rang.
The normal parameters of a faraday cage is any gaps have to be small compared to the wavelength of the radiation. The edges of the box overl... | <blockquote>
The normal parameters of a faraday cage is any gaps have to be small compared to the wavelength of the radiation. The edges of the box overlap by about 1 cm, and the gap is a fraction of a mm.
</blockquote>
The important dimension is the <strong>longest</strong> dimension of the gap. So if you have a se... | I'm not conversant in RF shielding, but it is possible that the simple friction fit of the cover on the box doesn't make a good RF shield. If it were that simple, microwave ovens would not require special RF shielding techniques to prevent microwave leakage from occurring where the inner perimeter of the door makes con... | https://physics.stackexchange.com |
194,670 | [
"https://stats.stackexchange.com/questions/194670",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/92844/"
] | I have come across a problem in textbook to estimate mean.
The textbook problem is as follows:
<blockquote>
Assume that $N$ data points, $x_1$, $x_2$, . . . , $x_N$ , have been
generated by a one-dimensional Gaussian pdf of unknown mean, but of
known variance. Derive the ML estimate of the mean.
</blockquote>
... | <blockquote>
Why do we need to estimate mean using MLE when we already know that mean is average of the data?
</blockquote>
The text book problem states that $x_1,x_2,\dots,x_N$ is from $$x\sim\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{(x-\mu)^2}{2\sigma^2}}$$
They tell you that $\sigma$ is known, but $\mu$ has to be esti... | In this case, the average of your sample <em>happens</em> to also be the maximum likelihood estimator. So doing all the work derive the MLE feels like an unnecessary exercise, as you get back to your intuitive estimate of the mean you would have used in the first place. Well, this wasn't "just by chance"; this was spec... | https://stats.stackexchange.com |
3,621,911 | [
"https://math.stackexchange.com/questions/3621911",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/464054/"
] | <blockquote>
Find the minimum value of <span class="math-container">$$f(x)=\frac{\tan \left(x+\frac{\pi}{6}\right)}{\tan x}, \qquad x\in \left(0,\frac{\pi}{3}\right).$$</span>
</blockquote>
My approach is as follows. I tried to solve it by segregating it
<span class="math-container">$$f(x)=\frac{1}{\sqrt{3}\tan x... | The first derivate of your function is:
<span class="math-container">$$f'(x)=\cot(x)\sec(x+\pi/6)^2-\tan(x+\pi/6)\csc(x)^2$$</span>
Now, we have to impose <span class="math-container">$f'(x)=0$</span> and so:
<span class="math-container">$$\sin(x)\cos(x)-\sin(x+\pi/6)\cos(x+\pi/6)=0$$</span>
That can be rewritten as:
<... | <span class="math-container">$$g(x)=1+\dfrac1{2\sin x\cos(x+\pi/6)}=1+\dfrac1{\sin(2x+\pi/6)-\sin\pi/6}$$</span>
Now we need to maximize <span class="math-container">$$\sin(2x+\pi/6)$$</span> in <span class="math-container">$$(\pi/6,2\pi/3+\pi/6)$$</span>
| https://math.stackexchange.com |
628,735 | [
"https://electronics.stackexchange.com/questions/628735",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/34426/"
] | I can't seem to find this information, but obviously I searched wrong, or Google is weighing my earlier search history too much.
So, what are these power ratings exactly for the CC1 pin?
| Valid range for CC1/VCONN pin is 3.0 to 5.5V and connector pin is rated for 1.25A, and how much power is available depends on which devices you support.
Compare that to CC2 connector pin, which has a rating of 0.25A, and pull-up maximum voltage is 5.5v.
You can read the details from the USB standard which is freely ava... | Without an emarker chip, 3A at 20V.
With an emarker chip and certified 5A cable, 5A at 20V.
And with the newer extended power range feature and a EPR cable, 5A at 48V.
As far as specs go anyway. Any given cable or connector will vary.
| https://electronics.stackexchange.com |
602,795 | [
"https://electronics.stackexchange.com/questions/602795",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/296951/"
] | I mean, if binary code is already generated by PC, wouldn't it be possible to just take this binary code, transfer it to a specific place in flash memory via specific bus, for example Serial Wire, and it would work?
Why is a programmer usually required in an embedded toolchain?
| That's what the programmer does.
It takes the binary output from the compiler and stores it in the MCU's Flash EPROM, usually over a serial bus.
Flash EPROM requires a programming algorithm to store data in it, with any erases first. The programmer carries out this algorithm. It's not like writing data to RAM. This is ... | A programmer is the implementation of " via specific bus,".
Some devices have inbuilt bootloaders (may be hardware or software or firmware) that allow the use of a port of some sort to load code.
Whenever a feature is included in a device that is not utilised during normal operation it adds an unproductive ov... | https://electronics.stackexchange.com |
645 | [
"https://stats.stackexchange.com/questions/645",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/9426/"
] | Having just recently started teaching myself Machine Learning and Data Analysis I'm finding myself hitting a brick wall on the need for creating and querying large sets of data. I would like to take data I've been aggregating in my professional and personal life and analyze it but I'm uncertain of the best way to do th... | If you have large data sets - ones that make Excel or Notepad load slowly, then a database is a good way to go. Postgres is open-source and very well-made, and it's easy to connect with JMP, SPSS and other programs. You may want to sample in this case. You don't have to normalize the data in the database. Otherwise, CS... | Your question is so broad that the answer is: it depends. Still, to give some more useful answer I'll indicate what I think are common in Research.
