qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
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282,792 | [
"https://electronics.stackexchange.com/questions/282792",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/128878/"
] | As the title suggests I am looking for a way to drop 12V to 5V**. Which circuit should I use? And if I am going to use one, Why can't I use the others in the list ? I am looking for:
1. If the current going in is the same as the current going out.
2. Least heat dissipation.
My options :
Voltage Divider ; DCDC Convert... | <blockquote>
<ol>
<li>A Very Low drop of current. 2. Least heat dissipation.</li>
</ol>
</blockquote>
First off, let's discuss your requirements. "Low drop of current" doesn't make much sense, typically you would specify something like "low dropout voltage", but that's not necessary in this case (12V is much mor... | <blockquote>
A Very Low drop of current.
</blockquote>
Meaningless unless you mean has the ability to drive a good amount of current or does not take too much current in standby. Both important.
<blockquote>
Least heat dissipation
</blockquote>
A DC-to-DC converter is your only option here. Specifically, you nee... | https://electronics.stackexchange.com |
3,071,453 | [
"https://math.stackexchange.com/questions/3071453",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/585053/"
] | Let <span class="math-container">$(X,\|\quad\|)$</span> be a normed vector space, and let <span class="math-container">$X^\prime$</span> be the set of all bounded linear maps on <span class="math-container">$X$</span>. I need help to clarify these questions.
<ol>
<li>Is it correct that the weak topology on <span class... | Yes, <span class="math-container">$f^{-1}(I)$</span> is always weakly open. It must be, because the weak topology is the coarsest topology that makes (norm) continuous functionals continuous. Since <span class="math-container">$I$</span> is open in <span class="math-container">$\mathbb{R}$</span>, the inverse image <sp... | In 1) 'is the topology ...' is is wrong. There are many topologies with this property and weak topology is the smallest topology for which <span class="math-container">$f^{-1}(I) \in \tau_w$</span> for every open interval <span class="math-container">$I$</span>. It is the topology for which sets of the form <span cla... | https://math.stackexchange.com |
242,889 | [
"https://softwareengineering.stackexchange.com/questions/242889",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/121368/"
] | I am about to make two assumptions. Please correct me if they're wrong:
<ol>
<li>There isn't a recursive algorithm without an iterative equivalent.</li>
<li>Iteration is always cheaper performance-wise than recursion (at
least in general purpose languages such as Java, C++, Python etc.).</li>
</ol>
If it's true that ... | Well, it's usually less code.
And to the extent that it's less code, it's less error-prone.
In particular, recursion is very beneficial when the iterative solutions requires that you <strong>simulate recursion</strong> with a stack. Recursion acknowledges that the compiler already manages a stack to accomplish precis... | Recursion uses the call stack to store function call returns. Function state is stored in between calls.
Iteration must also use a stack or some similar mechanism to store intermediate states, except that you create the stack yourself. Unless, of course, you can find a substitute algorithm that doesn't require such ... | https://softwareengineering.stackexchange.com |
108,150 | [
"https://electronics.stackexchange.com/questions/108150",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/17245/"
] | I don't understand how Sedra/Smith got \$R_{id} = 2R_1\$. Why doesn't any of the current go through the grounded \$R_2\$?
<img src="https://i.stack.imgur.com/VskfW.png" alt="Pg. 75 of Sedra/Smith Intro to Microelectronics 6E">
| The current <em>does</em> flow through the lower R2, but the opamp returns it (via the power supplies) to the upper R2, which is exactly equivalent to shorting the two inputs of the opamp together.
| Input current doesn't go to ground via R2 because there is no return path to allow it. If you want to model the input as a differential voltage (Vd) riding on top of a common mode voltage (Vcm), then you do have a return path, and the common mode impedance is R1 + R2. But the differential input impedance remains 2R1.
| https://electronics.stackexchange.com |
11,741 | [
"https://security.stackexchange.com/questions/11741",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/4508/"
] | On a large scale (~1500 workstations, ~100 servers, ~50 network routers and switches, etc), what should a vulnerability management system be scanning? Should it scan everything, or just samples?
I know that ideally the VMS have to scan everything, but I'm not sure if that is feasible.
| Scan everything; all ports and protocols.
Scan of open TCP ports:
<ol>
<li>Scanner sends TCP SYN to 1650 targets × 65,536 ports = 108,132,750 160-bit IP headers + 108,132,750 160-bit TCP SYN packets = 34,602,480,000 bits @ 1 Gbit/s = 32.23 seconds; of course, you'll have to go at least twice as slow so that responses... | There is more to scan than just ports and services. VMS can log into computers to perform checks on the OS configuration, patch level, password strength, even Windows AD settings. Depending on your purposes and intent, you should be doing these types of scans as well. You will get a deeper insight (and control) over wh... | https://security.stackexchange.com |
84,723 | [
"https://cs.stackexchange.com/questions/84723",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/63873/"
] | Quick sort algorithm can be divided into following steps
<ol>
<li>Identify pivot.</li>
<li>Partition the linked list based on pivot.</li>
<li>Divide the linked list recursively into 2 parts.</li>
</ol>
Now, if I always choose last element as pivot, then identifying the pivot element (1st step) takes $\mathcal O(n)$ t... | The memory access pattern in Quicksort is random, also the out-of-the-box implementation is in-place, so it uses many swaps if cells to achieve ordered result.<br>
At the same time the merge sort is external, it requires additional array to return ordered result. In array it means additional space overhead, in the case... | You can quick sort linked lists however you will be very limited in terms of pivot selection, restricting you to pivots near the front of the list which is bad for nearly sorted inputs, unless you want to loop over each segment twice (once for pivot and once for partition). And you will need to keep a stack of the part... | https://cs.stackexchange.com |
362,775 | [
"https://softwareengineering.stackexchange.com/questions/362775",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/291538/"
] | (JAVA) I have about 50 Getters, all return the same text, tag, type. Text and tag are String and type is int. The purpose is a forms that use repetitive fields along with form specific fields. I am having trouble with simplifying and reusing code?
public class DataTransferClass {
<pre><code>private DataTransferClass(... | User Stories are not system specifications or functional requirements. Rather, they are the beginning of a conversation that can lead to such specifications or requirements.
Accordingly, I would expect there to be overlap in the system implementation. User Stories are not meant to describe such functional overlap or... | Don't: Try and split the stories, Do one story and then the other.
Do: Ensure the dev team is aware of the second story.
The problem with trying to plan out the detailed tasks and thing up a generic model that can handle both in an elegant way is that it's hard.
The purpose of user stories is to get stuff done. Eleg... | https://softwareengineering.stackexchange.com |
130,937 | [
"https://physics.stackexchange.com/questions/130937",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/17361/"
] | Like all stars, large ones are stable as long as there is a sufficient amount of hydrogen (or helium) to fuse. This fusion process is what prevents them from collapsing in on themselves. However, once the main elements have been fused up to iron, the star becomes unstable. Eventually, it may supernova and leave a bl... | It wasn't a black hole because the density wasn't sufficiently high. The density was lower than what is needed for a black hole because the volume was larger. The volume was larger because the atoms (mostly hydrogen) were kept away from each other by the pressure produced by the fusion processes. Once the fusion proces... | The reason why a massive star does not <em>immediately</em> collapse to a black hole is radiation pressure.
When a star is in that phase of its life called Main Sequence (MS), its luminosity depends approximately on its mass roughly as $M^4$. This means a star 10 times as massive as the Sun would be 10,000 times more... | https://physics.stackexchange.com |
542,040 | [
"https://electronics.stackexchange.com/questions/542040",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7393/"
] | The mean noise voltage for Johnson (Thermal) Noise is given by the formula:
<span class="math-container">\$ v_n = \sqrt{4kTR\Delta{f}} \$</span>.
The bigger the resistance of a resistor or the higher the frequency of a voltage supply, the higher the thermal noise the resistor will have. Does the formula also indicate i... | yes. Even a resistor with no power source will generate Johnson noise. This is thermal noise due to random movement of electrons in the resistor itself.
f in the formula is the bandwidth across which you wish to calculate the noise, it has nothing to do with the signal applied (or not) to the resistor.
| Johnson-Nyquist noise has nothing to do with the power supply. The <span class="math-container">\$f\$</span> in the formula is the bandwidth of the <em>noise</em>, not any applied frequency.
| https://electronics.stackexchange.com |
49,361 | [
"https://cs.stackexchange.com/questions/49361",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/42265/"
] | True or false:
An intersection of a Turing-recognizable and a regular language is always Turing-decidable.
This was asked on a practice test and the answer is False. Why? I thought regular languages were a subset of decidable languages. So if you intersect regular and recognizable the result would also have to be a su... | <blockquote>
I thought regular languages were a subset of decidable languages. So if you intersect regular and recognizable the result would also have to be a subset of decidable.
</blockquote>
There are two confusions here.
First, your seamless switch from "decidable languages" to "recognizable" makes it sound as ... | A recognizable language is not necessarily decidable. If you intersect such a language with $\Sigma^*$ it doesn't suddenly become decidable.
| https://cs.stackexchange.com |
159,224 | [
"https://electronics.stackexchange.com/questions/159224",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/52245/"
] | I have many net labels in schematics, now I want to rename some of them. But when I do, it doesn't update other net labels with same name.