Storing of data is very often done in text files. When doing statistical analyses you mostly work with a collection of one type of vectors. This can be seen as a table and... | https://stats.stackexchange.com |
33,896 | [
"https://mathoverflow.net/questions/33896",
"https://mathoverflow.net",
"https://mathoverflow.net/users/290/"
] | I was always bothered by the definition of the cross product given in e.g. a calculus course because it's never made clear how one would go about defining the cross product in a coordinate-free manner. I now know, not one, but <em>two</em> ways of doing this, and I can't quite see how they're related:
<ul>
<li>The cr... | To expand on Victork Protsak's comment, if $V$ is an $n$-dimensional real vector space with inner-product, the inner-product gives an isomorphism $V\to V^*$ and hence $V\otimes V \to \mathrm{End}(V)$. Under this isomorphism, $\Lambda^2(V)$ is identified with skew-adjoint endomorphisms of $V$, which is precisely the Lie... | Let $\varepsilon( )$ be the volume form in $\mathbb R^3$. For given vectors ${\bf p}$ and ${\bf q}$ the function $f:{\bf x}\mapsto\varepsilon({\bf p},{\bf q},{\bf x})$ is a linear functional and so is represented by a vector ${\bf r}\in\mathbb R^3$, i.e., one has $f({\bf x})=\langle{\bf r},{\bf x}\rangle$. This vector... | https://mathoverflow.net |
112,642 | [
"https://softwareengineering.stackexchange.com/questions/112642",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12753/"
] | It's possible to publish daily updates for your application on Google's Android Market, but I have an assumption that users don't like to get frequent updates. How can I determine when I should publish updates? Is there an optimum interval to balance between delivering new features and bug fixes while not upsetting my ... | Erlang is a standalone language but there is work being done on Erjang which is targeting the JVM. You're right that Scala and Clojure are targeting the JVM, and there are versions of Ruby and Python targeting the JVM as well (JRuby, Jython).
Yes, the JVM is a very mature platform and modern JVMs are able to optimize ... | I'd say it's 10% option (a), 70% option (b) and 20% option (c).
Writing a reliable virtual machine is <em>hard</em>. It's a big part of why Perl6 was 10 years late - it runs on a register-based VM unlike the common ones and had to be written essentially from scratch). Also, you can leverage not just the VM but also t... | https://softwareengineering.stackexchange.com |
57,044 | [
"https://stats.stackexchange.com/questions/57044",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/24706/"
] | I am performing a generalized linear model, where I have to specify a family different from the normal one.
<ul>
<li>What is the expected distribution of residuals? </li>
<li>For example, should the residuals be distributed normally?</li>
</ul>
| <pre><code>What is the expected distribution of residuals?
</code></pre>
It varies with the model in ways that make this impossible to answer generally.
<pre><code>For example, should the residuals be distributed normally?
</code></pre>
Not generally, no.
| There is a whole cottage industry centered around designing residuals for GLMs that are more symmetric or even approximately "normal" (i.e. Gaussian), e.g. Pearson residuals, Anscombe residuals, (adjusted) deviance residuals, etc. See for example Chapter 6 of James W. Hardin and Joseph M. Hilbe (2007) "Generalized Line... | https://stats.stackexchange.com |
121,669 | [
"https://chemistry.stackexchange.com/questions/121669",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/84052/"
] | I was reacting <strong>pure sodium and tap water</strong>, and at one point I put some splattered sodium back into the water. I observed fumes that reacted with my respiratory system, producing a burning sensation.
I read that it is possible to produce sodium oxide fumes from sodium hydroxide at high temperatures (the... | I agree. This is a dangerous reaction and should not be tried without proper equipment, including a lab hood and fire extinguishing equipment.
The fumes could be "just" droplets of sodium hydroxide solution. I've seen similar fumes involving hydrochloric acid, just by adding water to rinse out traces of concentrated... | Well sodium hydroxide(NaOH) is solid at room temperature but at high temperatures it can be converted to gases.This happens due to the fact that the molecules of NaOH gain so much energy that the intermolecular bonds (dipole-dipole) between 2 sodium hydroxide molecules are broken.The reaction of sodium with water is ex... | https://chemistry.stackexchange.com |
46,542 | [
"https://security.stackexchange.com/questions/46542",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/34749/"
] | Let's say I have a really simple mobile app with a server API. For example some kind of Q&A app, where users answer questions to win some points ('Who wants to be a Millionaire' kind of game).
Users can download new questions from a server's API. Next, the users can upload new questions they made up to contribute ... | Do you care if a 3rd party monitors or modifies a request in transit from the client to you or from you to the client?
If you don't care, just use HTTP. If you do care, use HTTPS.
Is there a way to inject some malicious questions if simple HTTP is used? Absolutely, the real question is does it justify the extra cost... | Do you use any authentication for your API? If you do, then you should consider leakage of users credentials.
OAuth 1.0a lets you stay safe from this, as private key is never transmitted, but is used to create cryptographic signature instead. With OAuth2 or "classic" authentication schemes your users credentials are t... | https://security.stackexchange.com |
749,698 | [
"https://physics.stackexchange.com/questions/749698",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/291992/"
] | I'm trying to understand the situation where a roller coaster goes around a loop, and we need to find the minimum speed it takes not to fall off.
What I'm not understanding is why we would set the centripetal force equal to <span class="math-container">$mg$</span>.
At the top, the normal force is 0.
Centripetal force a... | Consider the case that the roller coaster <em>does</em> make it around the loop, and draw a free-body diagram at the top. Then write down the associated Newton's Second Law equation. It is:
<span class="math-container">$$
\vec{F}_N + \vec{F}_g = m \vec{a}
$$</span>
where all three vectors — the normal force, <span cla... | You wouldn't. You may be thinking of setting the magnitude of centr<em>fugal</em> force <span class="math-container">$m\omega^2 r \ge mg$</span> such that at the top of the loop the vector sum of centrifugal force (pointing radially outward, hence straight up at the top of the loop) and gravity (pointing down) is zero ... | https://physics.stackexchange.com |
25,918 | [
"https://electronics.stackexchange.com/questions/25918",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/712/"
] | I have a serial flash chip connected to an ARM microcontroller (AT91SAM9G20). I'd like to be able to program the serial flash after both chips are soldered on to the PCB. For each of the serial flash lines, I can add vias that I can hit with pogo pins pretty easily.
Do I also need to disconnect the serial flash pins f... | The impedance of microcontroller pins is likely quite high. However, the issue is that these pins likely (I'm not familiar with that micro and haven't looked it up) have protection diodes or similar circuitry to Vss and Vdd. The net result is that they look like high impedance within one voltage drop of ground (and p... | Microcontrollers and other digital IC's almost always include some circuitry to protect pins from static by draining away at least some current when the pin voltages would start to reach dangerous levels. Note that if there weren't any protection circuitry, and if a pin wouldn't leak at all until it failed catastrophi... | https://electronics.stackexchange.com |
25,058 | [
"https://security.stackexchange.com/questions/25058",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/16815/"
] | How do cookies' "secure" flag work to determine whether cookie itself should be included?
e.g. on an HTTP (unencrypted) connection...
<ol>
<li>user has no cookie yet and tries to log in;</li>
<li>user logs in successfully, server should send "secure" cookie to client;
<ul>
<li>Will the server send cookies to the cli... | The server can ask the browser to set cookies with the secure flag on over HTTP, but the browser should only include them in responses via HTTPS.
But you should never present a request for authentication over HTTP direct responses to authentication requests over HTTP. The former may be tampered with to copy the creden... | The <em>browser</em> should make sure, that the secure cookie is only <em>sent back</em> to the server for HTTPS requests. Your <em>application</em> should make sure, that secure cookies are only <em>created</em>, if the page was called with HTTPS.
| https://security.stackexchange.com |
176,917 | [
"https://dba.stackexchange.com/questions/176917",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/126992/"
] | I'm having two Azure Databases Lets say DB1(primary) and DB2(secondary).
I've Created two External Data sources for both the DB1 so that they can talk to each other
External Data Source for <em>DB1</em> is <strong>External_DB2</strong><br>
External Data Source for <em>DB2</em> is <strong>External_DB1</strong>
I'm ha... | SP_EXECUTE_REMOTE in Azure works very similar to native sp_executesql. So you should be able to bind the params & values. But I believe there is a limitation that you can't get a output param value from it. Try this and see if it works for your case. Thanks.
<pre><code>EXEC SP_EXECUTE_REMOTE
N'External_DB1',
... | please try this:
<pre><code> Create PROCEDURE prLocalProcCallingRemoteProcWithOutput
@LocalParam varchar(100)
AS
BEGIN
SET NOCOUNT ON;
EXEC SP_EXECUTE_REMOTE
N'External_DB1',
N' DECLARE @outparam nvarchar(max)
EXEC SP_EXECUTESQL N''EXEC DBO.[sp_DB1] @param1,@outparam OUTPUT'',
... | https://dba.stackexchange.com |
1,993,530 | [
"https://math.stackexchange.com/questions/1993530",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/377056/"
] | I am looking for three different right inverses of $f(x)=x^2$. So far I've only been able to come up with the positive and the negative square roots, $\pm \sqrt x$. Furthermore, the right inverse maps from the positive real numbers to the real numbers.
| The complete set of right inverse maps is given as follows:
For any $A\subseteq R^+$, be
$$g_A(x) = \begin{cases}
\sqrt{x} & x\in A\\
-\sqrt{x} & x\notin A
\end{cases}$$
Then $g_A(x)$ is a right inverse to $f(x)=x^2$, and further we have $g_A=g_B \iff A=B$. There are no further right inverses
Proof:
<ul>
<l... | You might get a combination of the two: $\sqrt x$ when $x<1$, and $-\sqrt x$ when $x\ge 1$, or any other combination (rationals vs irrationals, etc).
| https://math.stackexchange.com |
82,776 | [
"https://mathoverflow.net/questions/82776",
"https://mathoverflow.net",
"https://mathoverflow.net/users/19765/"
] | Can please someone help me with the following problem.
Say we have a sequence $nx \; \mathrm{mod} \; 1$, where $n$ is a whole number and $x$ is irrational.
Now I need to solve the inequality
$nx \; \mathrm{mod} \; 1 < v$
with respect to $n$, for some given small $v$.
According to Equidistribution Theorem, this se... | Here is a quick solution to your problem. Fix a positive integer $q$ such that $\{ qx \} <v $, and then fix a positive integer $s$ such that $1<s\{qx\}$. Now assume that $n$ is any integer satisfying $\{nx\}<v$. Let $r$ be the smallest positive integer such that $1<\{nx\}+r\{qx\}$. Clearly, $r\leq s$. In ad... | Basically you don't need the Weyl's Equi. theorem, it's enough to use Kronecker's lemma about density.
If you want to use measure theory, then your question follows from any ergodic theorem you would like + the fact that the system is uniquely ergodic.
If you want, you can use the theory of continued fractions to exp... | https://mathoverflow.net |
300,968 | [
"https://dba.stackexchange.com/questions/300968",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/240253/"
] | I created a <code>table2</code> from another <code>table1</code> with:
<pre><code>CREATE TABLE table2 AS SELECT * FROM table1;
</code></pre>
<code>table1</code> is 4.8 GB with 1.5 mio. rows and 20 columns of types integer (8x), charvar(1) (9x), real (2x) and geometry (1x). <code>table2</code> is 3.5 GB after doing that... | That is as expected. Since updating a row will write a new row version while leaving the old one in place, updating all rows of a table will double its size.
If you run several updates without giving autovacuum time in between to free the dead row version, the size can increase even more.
After your updates are done, r... | In stead of adding and updating the columns when table2 has been created, add the new columns to the select when you create table2.
<pre><code>CREATE TABLE table2 AS
SELECT t1.*,
... new_real1,
... new_real2,
... new_int
FROM table1 t1;
</code></pre>
| https://dba.stackexchange.com |
10,330 | [
"https://engineering.stackexchange.com/questions/10330",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/6861/"
] | 1) Under <em>Visualization</em> in Abaqus, contours for displacements-U1 and U2 are available. How could I generate contours for displacements in x-y direction, that is Ux and Uy? Similarly how can I get contours for stresses Sigma_x, Sigma_y and Sigma_xy?