Lets say I have 5 connection with 1 net label "Pin1", now I want to change it to "Pin5". Is there any way, that I change one and it updates all other 4. Yes there is Smart Edit rep... | Select the net label, right click on it, then select <em>Find Similar Objects</em> at the top of the list.
This window will appear:
<img src="https://i.stack.imgur.com/ackN5.jpg" alt="enter image description here" />
Select <em>SAME</em> for both <em>Object Kind</em> and <em>Text</em>. Now tick <em>Select Matching</em>... | <kbd>Ctrl</kbd>+<kbd>H</kbd> is the search and <em>replace</em> dialog shortcut for Altium. Additionally, you can restrict the scope of the search to just net identifiers.
If you want to change 'Pin1' to 'Pin5', just use a simple text replacement.
If your concern is accidentally matching 'Pin11' in your search for 'P... | https://electronics.stackexchange.com |
228,024 | [
"https://electronics.stackexchange.com/questions/228024",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/106611/"
] | Would it be possible to safely power the bbc micro:bit using coin cell batteries? Out of the box it requires x2 AAA batteries, although an earlier prototype did use cell batteries.
I was wondering if connecting x4 3V CR2032 batteries in parallel would work? I believe this would increase the typical capacity to approx... | From a voltage standpoint, yes it could be done.
However, voltage is not everything. You need to look at the datasheet for the coin cells to see if they can supply enough current. In almost all cases (apart from some Li-Ion rechargeable ones), the rated continuous current sourcing capability is only ~2mA at most - typ... | Just the core CPU - yes, it'll easily run from a single coin cell.<br>
BLE bluetooth radio - yes. Although you'd want to aim for a fairly low level of activity on the radio link or you ruin the battery life.<br>
LEDs - not well. You need to be careful, pwm the brightness and only light one at a time. If you try turning... | https://electronics.stackexchange.com |
48,607 | [
"https://mathoverflow.net/questions/48607",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4275/"
] | Example : Consider the (open, not compactified) moduli space of stable maps $ \mathcal M_g(1,d)$ of maps of smooth curves of genus $ g$ to $\mathbb P^1$. To each map
we associate its branch divisor, which is an element of $ Sym^r(\mathbb P^1)$. Then we should have a morphism from $ \mathcal M_g(1,d)$ to $ Sym^r(\mathbb... | It might help to identify $Sym^r(\mathbb P^1)$ with the Hilbert scheme of degree $r$ effective divisors on $\mathbb P^1$. The Hilbert scheme represents a functor, as does the space $\mathcal M_g(1,d)$, and so you can (try to) construct a map from one to the other by thinking in terms of the functors they represent.
A... | You have an answer to the 'example' version of your question already, but let me offer an answer to the "actual" question: if one is faced with two schemes $A$ and $B$, and for each $a\in A$ you have some way of constructing $f(a)\in B$, how might one check that $f$ is (or more precisely comes from) a morphism of schem... | https://mathoverflow.net |
142,549 | [
"https://softwareengineering.stackexchange.com/questions/142549",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/51037/"
] | I have the following problem. My UI interace contains several buttons, labels, and other visual information. I am able to describe every possible workflow scenario that should be be allowed on that UI. That means I can describe it like this - when button A is pressed, the following should follow ->
In the case of th... | don't try to combine everything in one place
if a button changes a parameter let it change the parameter (and nothing else)
if a button uses a parameter let it request the parameter
this is called limiting responsability
edit: the fact that you are trying to visualize all the possibilities of one action into a cu... | Sometimes, with complex functionality comes a complex implementation. Since the reaction of your UI to user input depends on so many variables, you may just have to accept that your code is not going to be short, sweet, and simple.
You may have to have a separate function to handle each UI component and encapsulate i... | https://softwareengineering.stackexchange.com |
273,560 | [
"https://stats.stackexchange.com/questions/273560",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/40447/"
] | When I run the linear regression using about 12 independent variables, I get insignificant F-test result overall.
So I discarded variables to make the F-test significant while having no multicolinearity problem checking by VIF test.
Then I come up with a linear regression with significant F-test and no multicolineari... | For variable selection try using LASSO or ridge regression. Both of these perform variable selection. LASSO has the added benefit of zero out coefficients of insignificant variables.
Both are forms of penalized regression. The penalization parameter can be obtained with cross validation.
All of this can be done with... | As whuber said, it's not really possible to recommend without more info. As already mentioned, make sure you really understand the assumptions ols regression makes, understand how to check such assumptions, and then you will be able to make the decision--and back it up. There are entire books on the topic as well as ma... | https://stats.stackexchange.com |
25,512 | [
"https://quant.stackexchange.com/questions/25512",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/17712/"
] | Say I am trying to find the probability of default on JP Morgan implied by the price of their fixed income assets. Can this be done? Are there any pitfalls to this approach? I have heard of this approach being used, but haven't been able to find many clear implementations in the literature. How can I estimate JP Morgan... | Assume :
<ul>
<li><span class="math-container">$R$</span> a recovery rate,</li>
<li>a continuous payment</li>
<li>a flat intensity <span class="math-container">$\lambda$</span> i.e <span class="math-container">$$\mathbb{P}(\tau>t)=e^{-\lambda t}$$</span></li>
<li>a flat discount rate <span class="math-container">$r$... | I think it depends on your goals and how sophisticated you wish to be. At the lowest level, one can just take the spread of JPM over some relatively risk free rate (Treasurys or swaps) and declare that is the probability of default. Others (e.g. Elton, Gruber, et al in Explaining the Rate Spread on Corporate Bonds) ... | https://quant.stackexchange.com |
151,680 | [
"https://softwareengineering.stackexchange.com/questions/151680",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/25771/"
] | I have been working on this project for more than a year now, and we are close to release, the project manager wants the product to be perfect and working in every single aspect.
I like that and I love working under the perfection idea, but it seems he is delaying the launch too much because of compatibility issues, h... | ask him/her to make a list of all possible compatibility issues and situations; note that a complete list cannot be created, and suggest that the number of possible compatibility issues is infinite and not all possible incompatibilities are worth delaying launch for; concentrate on the ones most likely to occur for you... | Such decisions should be made from a business point of view. Estimate how much would it cost to implement some compatibility feature, and what would the benefits be. Then just decide, if you really need it.
| https://softwareengineering.stackexchange.com |
181,305 | [
"https://stats.stackexchange.com/questions/181305",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/94809/"
] | I need to generate a Large Margin Classifier using python library cvxopt which allows me to solve the quadratic program.
I am trying to write a python function to take the training data and some test data and return the support vectors and the distance of each test data point from the optimal hyperplane.<br>
I am stru... | To answer your question, I would like to invite you to think of a broader picture for, then, take you back to your original question.
First, I would like to introduce a comparison between ANOVA and linear regression with one categorical independent variable; second, I would like to introduce a comparison between ANCOV... | ANOVA looks at the influence of one or more grouping variables (factors) on some continuous dependent measure.
ANCOVA includes at least one grouping variable, but also includes interval-or-ratio-scaled variables on the IV side that are assumed to relate to the DV in linear fashion as in a regression.
ANOVA will let m... | https://stats.stackexchange.com |
1,073,951 | [
"https://math.stackexchange.com/questions/1073951",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/148120/"
] | I attempted to integrate the following function from a practice problem in my Calculus textbook:
$$\displaystyle \int_{0}^{\frac{\pi}{2}}{\frac{1}{1+\tan^\sqrt{2}(x)}} \ {\rm d}x$$
I failed to find an indefinite integral, and I am assuming getting an indefinite integral is simply impossible. Using Wolfram|Alpha to es... | The $\sqrt{2}$ is a complete red herring. In fact consider
$$I=\int_0^{\frac{\pi}{2}}\frac{1}{1+\tan^{\alpha}(x)}\,dx$$
where $\alpha$ is any nonnegative real number. Then we have
\begin{align}
I&=\int_0^{\frac{\pi}{2}}\frac{1}{1+\tan^{\alpha}(x)}\,dx
\\&=\int_0^{\frac{\pi}{2}}\frac{1}{1+\frac{\sin^{\alpha}... | I finally figured it out due to a hint by Sameer Kailasa.
$$\int_{0}^{\frac{\pi}{2}}{\frac{1}{1+\tan^\sqrt{2}(x)}} \ dx$$
$$u=\frac{\pi}{2}-x \implies du=-dx$$
$$= -\int_{\frac{\pi}{2}}^{0}{\frac{1}{1+\cot^\sqrt{2}(x)}} \ dx = \int_{0}^{\frac{\pi}{2}}{\frac{\tan^\sqrt{2}(x)}{\tan^\sqrt{2}(x)+1}} \ dx $$
$$=\frac{1}{2}... | https://math.stackexchange.com |
25,889 | [
"https://quant.stackexchange.com/questions/25889",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/-1/"
] | I have just started reading Options Volatility and Pricing 2nd edition and I'm a little confused on forward contract pricing. The book states
<pre><code>F = C * (1+r*t) + (s*t) + (i * t)
</code></pre>
Where
C = commodity price
t = time to maturity
r = interest rate
s = annual storage cost per unit
... | What you describe is a very simple quasi monte carlo, where the 'random' points are equally spaced in probability space. Like numerical integration.
Sometimes you can use it, but in general you will need the cumulative distribution to do percentile mapping. This very frequently is not known in closed form, and can be... | Your approach is sensible for a single variate case if the cdf is available, but does (as your friend said) break down for more variates.