2) To find homogenized elastic constants of a representative ... | When gypsum is added to the concrete mix it changes some of its
characteristics.Curing is the process in which the concrete is protected from loss of moisture and kept within a reasonable temperature range.
Even if you were using gypsum alone, you would still need to add water: much less than concrete, but still...
... | This a bit late but I will add to the answers already given, with some additional technical and historical perspective.
Portland cement contains four Bogues compounds - C3A, C2S, C3S and C4AF. Of these, one is not hydraulic - C3A. C3A (tricalcium aluminate) was introduced to Portland cement during the 1920's as it w... | https://engineering.stackexchange.com |
1,593,318 | [
"https://math.stackexchange.com/questions/1593318",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/145551/"
] | I am looking to find all of the maximal ideals in $\Bbb{Z}_{12}$. I have mapped out $\langle 2\rangle$, $\langle 3\rangle$, $\langle 6\rangle$, $\langle 0\rangle$. I am still confused as to whether $\langle 2\rangle$ and $\langle 3\rangle$ are maximal ideals or if $\langle 6\rangle$ is a maximal ideal.
| Maximal really means what it means, i.e., not included in a larger proper ideal. This rules out <6> and <0>.
| <strong>Hint:</strong>
The maximal ideal in a quotient ring $R/I$ correspond bijectively to the maximal ideals in $R$ that contain $I$.
| https://math.stackexchange.com |
140,227 | [
"https://electronics.stackexchange.com/questions/140227",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/59074/"
] | I want to design a 4-bit PISO shift register with 4 DFFs and 3 AND gates. I have gone so far that these two designs can be implemented, but I can't go further minimizing it so as to use 3 AND gates for the implementation.
If there is anyone having any suggestions I would appreciate it.
<img src="https://i.stack.imgur... | The kind of cable you mean is missing the D+ and D- data lines. It simply doesn't have those wires inside the cable.
You can test for continuity or resistance using a multimeter. Probe between the corresponding data pins: D+ on one side to D+ on the other, or D- to D-. The D+/D- lines are the middle two pins of a USB ... | If the cable has any markings on it, look for the wire size and amount on it. They will typically say AWG 22-2 or similar for a 2 conductor of AWG size 22 cable. A 4 conductor cable would be different.
Of course, <strong><em>you could</em></strong> find a cable that has four conductors inside but not all four wires co... | https://electronics.stackexchange.com |
50,667 | [
"https://astronomy.stackexchange.com/questions/50667",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/47598/"
] | As of right now, both stars from Alpha Centauri are in their main sequence stages, but eventually Alpha Centauri A is going to quickly expand in a matter of time, and I’m pretty sure its luminosity is going to increase substantially. So, how bright would it be from Earth?
| First of all, by the time Alpha Centauri A becomes a red giant, it will no longer be this close to the Sun due to the orbit of the stars around the galaxy so it probably wouldn't be visible. But let's assume it does stay 4.2 ly away.
By the Stefan-Boltzmann Law, the luminosity of a star is given by
<span class="math-co... | In 1 billion years Sol and Alpha Centauri will have travelled about 4 times around the galaxy on different paths, so it could be 100k light years away. It's moving at 22km/s relative to Sol.
| https://astronomy.stackexchange.com |
352,048 | [
"https://physics.stackexchange.com/questions/352048",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/166466/"
] | Assume that a man is travelling in a space ship at a certain relativistic speed with respect to a man at rest at some point in space, such that <strong>3 minutes in the ship is equal to 5 minutes for the person at rest</strong>.
Also assume that the man in the ship has a lighter which contains gas of a certain amount ... | From the perspective of the stationary observer, the light is dimmer. Why? Because the chemical reaction is happening more slowly, so the fire emits fewer photons per second. The flame burns for longer, but it emits less energy per second. Both observers will agree on the total energy emitted by the flame (once they ha... | Following on from @Jahan Claes' answer we can do some maths!
Say the man on the spaceship is using an ethanol burner. Ethanol has an enthalpy change of $1058 \text{ kJ}/\text{mol}$ but for simplicity let's say that it's equal to $1050$. If he burns $1$ mole of ethanol then it gives out approximately $1050 \text{ kJ}$.... | https://physics.stackexchange.com |
228,821 | [
"https://physics.stackexchange.com/questions/228821",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/17308/"
] | Is the transverse field Ising model time-reversal invariant? Specifically consider a non-integrable variant:
\begin{equation}
H = -J \sum_i^{L-1} \sigma_i^z \sigma_{i+1}^z + g \sum_i^L \sigma_i^x + h \sum_i^L \sigma_i^z,
\end{equation}
so that it has both a transverse and longitudinal field. $\sigma$s are the usual P... | Basically, the answer is yes: $H$ is TRI because it is real. Reality condition really means that the Hamiltonian obeys a certain anti-unitary symmetry. In this case, the time-reversal operation is simply $T=K$ where $K$ is the complex conjugation. It is not the usual one($T=K\prod_i i\sigma^y_i$), and in particular $T^... | I would argue that there are two different antiunitary operators that are both commonly called the "time-reversal operator," and you need to specify which one you mean. Under one definition ($T = K \prod_i i\, \sigma_i^y$), all three Pauli matrices change sign under $T$. This definition is more "physical" because spi... | https://physics.stackexchange.com |
375,956 | [
"https://softwareengineering.stackexchange.com/questions/375956",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/311513/"
] | I'm creating a variable which should describe that an object is currently in use. Lets say we have a form with a password input, and I want to describe the state when someone is using that input.
Is that variable name correct?:
<pre><code>Boolean editingPassword = false;
</code></pre>
I don't have any idea how it sh... | I would work not only on the variable name but also on the variable values by using an enumeration:
<pre><code>enum editionStatus { blank, inProgress, filled };
enum editionStatus passwordEditionStatus = inProgress;
</code></pre>
| <blockquote>
Is that variable name correct?
</blockquote>
When naming boolean variables, as they represent states (like the editing), I'd suggest you perpend <code>is</code> on the name. That, along with camel case (which seems what you are using) should suffice:
<pre><code>Boolean isEditingPassword = false;
</code... | https://softwareengineering.stackexchange.com |
174,804 | [
"https://physics.stackexchange.com/questions/174804",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/76777/"
] | I understand that it is due to electron capture $(p + e \rightarrow n + v_e)$. My precise question is:
What are the conditions needed for a star core to start undergoing this process at a large scale?
| The combined rest mass of a proton and an electron is less than that of a neutron. Fundamentally then, what you need to start turning a star into a neutron star is that the protons and electrons need kinetic energy as well as rest mass energy.
How much energy: Well at a minimum (assuming the neutrino doesn't get much)... | The minimum mass for one to form is 1.44 solar masses.
Energy barrier:
Neutron mass - 1
Proton mass - 0.99862349
Electron mass - 0.00054386734
$p+e→n+v_e$
Assuming that the neutrino mass is negligible, we get the difference between the neutron mass and the electron-proton mass to be 780 keV, meaning this is the ener... | https://physics.stackexchange.com |
3,677,725 | [
"https://math.stackexchange.com/questions/3677725",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/569595/"
] | Let’s say we have a function <span class="math-container">$f$</span>, and let <span class="math-container">$L(f,P)$</span> denotes the lower sum of <span class="math-container">$f$</span> on any partition <span class="math-container">$P$</span> and <span class="math-container">$U(f,P)$</span> the upper sum of <span cla... | We have <span class="math-container">$$L(f,P_1) \leq L(f,P_2) ... \leq \sup L(f,P) \leq \inf U(f,P) \leq... U(f,P_2) \leq U(f,P_1),$$</span> no matter how the partitions are chosen. Both <span class="math-container">$\sup L(f,P)$</span> and <span class="math-container">$\inf L(f,P)$</span> are greater than or equal to... | This has nothing to do with upper or lower sums or partitions.
<blockquote>
<strong>Obvious result</strong>: If a non-empty set <span class="math-container">$A$</span> of real numbers is bounded above and another non-empty set <span class="math-container">$B$</span> of real numbers is bounded below with <span class=... | https://math.stackexchange.com |
366,234 | [
"https://mathoverflow.net/questions/366234",
"https://mathoverflow.net",
"https://mathoverflow.net/users/33278/"
] | This could be a soft question. I am trying to show that the <span class="math-container">$n$</span>-th Taylor series coefficient of a function is <span class="math-container">$O(n^{-5/2})$</span>. However, because the function is a function composition of another function with itself, it seems intractable to compute hi... | For a pre-20th century textbook: <A HREF="https://archive.org/details/3rdedlessonintro00salmuoft" rel="nofollow noreferrer">Modern Higher Algebra</A> by George Salmon (1876) has exercises (with solutions).
<hr />
If I may broaden the query from "abstract algebra" to more general "algebra", I note th... | Two important early 20th-century abstract algebra textbooks that were superseded by van der Waerden are:
Hasse, H., 1926. <em>Höhre Algebra</em>.
Haupt, O., 1929, <em>Einführung In Die Algebra, Zweiter Band</em> - Mit Einem Anhang Von W. Krull, Akademische Verlagsgesellschaft M. B. H., Leipzig.
For an in-depth histori... | https://mathoverflow.net |
138,348 | [
"https://electronics.stackexchange.com/questions/138348",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/58197/"
] | Though the question may sound naïve at first, I still wonder if it would somehow be possible to use an LCD/TFT/OLED or other Panel as an image-sensor.
From my understanding of how these kinds of displays work I’d imagine it would at least need a totally different type of controller to read out possible light exposures... | Individual LEDs can be used as light sensors: they behave like photodiodes.
OLEDs are potentially capable of behaving like this as well (they're also semiconductors), but I can't find reports of anyone having tried it. It's probably extremely inefficient.
LCDs cannot: they operate by applying a field to twist the cry... | It can't work, unless the display has a light sensor to regulate the luminosity, like you have on smartphones.
<ol>
<li>Physically, an LCD doesn't react to incoming light, and if it does, not to a significant extent. It may react to heat though.</li>
<li>The interface of a display is not made to output data, so you wo... | https://electronics.stackexchange.com |
34,145 | [
"https://cstheory.stackexchange.com/questions/34145",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/34813/"
] | I'm currently a sophomore interested in TCS. Recently I've been somewhat bothered by the difficulty of getting into PhD programs in the future since the selection is indeed very competitive.
I looked through the webpages of some top CS school and found that their current grad students mostly also come from top undergr... | <i>Disclaimer: I am just a student, so I cannot speak authoritatively about admissions. I haven't been on an admissions committee, but I can tell you my understanding of how it works.</i>
A PhD admissions committee looks at an application and asks "will this person do well in our PhD program?" Doing a PhD is first and... | Double your chances by also applying to their Math department. You are going to have to take their grad level Algebra and Combinatorics classes anyway, also real analysis if you want to do stuff like fractal dimension.
| https://cstheory.stackexchange.com |
244,372 | [
"https://electronics.stackexchange.com/questions/244372",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/40382/"
] | I am reading 4 bytes from EEPROM to make a float value.
The specific eeprom I use(24Lxx Series) has 0xFF as default value.
So, if I read four bytes of 0xFF into float variable, it will have 0xFFFFFFFF
I want to be able to check above condition.