One issue with multivariate case is the "curse of dimensionality" - as the number of variates increases your number of samples will get infeasibly large very quickly. To address th... | https://quant.stackexchange.com |
25,789 | [
"https://dba.stackexchange.com/questions/25789",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/12942/"
] | I've got data in this form:
<pre><code>CallNum Value Accepted
--------------------------------------
971374 81.482204444473609 True
971374 83.783551111089764 False
971374 97.936875555547886 False
971374 97.936875555547886 False
971374 77.037724444409832 False
971374 83.783551111118868 False
9... | The below script will give you a list of tables, and count of partitions, where there are tables with multiple partitions:
<pre><code>select schema_name(schema_id), name, COUNT(name) from sys.tables t
inner join sys.partitions p on t.object_id = p.object_id
group by schema_name(schema_id), name
having COUNT(name) >... | <pre><code>select t.name as table_name,
i.name as index_name,
ds.type_desc,
ps.name as partition_scheme_name
from sys.tables t
join sys.indexes i on t.object_id = i.object_id
join sys.data_spaces ds on i.data_space_id = ds.data_space_id
left join sys.partition_schemes ps on ps.data_space_id = ds.data_space_... | https://dba.stackexchange.com |
57,417 | [
"https://quant.stackexchange.com/questions/57417",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/41390/"
] | Given portfolio risk is <span class="math-container">$\mathbf{w}\boldsymbol{\Sigma}\mathbf{w}$</span> where <span class="math-container">$\boldsymbol{\Sigma}$</span> is the covariance matrix whose diagonal elements <span class="math-container">$\sigma^2_{n}$</span> are individual asset return variances and whose off-di... | The interpretation and units problem, ie the lack of an easily intuitive answer, is precisely why quants/econometricians etc. tend to shy away from talking too much about covariances [even if they are absolutely necessary; and frequently used]. Thus if anything involving covariances has to interpreted, let alone explai... | So let us assume that the portfolio is entirely made up of consols or single period discount bonds. This would be dubious for equities because <span class="math-container">$$_iR_t=\frac{_ip_{t+1}}{_ip_t}\times\frac{_iq_{t+1}}{_iq_t}-1$$</span> and <span class="math-container">$$_jR_t=\frac{_jp_{t+1}}{_jp_t}\times\frac... | https://quant.stackexchange.com |
134,299 | [
"https://mathoverflow.net/questions/134299",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3621/"
] | Do any of the standard methods of acceleration convergence of series, when applied to
the series $1 - 1 + 1/2 - 1/2 + 1/3 - 1/3 + ...$, give convergence to 0 with error $o(1/n)$?
I tried applying Euler's method to the series, and found that the estimates fall like $1/n$; in fact, the $n$th estimate seems to be to $2/n... | The Aitken delta squared method gives $O(1/n^2)$.
| This is perhaps naive, but your sequence of partial sums is squeezed between an upper and a lower series. Why privilege one over the other? I assume (perhaps incorrectly) that any standard convergence method applied to the harmonic sequence converges to $0$ with error $O(1/n)$.
Together with your sequence of partial ... | https://mathoverflow.net |
16,146 | [
"https://mathoverflow.net/questions/16146",
"https://mathoverflow.net",
"https://mathoverflow.net/users/84526/"
] | Fix an algebraically closed <b>†</b> ground field $k$ of any characteristic. I want to use the classical definition of projective $n$-space $\mathbb{P}^n$ as set quotient of $\mathbb{A}^{n+1}\setminus 0$ by the action of $k^*$, and for its Zariski topology the definition that closed sets are the "zero sets" of ... | Let $f$ be a polynomial which vanishes on $\hat{S}$. Write $f=\sum f_i$, where $f_i$ is homogenous of degree $i$. The set $\hat{S}$ is homogenous so, for any $\lambda \in k^*$, the polynomial $f(\lambda \cdot x) = \sum \lambda^i f_i$ also vanishes on $f$.
Since $k$ is infinite, we can find more equations of the form $... | Look at the subspace of $\mathbf{A}^{n+1}$ cut out by your polynomials. This set is invariant under the diagonal action of $k^\times$. So the functions that vanish on it will be an ideal $I$ (the radical of the ideal generated by your $f_i$) which is invariant under this action. But because $k$ is infinite, it's now re... | https://mathoverflow.net |
240,823 | [
"https://stats.stackexchange.com/questions/240823",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/135160/"
] | Is the following equation identified. Is it possible to obtain the estimates of parameters $\alpha$ and $\beta$ in OLS estimation.
$y_t=\alpha+\beta x_t +\frac{z_t}{\beta}+u_t. $
$x_t, y_t, z_t$ are observed.
| I'm no expert in identifiability, but I would say yes. Roughly speaking, you have more predictors than independent parameters. More precisely: it's unclear to me whether you are modeling a time series (because of the $_t$ suffix) or you are performing regression on a random sample (because you mention OLS). I'll go wit... | This problem is from book "Econometric Theory and Methods", Russell Davidson, 2009. It is numbered 6.7. I found the answer, so I decided to post it.
$y_t=\alpha+\beta x_t +\frac{z_t}{\beta}+u_t, $<br>
then if we define $\frac{1}{\beta}=\delta$, we would have the following<br>
$y_t=\alpha+\beta x_t +\delta z_t+u_t$.<br... | https://stats.stackexchange.com |
22,568 | [
"https://stats.stackexchange.com/questions/22568",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/4290/"
] | In general setting of gradient descent algorithm, we have $x_{n+1} = x_{n} - \eta * gradient_{x_n}$ where $x_n$ is the current point, $\eta$ is the step size and $gradient_{x_n}$ is the gradient evaluated at $x_n$.
I have seen in some algorithm, people uses <strong>normalized gradient</strong> instead of <strong>gra... | In a gradient descent algorithm, the algorithm proceeds by finding a direction along which you can find the optimal solution. The optimal direction turns out to be the gradient. However, since we are only interested in the direction and not necessarily how far we move along that direction, we are usually not interested... | What really matters is how $\eta$ is selected. It doesn't matter whether you use the normalized gradient or the unnormalized gradient if the step size is selected in a way that makes the length of $\eta$ times the gradient the same.
| https://stats.stackexchange.com |
336,483 | [
"https://mathoverflow.net/questions/336483",
"https://mathoverflow.net",
"https://mathoverflow.net/users/121643/"
] | I came across the following conjecture, reading a recent paper in the Monthly, an orthogonal matrix of order <span class="math-container">$n\neq 0 \pmod 4$</span> has a nonnegative (up to a scalar) row vector.
It should be straight in dimensions <span class="math-container">$2$</span> and <span class="math-container"... | This is <strong>false</strong> already for <span class="math-container">$n=3$</span>. A counterexample is given by the matrix
<span class="math-container">$$A=\frac{1}{3}\begin{bmatrix}
2 & 2 & -1\\
2 & -1 & 2\\
-1& 2 & 2
\end{bmatrix}.
$$</span>
How did I construct this matrix? Start with <s... | Here's a simple argument that this is false for <span class="math-container">$n > 2$</span>.
In dimension <span class="math-container">$n$</span> there are <span class="math-container">$2^{n}$</span> orthants, <span class="math-container">$2^{n-1}$</span> if one considers them modulo sign. A pair of antipodal ortha... | https://mathoverflow.net |
302,688 | [
"https://mathoverflow.net/questions/302688",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | Does there exists a smooth projective surface $X$ which contains a projective line $L$ and a smooth conic $C$ such that $L\cap C=$empty?
| Yes. This holds for any cubic surface over an algebraically closed field $k$.
Let $S$ be such a surface. Let $L'$ be a line. The pencil of hyperplanes containing $L'$ forms a conic bundle $\pi: S \to \mathbb{P}^1$. This conic bundle has $5$ singular fibres, which are each a pair of lines meeting in a point. Take $C$ a... | Consider a smooth cubic surface $X$, namely the blow up of $\mathbb{P}^2_k$ at six distinct points $\{p_1, \ldots, p_6 \}$ in general position.
Then you can take as $C$ the strict transform in $X$ of a conic through $4$ of the points $p_i$ and as $L$ the exceptional divisor at one of the remaining points.
| https://mathoverflow.net |
26,781 | [
"https://scicomp.stackexchange.com/questions/26781",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/4532/"
] | In case B(size ~ 2k, complex double) is block-diagonal, where block size is small(e.g. 2), is there any more efficient way to compute this other than Lapack gesv?
| Supposing you already have an LU factorization, you can save a half of a forward substitution step. In the system $Lx=b$, you would have
$$ \begin{pmatrix}
l_{11}&0&&&&\cdots&0\\
\vdots&&&&&&0\\ l_{k-1,1}&\cdots&l_{k-1,k-1}&0&\cdots&\cdots&0\\
l_{k... | When solving $AX = B$ with dense $A$, the fact that $B$ is sparse <em>does not</em> imply that $X$ is sparse: this means that when computing $X$ little can be gained from the structure/sparsity of $B$.
It is true (as noted by Kirill) that <del>with a custom implementation of the back solve step</del> in the forward s... | https://scicomp.stackexchange.com |
44,120 | [
"https://mathoverflow.net/questions/44120",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9645/"
] | Consider the Lie algebra $sl_2$
with the standard basis $(e,f,h),$ where
\begin{equation*}\label{sl2}
[h,e]=2\,e, [h,f]=-2\,f,[e,f]=h.
\end{equation*}
Let $V$ be finite-dimensional $sl_2$-module and let we know that element $e$ acts on $V$ as linear operator with a matrix $E$ (in some fixed basis).
<stron... | Edited in light of clarifications made by OP:
Given a nilpotent matrix $E$ acting on a finite dimensional vector space $V$, it is always possible to extend it to a representation of $sl_2$ in such a way that it represents $e$. The extension is almost never unique: conjugating the representing matrices $F$ and $H$ by ... | This is all very classical and dealt with in numerous books on Lie algebras. For instance, analyzing finite dimensional representations depends on complete reducibility and the (easy) explicit construction of all irreducibles. The dependence of <em>h</em> and <em>f</em> on <em>e</em> (up to certain conjugacy conditi... | https://mathoverflow.net |
323,995 | [
"https://stats.stackexchange.com/questions/323995",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/4894/"
] | Given a random variable $x$ with a well-defined expected value $\mu$, is the mean of the set of samples $\{x_1,\ \cdots,\ x_n\}$, which we'll call $\widehat{\mu}$, always an unbiased estimator of $\mu$? In other words, is it always true that:
$$
E[\widehat{\mu}] = E[\frac{\sum_{i=1}^n x_i}{n}] = \mu = E[x].
$$
regardle... | Answered in comments: The first question is answered immediately using the linearity of expectation. The second conclusion is true only when the underlying distribution has finite variance, in which case it follows with a simple computation of the variance. – whuber
The second conclusion even follows without assum... | One case in which $\hat \mu$ may be a biased estimator of $\mu$: the samples $x_1,..., x_n$ are <em>not</em> uniformly randomly sampled from the population of interest. This is really two problems:
(1) Some values in the population are more likely to be sampled than others. A classic example of this is when we are lo... | https://stats.stackexchange.com |
86,671 | [
"https://dsp.stackexchange.com/questions/86671",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/59971/"
] | I am trying to write a Matlab code to produce motion and Gaussian blur. Here is my code:
<pre><code>f0=imread('cameraman.png');
[Nx,Ny,Nz]=size(f0);
if Nz>1;f0=double(rgb2gray(f0));
else
f0=double(f0);
end
blurfilter1 = fspecial('gaussian', [7 7], 1);
blurfilter2 = fspecial('motion',5,30);
Au = @(u) imfilt... | <h1>Gaussian</h1>
To start, <code>fspecial('gaussian'</code> is deprecated; the <code>fspecial</code> documentation explains how to do the same thing, but better.
Why do you use an n-dimensional convolution (<code>imfilter</code>) if you're actually after 2 sequences of 1-dimensional convolutions?
Something like (excus... | First there are functions convmtx and convmtx2 which returns the matrix operator form of any convolution kernel.
Second, if you consider the convolution operator, the complex sinusoidal are their eigenfunctions and the amplitude of transfer function is their eigenvalues. So, if the operator is selfadjoint, it must have... | https://dsp.stackexchange.com |
229,390 | [
"https://softwareengineering.stackexchange.com/questions/229390",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/120325/"
] | As a programmer, I have always wondered whether it is preferable to write <strong>(a)</strong> short modular functions that are each stored in their own script (i.e., file) or <strong>(b)</strong> long comprehensive scripts that contain all of their relevant functions.
For example, if I code a data analysis stream tha... | Things that belong together should be kept together. Don't have me open another file just to find some <code>_internal_helper_function()</code> that can't be reused in another context. This re-usability is another important point: If the code you've written could be useful in future projects, structure it as a reusable... | I would say it really much is dependent on how the language itself is structured:
In Mathematica, you tend to end up with quite large packages, that may contain several K lines. In java, you don't have much choice, the file to functionality is determined by the objects.
If you get annoyed by having too many files, or... | https://softwareengineering.stackexchange.com |
126,847 | [
"https://cs.stackexchange.com/questions/126847",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/122140/"
] | Show that if <span class="math-container">$d(n)$</span> is <span class="math-container">$O(f(n))$</span>, then <span class="math-container">$ad(n)$</span> is <span class="math-container">$O(f(n))$</span>, for any constant <span class="math-container">$a > 0$</span>?
Does this need to be shown through induction or i... | No, it is not sufficient to say "let <span class="math-container">$d(n) = n$</span> which is <span class="math-container">$O(f(n))$</span>. Therefore <span class="math-container">$ad(n) = an$</span> which is trivially <span class="math-container">$O(f(n))$</span>". Although that is a reasonable way to to understand the... | It is not difficult. A meaning of <span class="math-container">$d(n) = O(f(n))$</span> is <span class="math-container">$\lim_{n\to\infty} \frac{d(n)}{f(n)} = c$</span> which <span class="math-container">$c$</span> is constant. Hence, <span class="math-container">$\lim_{n\to\infty} \frac{a\times d(n)}{f(n)} = a\times c... | https://cs.stackexchange.com |
746,885 | [
"https://physics.stackexchange.com/questions/746885",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/251599/"
] | It is well known that the set of density operators <span class="math-container">$\{\rho\}$</span> for a quantum theory form a convex set. As I have seen them defined, we simply say that a state corresponds to some linear operator <span class="math-container">$\rho$</span> which is self-adjoint, positive semidefinite, a... | The heuristic I've seen before is to stipulate that there should be two kinds of averages,
<ul>
<li>a coherent (quantum) one in which we take expectation values as <span class="math-container">$\langle \psi | \hat{A} | \psi \rangle$</span>, and
</li>
<li>an incoherent (classical) one in which we take averages over a pr... | Short answers : yes.
I guess that your confusion comes from the different natures of randomness.
<ol>
<li><strong>Quantum randomness</strong> : as you raised it, quantum systems possess an intrinsic randomness, absent from classiscal systems. Indeed, even when there is no uncertainty about the state of the considered s... | https://physics.stackexchange.com |
3,230 | [
"https://electronics.stackexchange.com/questions/3230",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/876/"
] | I have a design that uses an Altera Cyclone FPGA to implement a Physically Unclonable Function (PUF) and an ARM device to do cryptographic work and I/O with the PUF. The PUF is very large, and takes quite a bit of space (only about 1/4th will fit on the Cyclone)
My question is, would I be best served by getting a larg... | I can't comment on your specific application (not being a cryptography expert), however placing a processor on board with a FPGA is an exceedingly common thing to do. Mostly the reason is that you now free up FPGA space to do what FPGA is good at, while using the less expensive separate processor to do what it is good ... | I think the right answer of two chips vs. big FPGA will boil down to what sort of attacks the device will face. That means you need to know something about your possible attack scenarios and security needs.
What's the harm if the attacker does probe that SPI communication? Does he get keys? Plaintext? Intermediate sta... | https://electronics.stackexchange.com |
37,893 | [
"https://security.stackexchange.com/questions/37893",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/27549/"
] | I have been browsing the web looking for some help regarding the following issue. I am currently performing an web application penetration test, and I had come accross a beautiful blind SQL Injection.
Using sqlmap, I am able to retrieve the whole database. I would like to jump into the OS level, by using the xp_cmdshe... | The theory is that as long as you keep your old keys, your email software will still be able to decrypt your received emails. That the certificate is expired means that <em>other people</em> won't accept to use your old public key to send you new encrypted emails, but reading your mailbox on your side does not entail u... | There are certain rules Certificate Authorities need to follow in order to issue trusted certificates (one of these is that the certificate can not be valid for longer than 3 years)
In the case of archiving you can keep a copy of old certificates (it will show as expired if you try and use it for sending emails after... | https://security.stackexchange.com |
420,380 | [
"https://physics.stackexchange.com/questions/420380",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/196403/"
] | If you have a wire of area A and length x with a constant current flowing through it, is it reasonable to say that:
$I=\dfrac{dQ}{dt}\Rightarrow dQ=Idt\Rightarrow Q=It \Rightarrow Q=\dfrac{Ix}{v_d}$?
| I believe the answer is no. Current is not defined as the velocity of charge in a conductor. "Electric current through a surface is defined as the rate of charge transport through that surface". (Re NCEE reference handbook for the PE FE exam in Electrical and Computer Engineering). Picture yourself looking edgewise at ... | Based on comments on other answers, let's be a bit more careful.
Let's say we have a uniform current density $J=\frac IA\space$ as well as a uniform charge carrier density $n=\frac NV\space$ Where
$N$ is the number of charge carriers in the volume $V$ of the wire.
Now let's think about how much charge $dQ$ passe... | https://physics.stackexchange.com |
472,482 | [
"https://math.stackexchange.com/questions/472482",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/91175/"
] | Let $n$ be a positive integer. Prove that $\lceil(\sqrt{3}+1)^{2n}\rceil$ is divisible by $2^{n+1}$.
I tried rewriting $\lceil(\sqrt{3}+1)^{2n}\rceil$ as $m*2^{n+1}$ for some m, but couldn't get anywhere.
| Let $(1+\sqrt{3})^{2n}=a_n+b_n\sqrt{3}$. Then $(1-\sqrt{3})^{2n}=a_n-b_n\sqrt{3}$.