However, statement, if(floatVariable==0xFFFFFFFF){....} doesn't check o... | In general, when you're looking at the bit representation of data in memory, you only have two options:
<ol>
<li>Use a pointer to the variable, and "lie" as to what it is pointing to:
<blockquote>
Note @erebos' and @Lundin's comments below: while you'll <em>often</em> see something like the following, it is NOT str... | super quick test based on my comments to selected answer. Compiler did what we wanted/desired:
<pre><code>void fdummy ( float );
void dummy ( unsigned int );
union
{
unsigned int ui;
float f;
} myun;
void fun ( unsigned int a, float b )
{
myun.f = b;
fdummy(myun.f);
myun.ui = a;
dummy(myun.u... | https://electronics.stackexchange.com |
31,228 | [
"https://dba.stackexchange.com/questions/31228",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/16630/"
] | Getting time out on this script
<pre><code>UPDATE
uk_data AS ud
INNER JOIN
uk_pc AS up
ON ud.cat10 = up.WardCode
SET
ud.cat8 = up.Latitude,
ud.cat9 = up.Longitude;
</code></pre>
<code>uk_pc</code> Table has 1,755,213 entries and <code>uk_data</code> has 24,510 entries.
Is there any othe... | At the very least, you should have an index on WardCode on uk_pc. If you also add Latitude and Longitude it will become covering for this query and so the table will not need to be used at all.
Your datatypes aren't really the most efficient, so I'd definitely revisit your table designs. narrower columns (Latitude a... | Try something like this:
<pre><code>UPDATE uk_data ud, uk_pc up
SET ud.cat8 = up.Latitude, ud.cat9 = up.Longitude
WHERE ud.cat10 = up.WardCode
</code></pre>
| https://dba.stackexchange.com |
3,105,716 | [
"https://math.stackexchange.com/questions/3105716",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/190900/"
] | I tried to get rid off cube root as written below but still can not get throught the next steps. What should be the right step to take after the steps below? Did I start as I should or do I have to take completely different approach?
<span class="math-container">$\lim_{n->\infty}\dfrac{\sqrt[3]{n+1}-\sqrt[3]{n+\cos... | To complete your approach, let
<span class="math-container">\begin{align*}
a &= \frac{\sqrt[3]{n + 1}}{\sqrt[3]{n}} = \sqrt[3]{1 + \frac{1}{n}} \\
b &= \frac{\sqrt[3]{n + \cos \frac{3}{n}}}{\sqrt[3]{n}} = \sqrt[3]{1 + \frac{1}{n}\cos\frac{3}{n}} \\
c &= \frac{\sqrt[6]{n^2 + \sin \frac{2}{n}}}{\sqrt[3]{n}} =... | As said in comments, using Taylor series would make life much easier.
Start dividing all terms by <span class="math-container">$n^{\frac 13}$</span> and let <span class="math-container">$x=\frac 1n$</span>. Now, use the well known Taylor series for the sine and the cosine. Continue with Taylor or with the binomial exp... | https://math.stackexchange.com |
149,845 | [
"https://physics.stackexchange.com/questions/149845",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/65741/"
] | Ok I have no idea if this is the right stackexchange so if you know who would know please tell me :)
In music there are groups of notes that, when played togheter, are basis to harmony. Since both sounds and light are waves (at least light acts like one). Is there a relation between the proportion of wavelength in an ... | Sadly, there is no relation. While at least some chords have a nice physical basis - octaves are literally harmonics of each other - human perception of color has very little connection to the physics of light. Color is cyclical: we see high-frequency blues as near low-frequency reds with mixed-frequency purples in bet... | As a physics & music major I've thought about this a lot.
Our visible light range doesn't even cover one octave (400nm - 700nm), but you can see how 400nm light (violet) almost completes the octave from 700nm light (red). Perhaps if we could see 350nm light we'd perceive it similarly to red? I think there's an evo... | https://physics.stackexchange.com |
91,190 | [
"https://mathoverflow.net/questions/91190",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | I asked this over stackexchange with no answer so here we are,
I know by constructing some particular cases that I can find unitary matrices $X$, $Y$ and $Z$ such that
$X^m = Y^n = Z^p = XYZ = 1$
with
$$
\frac{1}{m} + \frac{1}{n}+\frac{1}{p} < 1
$$
indicating an infinite von Dyck group unless the fact that the... | So, if I understand things right, we have a random walk on an undirected connected graph with possibly multiple edges and degree 4 at each vertex that starts at some vertex $x$.
The usual way to proceed is to consider the vector $P=P_n$ whose components $P_n(y)$ are the probabilities to end at $y$ after $n$ steps. Th... | While Fedja has given a concrete argument, it occured to me that it also follows from (more or less) abstract nonsense, by compactness-and-contradiction.
Let me explain in more detail. Let $\delta_n$ be the supremum over all actions $G \curvearrowright X$ and $x \in X$ of the return probability after $n$ steps.
We n... | https://mathoverflow.net |
18,239 | [
"https://dba.stackexchange.com/questions/18239",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/8244/"
] | Is there a "better" way to rewrite a <code>SELECT</code> clause where multiple columns use the same <code>CASE WHEN</code> conditions so that the conditions are only checked once?
See the example below.
<pre><code>SELECT
CASE testStatus
WHEN 'A' THEN 'Authorized'
WHEN 'C' THEN 'Completed'
... | I would probably just do this the brute force way, and add indexes to support these joins where they don't exist. Not much gain to treating new customers and old customers any different once you've inserted all the customers that don't already exist:
<pre><code>INSERT dbo.Customer(fname, lname, address, city, state, z... | I think you need the OUTPUT clause to return any new recordids. Further depending on what you want to do, you may be interested in using a MERGE statment instead of just an insert. For instnce someone whose email has remained teh same but whose address has changed coudl be updated rather than having a new record added ... | https://dba.stackexchange.com |
139,045 | [
"https://dba.stackexchange.com/questions/139045",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/95019/"
] | We have a production server with 500GB RAM. <em>max server memory</em> is set to 450GB. Whenever we checked the memory usage it's showing 450GB, but maybe SQL Server reached 450GB for some time? The memory is not released and it will be used whenever it is needed in future. So we have a free space for utilizing by SQL ... | 3 foreign keys version
<pre><code>create table tRegions (
ID int not null primary key,
name varchar(20)
);
create table tCountries (
ID int not null primary key,
name varchar(20),
regionID int,
--any superset of PK is undoubtly UNIQUE
constraint cu1 unique (ID, regionID),
foreign key (regionID) ... | Rather than making sure <em>tUsers.regionID</em> matches <em>tCountries.regionID</em> when <em>tUsers.countryID</em> is set, you could simply prevent both <em>countryID</em> and <em>regionID</em> from being set simultaneously on a row by adding a check constraint like this:
<pre><code>ALTER TABLE
dbo.tUsers
ADD
CO... | https://dba.stackexchange.com |
148,644 | [
"https://mathoverflow.net/questions/148644",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4181/"
] | I've been learning about non-projective complete varieties and I am trying to get a handle on how crazy they can get.
$\textbf{Question:}$ Let $V$ be a complete threefold over $\mathbb{C}$. Given distinct points $P,Q$ on $V$, does there exist a complete surface $S\subset V$ which contains neither $P$ nor $Q$?
I woul... | I do not know the answer to the question. However, let me point out that the answer is negative if you look for surfaces avoiding more points. More precisely, there exists a smooth complete threefold that does not satisfy Sándor's property $NC_{10}$: it contains 10 points that cannot be simultaneously avoided by a divi... | This is just a partial answer to restrict the search.
<strong>Condition</strong> $NC_q$ Let us say that $Z$ satisfies condition $NC_q$ if for any $z_1,\dots,z_q\in Z$ there exists $D=D_{z_1,\dots,z_q}\subset Z$, a codimension one subscheme of $Z$ such that $z_i\not\in D$, for any $i=1,\dots,q$.
<strong>Example</stron... | https://mathoverflow.net |
155,903 | [
"https://math.stackexchange.com/questions/155903",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/26068/"
] | <blockquote>
Assume that $p$ and $q$ are distinct add primes such that $p-1\mid q-1$. If $\gcd(a,pq)=1$ ,show that: $$a^{q-1} \equiv 1 \pmod{pq}$$
</blockquote>
I have tried as follows:
$$a^{q-1} \equiv 1 \pmod{q} \quad \text{and} \quad a^{p-1} \equiv 1 \pmod{p}$$
$$\implies a^{(q-1)(p-1)} \equiv 1 \pmod{q} \quad \t... | Remember that you are told that $p-1$ divides $q-1$. Note that you have not yet used this hypothesis. That suggests that you should <em>really</em> try to use it somehow.
Since $p-1$ divides $q-1$, then there exists $k$ such that $q-1 = k(p-1)$. That means that, since $a^{p-1}\equiv 1\pmod{p}$, then
$$1 \equiv 1^k \eq... | Note that $p-1\mid q-1$ means that $q-1=k(p-1)$ for some $k$. Thus,
$$a^{p-1}\equiv 1\bmod p$$
implies that
$$a^{q-1} = a^{k(p-1)} = (a^{p-1})^k\equiv 1^k= 1\bmod p.$$
Now use the Chinese Remainder Theorem.
| https://math.stackexchange.com |
1,058,414 | [
"https://math.stackexchange.com/questions/1058414",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/361684/"
] | Is number 1 prime as per the definition of prime numbers? Because as per the definition for being prime it should be divided only by 1 and number itself.
| The number 1 is not a prime because it is defined that way. It is really important because if 1 was a prime number, there would be no unicity of an integer decomposition into prime number factors.
| As in @Thekwasti's comment, the "question" of whether $1$ is a prime or not has no genuine mathematical content, but is only a question of convention. Indeed, for a long time it was considered a prime "by definition", and the assertions about unique factorization were all the more clumsy because of that. Thus, historic... | https://math.stackexchange.com |
88,448 | [
"https://mathoverflow.net/questions/88448",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1874/"
] | I'm studying a small category $A$ and diagrams of based spaces or spectra indexed by $A$ (so let's say diagrams in a category $C$ that's closed symmetric monoidal, has a compatible model structure, etc.). I'm told that in this setting there's a projective model structure on diagrams $A \rightarrow C$, where the fibrati... | Let me mention yet another approach using the simplicial localization due to Dwyer and Kan.
Given any category $\mathcal{C}$ equipped with a class of morphisms $W$ one can form a simplicial category $L(\mathcal{C}, W)$ which depends only on $\mathcal{C}$ and $W$ and not on any auxiliary structure like model structure.... | (I deleted my first attempt at an answer, as I had right and left reversed and anyway I wanted to try to say it better.)
I would advocate the following broad and comparatively low-tech view of the matter.
You are asking why two homotopy invariant versions of Hom of diagrams should be equivalent.
In general if you ar... | https://mathoverflow.net |
538,460 | [
"https://stats.stackexchange.com/questions/538460",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/331234/"
] | Apologies if the question seems basic or technical terms are used incorrectly, but I am not very experienced in statistics.
I have collected data concerning different properties of objects, let's say animals, that are classified into 5 classes. The classes are equidistant and ordered Likert ratings 1-5 (for example rep... | No. The z score is <em>not</em> 'the number of standard deviations'. Instead the z-score of a value is the number of standard deviations that value is above the mean. A z-score of 1.7 is 1.7 standard deviations above the mean. A z score of -1 is one standard deviation below the mean, and so on.
This is not mere nitpick... | Yes. A Z value of a particular data point tells you how many standard deviations it is from its mean. Z=0 means it has the same value as the population mean, Z=-1 means it is 1std lower than its mean etc. The probability that an observation will lie within the interval of its population mean plus/minus two times the st... | https://stats.stackexchange.com |
223,903 | [
"https://stats.stackexchange.com/questions/223903",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/73984/"
] | Let $x_1 ... x_n$ be $Pois(\lambda)$
Find UMVUE of $e^\lambda$
From a previous question, I found the UMVUE of $e^{-\lambda}$ to be $(\frac{n-1}{n})^{t}$ where $t = \sum_{i=0}^n(x_i)$. $\sum_{i=0}^n(x_i)$ is our complete and sufficient statistic for $\lambda$ and has the distribution $Pois(n\lambda)$.