Thus $(1+\sqrt{3})^{2n}+(1-\sqrt{3})^{2n}$ is the integer $2a_n$. Since $|1-\sqrt{3}|\lt 1$, we have
$$2a_n=\left\lceil(\sqrt{3}+1)^{2n}\right\rceil.$$
Note that
$$(1+\sqrt{3})^{2n+2}=(1+\sqrt{3})^{2n}(4+2\sqrt{3})=(a_n+b_n\sqrt{3})(... | A succession of hints:
<ol>
<li>Show that $a_n=(\sqrt{3}+1)^{n}+(1-\sqrt{3})^{n}$ is an integer</li>
<li>Show that $\lceil(\sqrt{3}+1)^{2n}\rceil = (\sqrt{3}+1)^{2n}+(1-\sqrt{3})^{2n} (=a_{2n})$ (note that the latter term is positive since it's being raised to an even power, and that $|1-\sqrt{3}|\lt 1$).</li>
<li>Sho... | https://math.stackexchange.com |
734,343 | [
"https://physics.stackexchange.com/questions/734343",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/343935/"
] | In adiabatic processes, when a gas is compressed rapidly, the internal energy of the gas increases and work is done on the gas. Similarly in expansion the internal energy decreases and work is done by the gas. Here, how does change the internal energy of gas (kinetic energy of molecules) and how is work done by gas or ... | If the particle starts in the state
<span class="math-container">$$ \require{physics} \psi = \tfrac{1}{\sqrt{2}} |{\uparrow}\rangle+\tfrac{1}{\sqrt{2}} |{\downarrow}\rangle $$</span>
and some time elapses, how the state develops depends on the hamiltonian of that particle and any other particle it may interact with. B... | Note that your spin 1/2 wave function:
<span class="math-container">$$ \require{physics} \psi = \tfrac{1}{\sqrt{2}} |{\uparrow}\rangle+\tfrac{1}{\sqrt{2}} |{\downarrow}\rangle = |\rightarrow\rangle $$</span>
where:
<span class="math-container">$$|\rightarrow\rangle \equiv |S=\tfrac 1 2, S_x=\tfrac 1 2 \rangle $$</span>... | https://physics.stackexchange.com |
385,313 | [
"https://softwareengineering.stackexchange.com/questions/385313",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/267828/"
] | I am reading Eric Evan's <em>Domain Driven Design</em>, and I encountered this concept on p108. I am having a hard time grasping the concept, in spite of the explanations mentioned on the pages 107 and 108.
Here is an excerpt of the topic from the book:
<blockquote>
Medium-grained, stateless SERVICES can be easier... | Coarser and finer grained means implementing more or less functionality respectively. It is somewhat related to the size too.
So a "fine grained" service is something that does very little. Like a service that just multiples two numbers. A "coarse grained" service is something that does something more complex, like bo... | <strong>Think sugar</strong>
<ul>
<li>There is raw sugar, it has a big grain.</li>
<li>Refined or white sugar, has a smaller grain.</li>
<li>Icing sugar, has a very small grain, it looks like dust.</li>
</ul>
<strong>For a computer</strong>
Granularity is talking about how much is in a thing, when you look at it fro... | https://softwareengineering.stackexchange.com |
2,163,999 | [
"https://math.stackexchange.com/questions/2163999",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/309286/"
] | Is there a continuous function $f : ]1, \infty[ \to \Bbb R_{>0}$ such that $f(x) \to 0$ when $x \to +\infty$ but
$$\lim_{x \to +\infty} \dfrac 1 x \int_1^x f \;\neq\; 0$$
(either the limit doesn't exist but a better example for me would be when it exists and is $>0$)?
I tried something like $f(t) = \dfrac 1 {... | No.
If $f(x)\to 0$, then you can find an $x_0$ such that $f(x)<\varepsilon/2$ everywhere to the right of $x_0$, and then no matter how large $\int_1^{x_0} f(t)\,dt$ is, you can always push $\frac1x \int_1^x f(t)\,dt$ below $\varepsilon$ by choosing $x$ far enough to the right of $x_0$.
Of course you do need to ass... | No, there is not.
Lets take $\varepsilon$ and prove that there exists $N$ s.t. for $x>N$ the mean
$M(n) =\dfrac 1 x \int_1^x f(x)\,dx \in [-\varepsilon,\varepsilon]$
Suppose that for $x> Q~|f(x)| < \delta $. Then
$$M(2Q) = \frac12M(Q)+\frac1{2Q} \int_1^{2M} f(x)dx\le \frac12M(Q)+\frac1{2Q} \int_1^{2Q} \... | https://math.stackexchange.com |
169,867 | [
"https://softwareengineering.stackexchange.com/questions/169867",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/60816/"
] | It's not meant to be subjective or get advice on what would be the best path to take, but an objective list of things that must be known in order for me to pick up a book on compiler theory and understand it.
What level of mathematics, and related skills are required?
| The key question really is: at what level? I'm going to assuming a fairly introductory one if you're asking this question. I have only done one course on compilers, so perhaps my knowledge is too elementary, but here's what is useful to know:
<ul>
<li>Basic 32-bit assembler, including how the stack works, and the usag... | Use different compilers and understand what a compiler can do, as a black box, before you adventure into writing one. Try to use different compilers from command line, see what options they have and what are the effects, what do they have in common, etc.
After that, you need to know a few things:
<ul>
<li>Basic arith... | https://softwareengineering.stackexchange.com |
237,854 | [
"https://mathoverflow.net/questions/237854",
"https://mathoverflow.net",
"https://mathoverflow.net/users/61993/"
] | It is easy to see that within the disk algebra $A(D)$
$$\Delta(z):= \begin{pmatrix} 1&0\\z&1 \end{pmatrix}\; \begin{pmatrix} 1&1\\0&1 \end{pmatrix}=
\begin{pmatrix} 1&1\\z&1+z
\end{pmatrix} $$
is a product of two exponential matrices. Is $\Delta(z)$ itself an exponential matrix of a holomo... | $\Delta(z)$ does not have a nonpositive real eigenvalue for $|z| < 4$, so the principal branch of the logarithm is defined and analytic on a neighbourhood of its spectrum, and thus the holomorphic functional calculus produces the desired analytic logarithm $M(z)$ for $|z| < 4$.
| It seems that $\Delta(z)$ is the exponential of an holomorphic $M(z)$. Using the eigenvalues and eigenvectors of $\Delta$, I find
$$M(z)=\frac\mu{\sqrt{z(z+4)}}\begin{pmatrix} -z & 2 \\ 2z & z \end{pmatrix},$$
where $\mu$ is the solution of
$$\sinh\mu=\frac12\sqrt{z(z+4)}.$$
Because $\sinh^{-1}$ is an odd holom... | https://mathoverflow.net |
88,709 | [
"https://physics.stackexchange.com/questions/88709",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/35102/"
] | When I was taking Optics course, I found there were several questions about polarization of light. I use the textbook of Hecht.
<ol>
<li>It seems that the definition of degree of polarization may be not so well-defined if $V=\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$. For a elliptical polarized light, there is no natura... | In the situation at hand, you'll never be able to achieve uniform circular motion.
$\frac{d\vec{v}}{dt} = \frac{1}{m}\sum \vec{F}_{\text{ext}}$
This is a vectorial equation. If you look at the picture you've drawn, you have forces on the radial as well as the tangential direction.
On the radial direction, there is ... | The answer to your question is "Yes, if you want it badly enough.
Uniform vertical circular motion implies that an object is moving in a circle, that the plane of the circle is vertical, and that the speed of the object does not change as it moves around the circle. An example of such motion is that of a point on the... | https://physics.stackexchange.com |
1,085 | [
"https://mechanics.stackexchange.com/questions/1085",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/439/"
] | I have never torqued them before on several vehicles that I do tune ups on. I just apply a bit of anti-seize lube and get them "snug" and everything seems to work fine. Should I be using a torque wrench to ensure they are properly installed?
| Ideally anything that has a torque value should be torqued to that value.
With spark plugs the concern is not normally getting them tight enough, but instead to prevent over-tightening. Stripping the threads on a spark plug is not good. With that said, personally, I get them "snug" just as you describe.
| The interesting problem I've noticed is that torque values are typically given for "clean and dry", but one will want to use anti-seize, which will affect the torque required for the correct stretch... I always torque to spec with the anti-seize and hope for the best. So far, no issues.
| https://mechanics.stackexchange.com |
202,073 | [
"https://mathoverflow.net/questions/202073",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2011/"
] | In approximation theory, it is classical to use a result that can be considered a generalization of the Schwarz Lemma:
Let $f:[-1,1]\rightarrow\mathbb{C}$ be a function that is analytic in a domain $S$ containing all the points that are at a distance of $\leq \beta$ from $[-1,1]$, where $\beta>2$. Moreover, suppos... | Such estimates are standard tools in transcendental number theory. The following is a simplified version (usually one also require that derivatives are small):
Suppose that $D$ is a domain with a nice boundary $\Gamma$ (piece-wise smooth is fine). Let $f$ be a holomorphic on $D$ and continuous on $\overline{D}$. Let $a... | I am somewhat confused as to what you are looking for. Surely as stated, any function that has at least one zero has infinitely many "near-zeros" in your sense, for every $\varepsilon$. Hence you cannot say anything.
If you assume that your function has no zeros, and perhaps (?) require your near-zeros to be local min... | https://mathoverflow.net |
260,228 | [
"https://electronics.stackexchange.com/questions/260228",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/86668/"
] | I have recently coded a filter in VHDL to be synthesized for an FPGA and I did it using the conventional method where you first design the finite state machine(FSM) and then implement it in your code. But I realized that when I reduced the number of states in the FSM by combining a few states, the filter worked much fa... | Depends on how you want to build your filter. The real questions are these: what sample rate do you need, and how long is your filter? If your sample rate is low, then you can get away with an FSM driven design that can use many clock cycles to produce each output sample. It's certainly a good idea to make the FSM a... | Ultimately when writing HDL (whether VHDL or verilog) you have to remember that you are writing code as a way of desinging hardware.
Your synthisis tool will often give you tools that let your view what it has done with your code at different stages in the processing. In quartus for example you can find these under "t... | https://electronics.stackexchange.com |
338,735 | [
"https://electronics.stackexchange.com/questions/338735",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/86242/"
] | I try to measure a 9volt battery and it displays "9.14V". But the battery is empty. What is happening? Does the multimeter measures it's own 9V battery?
Can someone explain to me what i observe? How does a completely empty battery acts in a circuit with a multimeter?
EDIT
When I connect a LED (without resistors) the ... | As pointed out in the comments, the voltage of a battery measured with a DM may be misleading, since there is nearly no power/current required. To get a better picture of the battery state, the voltage should be measured while the battery is connected to the application, in this case to the motor. Probably that battery... | To a rough approximation, an ordinary zinc or alkaline battery looks like a perfect voltage source with a resistor in series with it. As the battery runs down, this internal resistance increases. The voltage only drops significantly when the battery is totally flat.
A digital multimeter has a very high resistance, u... | https://electronics.stackexchange.com |
3,334,550 | [
"https://math.stackexchange.com/questions/3334550",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/698525/"
] | So the task is that I should calculate the antiderivative of <span class="math-container">$$(6x-2)^\frac{1}{3}.$$</span>
The solution takes the approach of exchanging <span class="math-container">$6x-2$</span> with a <span class="math-container">$t$</span> and then writing <span class="math-container">$$t^\frac{1}{3}.... | The rule is <span class="math-container">$$\int x^n dx=\frac{x^{n+1}}{n+1}$$</span> or for example <span class="math-container">$$\int u^n du=\frac{u^{n+1}}{n+1}$$</span> (these 2 are basicly the same, I just wanted to show you different notations).
But you used the rule in its wrong place because you have <span class... | You have to multiply by <span class="math-container">$\frac{1}{6}$</span> for "cancelling the inner derivative". When you differentiate your solution, you obtain with the chain rule
<span class="math-container">$$\left ( \frac{3}{4} \cdot (6 x - 2)^{\frac{4}{3}} \right)' = \frac{3}{4} \cdot \frac{4}{3} \cdot (6 x - 2)... | https://math.stackexchange.com |
54,353 | [
"https://security.stackexchange.com/questions/54353",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/41650/"
] | Maybe this question sounds obvious, but I wonder how dangerous might be publishing a public key for an <em>asymmetric</em> encryption system?
I know public keys are meant for encrypting messages by anyone who's meant to do so, that's why we can even download a public cert of the most common CAs from web browsers.
But... | None, that's why it is called a public key. It can not be used to access anything encrypted for you without solving math problems that are currently prohibitively difficult to solve. It is possible that in the future it may be possible to solve these problems and that would cause the public key to allow messages to b... | Just to expand on a couple bits of info alluded to above, there are basically two risks to consider, neither of them relating to the algorithms (those are safe).
First, is incidental data leakage. Do you run slaterockandgravel.com as Mr. Slate but have your key signed fflintstone@slaterockandgravel.com? Did Betty si... | https://security.stackexchange.com |
20,055 | [
"https://electronics.stackexchange.com/questions/20055",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5904/"
] | I have a question about logic gates.
I am wondering how to construct a logic circuit that makes its outputs c and d equal to its inputs a and b when a control is set to 0. If the control is set to 1, the outputs are flipped. I have had trouble constructing the circuit. Should I use and and nor gates? I have looked at ... | Look up XOR gate. One way of thinking about a XOR gate is that it inverts or passes the value on one input as a function of the other input. Here is a simple truth table:
<pre>
In 1 In 2 Out
---- ---- ----
0 0 0
0 1 1
1 0 1
1 1 0</pre>
Think about this a bit an... | You might be at a point in your education where you're not allowed to use XOR gates. In that case, you're going to want to just construct a 4 column truth table. And simplify with K-Maps/Boolean algebra.
A B Control Out
--- --- --- ---
| https://electronics.stackexchange.com |
39,793 | [
"https://datascience.stackexchange.com/questions/39793",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/60648/"
] | I want to train an LSTM network for time-series predictions, and want to get to the bottom of LSTM's.
In my understanding, the number of cells in a single LSTM layer can vary. However, since each cell takes an input at time-step t, wouldn't the number of cells need to be equal to t?
For example (from TensorFlow tutori... | You can convert <code>df2</code> to a dictionary and use that to replace the values in <code>df1</code>
<pre><code>cat_1 = [10, 11, 12]
cat_2 = [25, 22, 30]
cat_3 = [12, 14, 15]
df1 = pd.DataFrame({'cat1':cat_1, 'cat2':cat_2, 'cat3':cat_3})
all_cats = [10, 11, 12, 25, 22, 30, 15]
cat_codes = ['A', 'B', 'C', 'D', 'E'... | <pre><code>df3 = pd.merge(df1,df2,left_on=['cat'+str(i)], right_on = ['cat_codes'], how = 'left')
</code></pre>
I would iterate this for cat1,cat2 and cat3. This does not replace the existing column values but appends new columns.
| https://datascience.stackexchange.com |
360,688 | [
"https://mathoverflow.net/questions/360688",
"https://mathoverflow.net",
"https://mathoverflow.net/users/151842/"
] | Let <span class="math-container">$X$</span> be a proper scheme over field <span class="math-container">$k$</span> and <span class="math-container">$\mathcal{L}, \mathcal{M}$</span> two invertible <span class="math-container">$\mathcal{O}_X$</span>-modules. Then <span class="math-container">$Hom_{\mathcal{O}_X}(\mathcal... | Remark. Exact sequence <span class="math-container">$0 \to L \to E \to M \to 0$</span> corresponds to <span class="math-container">$Ext^1(M,L)$</span>, not to <span class="math-container">$Ext^1(L,M)$</span>.
Q1. <span class="math-container">$a \in k^\times$</span> acts on <span class="math-container">$Ext^1(L,M)$</sp... | That is we start with an arbitrary extension <span class="math-container">$0 \to M \to e_2 \to L \to 0$</span> represented by the class of the image <span class="math-container">$\Phi_{e_2}:=\delta(id_L)$</span> with respect the delta-map in lower row in second diagram below and it's pullback extension <span class="mat... | https://mathoverflow.net |
220,347 | [
"https://dba.stackexchange.com/questions/220347",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/3787/"
] | I added some entries from <code>table2</code> to <code>table1</code> as
<pre><code>INSERT INTO table1 (title) SELECT title from table2 WHERE ...
</code></pre>
how can I UPDATE <code>table2</code> for the <code>SELECT</code>ed or <code>INSERT</code>ed entries as
<pre><code>UPDATE table2 SET status='Used'
</code></pre... | Not sure, what you are after. There is no automated way to do this. You could of course write a trigger, but that would execute for every insert that happens on table1, which is most likely not what you want.
Usually you would just put your statements in a transaction and put a lock on the to be updated rows. Like thi... | You could try using <code>INSERT INTO ... ON DUPLICATE KEY UPDATE</code>. This will only work if you have PRIMARY KEY (title) on table1.
<pre><code>INSERT INTO table1 (title)
SELECT title FROM table2
ON DUPLICATE KEY UPDATE status = 'Used'
</code></pre>
The statement <code>INSERT</code>s rows on table1 unless the ne... | https://dba.stackexchange.com |
38,469 | [
"https://astronomy.stackexchange.com/questions/38469",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/34837/"
] | Despite the revolution of the earth around the sun, why does the Polestar appear to be at the same place all through the year?
My daughter, a class 8 student, asked me this question.
| Short Answer:
Polaris is many times too far away for humans to notice any yearly changes in its position with the naked eye or without incredibly advanced astronomical instruments.
Long Answer:
If you are interested I will explain just how incredibly far away Polaris is, and how hard it would be to notice any shift in ... | The Pole star, and all other stars, are a long long long long way away. Space is big. Also, the pole star just happens to be very close to the axis of the Earth's rotation.
As the Earth goes around the sun, it would cause the position of the pole star (and other stars) to move with a regular annual motion. The more d... | https://astronomy.stackexchange.com |
18,447 | [
"https://electronics.stackexchange.com/questions/18447",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5430/"
] | Could someone knowledgeable on the subject explain what exactly is this back emf?
How is it caused in a motor/generator, which components and which effects determines it?
| Inductive components like motor winding resist sudden changes in current. That's because the magnetic field caused by the current needs time to build up or decrease. That means that when current is flowing and this is suddenly cut off, the winding will try to maintain that current, and becomes a power source generating... | Motors and generators are somewhat interchangeable things. If you spin a motor, it can generate voltage - even if you spin it by electrical means. Back emf is the voltage produced (generated) in a motor as it spins.