So I considered... | For 1, You're interested in $E[a^t]$ where $t$ is poisson with rate $n\lambda$. Explicitly:
$$E[a^x]=\sum_{x=0}^\infty a^x\frac{1}{e^{n\lambda}}\frac{n\lambda^x}{x!}=\frac{1}{e^{\lambda}}\sum_{x=0}^\infty \frac{(na\lambda)^x}{x!}=e^{na\lambda-n\lambda}=e^{n\lambda(a-1)}.$$
Now plug in $a=\left(\frac{n-1}{n}\right)^{-... | <blockquote>
1) How did my calculator come up with this answer?
</blockquote>
Alex R. has already explained this.
<blockquote>
2) Can I get to the umvue by modifying my estimator? How?
</blockquote>
Using Alex R. 's answer, clearly you don't have an unbiased estimator. However, if you can find $a$ such that,
$$... | https://stats.stackexchange.com |
273,981 | [
"https://stats.stackexchange.com/questions/273981",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/52332/"
] | I'm reading about the conjugate prior of classic probability distributions (e.g. beta distribution for binomial distribution); it's explained just as "algebric trick" to have easier calculation in computing
$$
Pr(x|\theta)=\frac{Pr(\theta|x)Pr(x)}{Pr(\theta)}
$$
my questions are:
<ol>
<li>is conjugate prior the onl... | As you said, conjugate priors make things easier and an additional nice property is that when you refresh the model using the posterior as the new prior things are nice and consistent. For instance you can refresh a specific analysis with new data every month, substitute the prior with the old posterior see how the par... | How do you define optimal?
Typically, the conjugate priors won't be the best choice, but they may be reasonable choices. Typically conjugate priors are chosen for computational efficiency. Jeffrey's priors can often be shown to have many favorable "optimal" properties.
In terms of MLE you can think of Bayesian prio... | https://stats.stackexchange.com |
327,656 | [
"https://physics.stackexchange.com/questions/327656",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/57847/"
] | I have been taught that, given a force field <strong>F</strong>, the work done by the force over a certain curve $\gamma$ is defined as the line integral of said field along $\gamma$.
But this makes sense only if force can be written as a function of position, as it is the case with gravity, or a spring. Unlike these,... | Wonderful question. You are absolutely correct, we cannot define a force field for friction like we do for gravity. But the formula for work
$$W=\int_\gamma \vec{F}\cdot\vec{dr}$$
still holds. We just need to be a bit more careful about how we write $\vec{F}$. Naturally (like for gravity), we want to write down $\vec... | <em>I have been taught that, given a force field <strong>F</strong>, the work done by the force over a certain curve $\gamma$ is defined as the line integral of said field along $\gamma$.</em>
Friction is a force, but is not derived from a force field (in any useful sense). So your statement, while true, is inapplicab... | https://physics.stackexchange.com |
525,526 | [
"https://physics.stackexchange.com/questions/525526",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/251933/"
] | Question from the olympiad.
<blockquote>
Two planes move perpendicular to each other with speeds <span class="math-container">$v = 1m/s$</span>. A body flies at them with a velocity of <span class="math-container">$u = 1 m/s$</span> at an angle <span class="math-container">$a=45$</span> to the surfaces of the planes... | So indeed, a free electron is described by plane wave <span class="math-container">$$\Psi(r) =A e^{ikr}$$</span> where <span class="math-container">$A$</span> is constant. This means the probability to observe the electron will be equal to <span class="math-container">$|\Psi(r)|^2=A^2$</span> for every <span class="mat... | Strict definition of "plane wave" means that the phase of the wave is constant along parallel planes, and subsequently the phase velocity is perpendicular to these planes. It doesn't matter if the wave represents classical light of quantum electrons. Mathematically it means that the phase velocity of the wave is consta... | https://physics.stackexchange.com |
41,750 | [
"https://scicomp.stackexchange.com/questions/41750",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/20541/"
] | To the best of my knowledge, stiffness of ordinary differential equations is difficult to capture but can be roughly described as problems where explicit methods don't work while implicit ones do. Alternatively, the stiffness ratio of the Jacobian of the dynamics (i.e. the ratio of its largest to smallest eigenvalues) ... | There are non-stiff problems which are unconditionally unstable with some explicit methods, and conversely there are stiff problems which can be stable with explicit methods. Consider the oscillating problem:
<span class="math-container">$$
\partial_t a = -b\\
\partial_t b = a
$$</span>
This has the eigenvalues <span c... | I'd like to add a few complements to the accepted answer.
Some problems possessing some eigenvalues with positive real parts have "physically" unstable modes, which may actually be damped by many implicit methods (even some explicit ones which have some parts of their stability domain in the right half of the... | https://scicomp.stackexchange.com |
173,734 | [
"https://electronics.stackexchange.com/questions/173734",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/76835/"
] | I wanted to know if it is possible to measure how much energy is being consumed in the entire house by plugging in a power meter in any power outlet in the house?
I am aware of some portable meters but they can only measure energy consumed that specific appliances but not of entire house.
Sorry if the question sounds... | I once heard someone describing such a device and was very confused.<br>
The usual method is something like the Kill-A-Watt, which goes between the appliance you're measuring, and the wall. But this can only measure the consumption of something plugged into it!<br>
<img src="https://i.stack.imgur.com/gq7Zy.jpg" alt="ki... | Energy is the accumulation (or integration) of power over time.
Power is voltage x current.
To measure current you need to have something that is "in-line" with the current flow.
You can't do that from any particular outlet.
If you can't determine what the current taken is you can't calculate power.
If you can't c... | https://electronics.stackexchange.com |
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