At a dead stop, a motor produces no voltage. If you apply a voltage, and the motor begins to spin, it ... | https://electronics.stackexchange.com |
231,654 | [
"https://math.stackexchange.com/questions/231654",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/46347/"
] | Given $A = \{(x,y) \in \mathbb{R^2}: y = \frac{1}{x}, x > 0\}$. Show (by considering convergent sequences or otherwise) $A$ is closed in $\mathbb{R^2}$.
Anyone able to give me some advice on how to approach this problem. I know that if every convergent sequence $(x_n, y_n) \in A$ converges in $A$ then $A$ is closed... | HINT: Suppose that $\langle p_n:n\in\Bbb N\rangle$ is a sequence in $A$ that converges in $\Bbb R^2$. Then there are sequences $\langle x_n:n\in\Bbb N\rangle$ and $\langle y_n:n\in\Bbb N\rangle$ in $\Bbb R$ such that $p_n=\langle x_n,y_n\rangle$ for each $n\in\Bbb N$. Let $p=\langle x,y\rangle\in\Bbb R^2$ be the limit ... | Note that $A$ consists of all $(x,y)$ such that $xy-1=0$, so it is the preimage of $0$ under the continuous function $f(x,y)=xy-1$.
| https://math.stackexchange.com |
16,249 | [
"https://stats.stackexchange.com/questions/16249",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/2237/"
] | In OLS, is it possible for the $R^2$ of a regression on two variables be higher than the sum of $R^2$ for two regressions on the individual variables.
$R^2(Y \sim A + B) > R^2(Y \sim A) + R^2(Y \sim B) $
Edit: Ugh, this is trivial; that's what I get for trying to problems issues that I thought of while at the gy... | Here's a little bit of R that sets a random seed that will result in a dataset that shows it in action.
<pre><code>set.seed(103)
d <- data.frame(y=rnorm(20, 0, 1),
a=rnorm(20, 0, 1),
b=rnorm(20, 0, 1))
m1 <- lm(y~a, data=d)
m2 <- lm(y~b, data=d)
m3 <- lm(y~a+b, data=d)
r2... | It isn't possible. Moreover, if A and B are correlated at all (if their <em>r</em> is nonzero), the rsq of the regression on both will be less than the sum of their individual regressions' rsq's.
Note that even if A and B are completely uncorrelated, <em>adjusted</em> rsq's (which penalize for a low case-to-predictor... | https://stats.stackexchange.com |
41,816 | [
"https://cstheory.stackexchange.com/questions/41816",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/16208/"
] | In the simply typed lambda calculus, one can show the following result, known as "preservation under substitution":
<ul>
<li>If <span class="math-container">$\Gamma \vdash v : \tau_1$</span> and <span class="math-container">$(x : \tau_1) \vdash t : \tau_2$</span>,
then <span class="math-container">$\Gamma \vdash [v/x]... | The property, which I would call "typing of substitution" should hold in any type theory, and is not dependent on the <em>exchange</em> property (which I assume is what you mean by permutation)
The key is that you need to generalize the inductive hypothesis to when the variable in t appears in a context. So for a depe... | The most general form of substitution theorems speaks about arbitrary contexts:
<ol>
<li>Define what it means to have a substitution <span class="math-container">$\sigma : \Gamma \to \Delta$</span> from a context <span class="math-container">$\Gamma$</span> to a context <span class="math-container">$\Delta$</span> (it... | https://cstheory.stackexchange.com |
128,838 | [
"https://math.stackexchange.com/questions/128838",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/26919/"
] | I was looking for an example of a non-Noetherian complete local commutative ring with $1$. I would appreciate if anyone can point to a reference.
| I think that you should look at the ring $k[[X_1,X_2,...]]$ of power series with an infinity of variables. This ring is complete (as the completion of the ring $k[X_1,X_2,...]$ of polynomials with an infinity of variables) and its unique maximal ideal is the one consisting of power series without constant term. It is c... | Take an algebraic closure of $\mathbb{Q}_p$, the field of $p$-adic numbers, and complete it to get a complete field $\mathbb{C}_p$. It turns out that $\mathbb{C}_p$ is still algebraically closed. The valuation ring $R$ of $\mathbb{C}_p$ is a complete local ring whose maximal ideal $\mathfrak{m}$ satisfies $\mathfrak{m}... | https://math.stackexchange.com |
37,724 | [
"https://electronics.stackexchange.com/questions/37724",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/11453/"
] | I'm using a repurposed ATX power supply for my hobby projects since it's got 3.3/±5/±12 outputs, all of which are really convenient. But one thing I didn't really think about until I slipped my probes across the pins of an opamp, since I've always dealt with commercial/proper lab power supplies in my school labs, was t... | Use a fuse. You can buy e.g. PTC resettable fuses that will limit the high current and will automatically reset after some time.
| The 'big spark' is hard to limit if the output of the ATX supply has lots of capacitance. There isn't a protection circuit fast enough to save you from that sort of instantaneous energy.
You may want to consider using the 12V rail to feed some buck converters, generating your own 5V and 3.3V rails. The bucks will have... | https://electronics.stackexchange.com |
96,213 | [
"https://electronics.stackexchange.com/questions/96213",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/34290/"
] | What does 'integration density' in the context of integrated circuits and electronics mean? I've seen the term tossed around a lot, but I've never found a satisfactory definition.
| The "integration" is as in "integrated circuit". A high integration density means a large number of components (usually transistors, in contexts where integration density is being discussed) in a small area.
| Low integration density - CPU made of discrete transistors (takes up half a sq kilometer)
High integration density - CPU made of silicon monocrystal (takes up half a sq centimeter)
| https://electronics.stackexchange.com |
353,107 | [
"https://stats.stackexchange.com/questions/353107",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/189617/"
] | The text I'm reading claims that for multivariate $X$, $Y$, and $Z$, and $\hat X$ and $\hat Y$ are the regression of $X$ and $Y$ on $Z$ we have that
<blockquote>
$$\operatorname{Corr}\left(X, Y\middle|Z\right) = \operatorname{Corr}(X-\hat X, Y-\hat Y)$$
</blockquote>
However, there was no derivation of this claim. ... | It depends how sophisticated you want to be. If you're only interested in the linear association (i.e., correlation) between these variables, what you have done is enough. A significant F-value means there is evidence of a relationship between the variables. A small R2 means there is much variability in the outcome tha... | I agree with @Noah 's answer. Additionally, which is seems beyond the task at hand, is there are likely better explanatory variable at play which were a part of the data generating process, which are likely not discernible given data engineering of WindSpeed. I mention this given the orthogonal mass of observations at ... | https://stats.stackexchange.com |
72,593 | [
"https://mathoverflow.net/questions/72593",
"https://mathoverflow.net",
"https://mathoverflow.net/users/17069/"
] | I know that minimal flows are actions for which no proper closed invariant subsets exist, but I am unclear how to understand this concept.
If a coset flow on a quotient space Gamma/S is ergodic, strongly mixing, and minimal, does minimal mean that the orbits are neither periodic nor have an infinite number of periodi... | Your question is about a theorem of Furstenberg.
About the definitions - obviously every periodic orbit is minimal, if exists, hence in the case the action is minimal, you won't have any periodic orbits.
Notice that in the case of homogeneous flows, "usually" (due to measure classification, which is known for many ca... | I'm reading R. Ellis, A semigroup associated with a transformation group, Trans. Amer. Math. Soc. 94(1960), 272-281 and trying to grasp the distinction of minimal in the following theorem:
THEOREM: Let G be the three-dimensional connected, simply connected non-compact simple Lie group (that is, let G be the univers... | https://mathoverflow.net |
102,394 | [
"https://mathoverflow.net/questions/102394",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3848/"
] | Let $S=\mathrm{Spec}(R)$, $s=\mathrm{Spec}(k)$ and $\eta=\mathrm{Spec}(K)$, where $R$ is a d.v.r. with fraction field $K$. Let $j:\eta\rightarrow S$
Now how to compute the sheaf $R^1j_*(\mathbb{G}_{m,\eta})$ in the fppf topology?
The case for etale topology is zero by considering the stalks and use the Hilbert 90.
| The answer to your second question (assuming the axiom of choice, to dodge Asaf's comment) is that $2^{\mathbb R}/\Sigma$ has dimension $2^{\mathfrak c}$, where $\mathfrak c=2^{\aleph_0}$ is the cardinality of the continuum. The main ingredient of the proof is a partition of $[0,1]$ into $\mathfrak c$ subsets, each of... | $\Sigma$ is clearly not a measurable set in the product sigma-algebra, moreover it is so non-measurable that every measurable set containing it is the whole set (any any measurable set contained in it is trivial).
Proof: Consider the set of sets of sets of real numbers consisting of all sets of sets of real numbers $S... | https://mathoverflow.net |
574,782 | [
"https://electronics.stackexchange.com/questions/574782",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/290579/"
] | I have tested the resistance of the solenoid valve (variable force solenoid) and it was 3.6 ohm, however, when I connected it to a square 9V battery, the plunger didn't move. Does that mean it's faulty?
This the solenoid valve I have :
<img src="https://i.stack.imgur.com/NYmoZ.jpg" alt="enter image description here" />... | Eight cells in series is an 8S battery pack (<strong>8 S</strong>eries) not 9S.
The problem with charging cells in series is balancing them. You need to effectively charge each cell separately to get it to its own individual full capacity, otherwise you end up with cells being over-discharged which kills the cell.
A ba... | Just open it up to see what kind wiring is going on there. Balancing is always required for Li-on / LiPo packs.
| https://electronics.stackexchange.com |
7,325 | [
"https://softwareengineering.stackexchange.com/questions/7325",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/1325/"
] | A typical curly brace programming lang has two types of AND and OR: logical and bitwise. <code>&&</code> and <code>||</code> for logical ops and <code>&</code> and <code>|</code> for bitwise ops. Logical ops are more commonly used than bitwise ops, why logical ops are longer to type? Do you think they shoul... | Probably a legacy thing. Bitwise operations may not be very common nowadays, but when coding on very low level you use them all the time. So when C was deviced in the 70's or whenever it was created, bitwise OPs were probably more common than logical OPs. And since C has it that way, I take it many other languages (suc... | Answering the last part of your question: Do you think they should be switched? I have to assume that because you didn't ask "if I'm creating a new language..." that means for existing languages.
NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO
If this was switched in an existing language, I wouldn't even want to b... | https://softwareengineering.stackexchange.com |
1,837,681 | [
"https://math.stackexchange.com/questions/1837681",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/170489/"
] | Let $I\subseteq\mathbb{R}$ and $f:I\to\mathbb{R}.$
<blockquote>
$(0)$ If $f$ is discontinuous on $I$, then it is not uniformly continuous.
$(1)$ Suppose $I$ is open and bounded. If $f$ is unbounded on $I$, then it is not uniformly continuous. Otherwise, let $I=(a,b)$. If we can extend $f$ to $[a,b]$ by continui... | <blockquote>
So one may note that the only functions whose uniform continuity is <em>really</em> interesting to investigate, are the ones defined on an unbounded interval, being globally continuous, non-periodic and non-differentiable on an unbounded subinterval of their domain.
</blockquote>
At risk of contradictin... | Just an idea already mentioned in my comment:
Consider a Weierstraß-function
\begin{align*}
\omega(x):=\sum_{k=0}^\infty\frac{1}{2^k}\sin(2^kx).
\end{align*}
Then it is well-known that $\omega$ is uniformly continuous but nowhere differentiable in $\mathbb R$. However, $\omega$ is $2\pi$-periodic.
Consider $f(x):=x\... | https://math.stackexchange.com |
45,382 | [
"https://dba.stackexchange.com/questions/45382",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/25440/"
] | Is there any way I can query a SQL-Server-CE database that will return the number of matches found in a cell value using LIKE (or MATCH AGAINST or any other method I'm not aware of, really)?
EXAMPLE table, "exampleTable":
<pre><code>**ObjectID** **value**
1 I Love Lemonade
2 I L... | You compare the length of the string with and without the text you're searching for:
<pre><code> select
ObjectID
,value
,(len(value) - len(replace(value,'love',''))) / 4 as occurs
from exampleTable
where value like '%love%'
</code></pre>
| With the aid of a <code>Numbers</code> table:
<pre><code>CREATE TABLE Numbers
( i INT NOT NULL PRIMARY KEY ) ;
INSERT INTO Numbers (i)
VALUES -- fill the table up to 10
(1), (2), ... (10) ;
INSERT INTO Numbers (i) -- fill the table up to 100
SELECT m.... | https://dba.stackexchange.com |
582,135 | [
"https://physics.stackexchange.com/questions/582135",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/265226/"
] | My understanding is this: angular momentum of a body about a point cannot be in two directions at once, which is why a wheel already rotating about its axle, cannot also rotate about its diameter at the same time; it tilts sideways. However this doesn't seem to be the case for points of reference outside the body?
For ... | Both situations can be described in the same way. I think your issue is that you are treating each object as one object, but in reality you should consider these objects as extended objects made up of many mass elements.
The angular momentum of a point particle about some reference point is given by
<span class="math-c... | The angular momentum is a vector, thus for the components of the angular momentum we have to define a coordinate frame .
<strong>I) Wheel</strong>
the coordinate system is at the center of the wheel and the angular momentum is:
<span class="math-container">$$\vec L=I_W\,\vec\omega$$</span>
where <span class="math-conta... | https://physics.stackexchange.com |
219,648 | [
"https://physics.stackexchange.com/questions/219648",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/96867/"
] | In general relativity we introduce local inertial frames to be such frames where the laws of special relativity holds.
Let $\xi^{\alpha}$ the coordinates in the local inertial frame, so we get $$ds^2=\eta_{\alpha \beta}d \xi^{\alpha} d \xi^{\beta}.$$ If we switch the frame of reference to coordinates $x^{\mu}$ : $\xi^... | If $ds^2=\eta_{\alpha \beta}d \xi^{\alpha} d \xi^{\beta}$ were true for all points of space, we would have no curvature, hence no gravity!
Take for example a sphere (the Earth), locally we can measure distances by
$ds^2=dx^2+dy^2$, but this can't hold for two arbitrary points on the sphere.
In fact, this coordinate ... | In Riemannian geometry there is a beautiful theorem which states that a manifold with a symmetric connection is locally flat everywhere if and only if the curvature tensor vanishes. Therefore, in a locally flat coordinates such that $\Gamma_{jk}^i=0$, $g_{ij}$ is constant throughout the chart and a linear transformatio... | https://physics.stackexchange.com |
2,423,766 | [
"https://math.stackexchange.com/questions/2423766",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/416516/"
] | <blockquote>
If $A$ and $B$ are two different complex numbers and $|B| = 1$, find the value of
$$\frac {|B-A| }{|1-\overline AB|}$$
where, as usual, $\overline A$ denotes the conjugate of $A$.
</blockquote>
If possible please don't tell me the entire answer just tell me from where to begin.
| The first equality is true: $\sqrt{2^{2t}}=\sqrt{2^{t+t}}=\sqrt{2^t\cdot2^t}=2^t$.
The second holds only for $t=1$ and $t=2$. Indeed, define for $t\in\Bbb R$ $$f(t)=\cfrac{2^{t}}{2t}$$ and $$g(t)=\ln f(t)=t\ln 2-\ln 2-\ln t$$
Now,
$$g'(t)=\ln2-\frac1t$$
We see that $g'$ vanishes only at one point, namely $t=1/\ln 2$.... | Proposition:
$2^t \gt 2t$ for $t \gt 2,$ $ t \in \mathbb{N}.$
Proof by induction:
0)True for $t=3.$
1) Assume true for $t.$
2) Step: Show for $t+1.$
$2×2^t = 2^{t+1} \gt $
$2×2t =4t \gt 2(t+1)$.
| https://math.stackexchange.com |
190,916 | [
"https://softwareengineering.stackexchange.com/questions/190916",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/84636/"
] | I'm writing my CV, and having trouble explaining about the software for enterprise I developed in my previous job. Now I'm thinking of writing following 4 things for each software.
<ul>
<li>Abstract explanation about what the software is used for</li>
<li>How much was the software sold</li>
<li>About how many data doe... | If you simply label the software you've developed/been on teams that developed as "enterprise", the person reviewing your CV either knows what that means or doesn't, and neither situation requires you to spend any time (or space) going into detail on longer than a single bullet point.
<ul>
<li>If the person reviewing ... | When I'm screening resumes (note resumes not CVs, and yes they are different), I don't necessarily care to read a dissertation on the overall product you wrote for. I care a lot more about <em>what you actually did</em> while you were on the project. I have seen too many candidates relying upon presumed transference ... | https://softwareengineering.stackexchange.com |
4,075,596 | [
"https://math.stackexchange.com/questions/4075596",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/905136/"
] | We have <span class="math-container">$\int_{0}^{\infty}xe^{-\lambda x}dx$</span> = <span class="math-container">$\frac{1}{\lambda^2}\int_{0}^{\infty}ye^{-y}dy $</span>
[Set <span class="math-container">$y=\lambda x$</span>]
I have been so confused about the <span class="math-container">$\frac{1}{\lambda^2}$</span> term... | <span class="math-container">$E(X|X>t)>t$</span> so we cannot have <span class="math-container">$E(X|X>t)=EX$</span> for all <span class="math-container">$t$</span>. Memoryless property is not useful in evaluating this.
<span class="math-container">$E(X|X>t)=\frac {\int_t^{\infty} x\lambda e^{-\lambda x} dx... | The memoryless property works in deriving this conditional expectation like so:
<span class="math-container">$$\begin{align}\mathsf E(X\mid X>t)&=\int_0^\infty (t+s)\,f_X(t+s\mid X>t)\,\mathrm ds\\&=\int_0^\infty (t+s)\,f_X(s)\,\mathrm d s&&\star\\&=t\int_0^\infty f_X(s)\,\mathsf ds+\int_0^\in... | https://math.stackexchange.com |
151,403 | [
"https://cs.stackexchange.com/questions/151403",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/150559/"
] | I'm having a problem with an exercise, I'm supposed to calculate the <em>exact</em> worst case runtime and the worst case runtime in <em>Big O Notation</em> for a given algorithm.
This is what I'm struggling to understand, I think I know how to recognize what's the runtime using the big O Notation as it's only a nes... | Consider the bubble sort algorithm shown below:
<pre><code>function sort(A)
n = A.length
for i = 1 to n-1
for j = n downto i+1
if A[j] < A[j-1]
swap A[j] with A[j-1]
</code></pre>
One way to measure the performance of this algorithm is to count the number of swaps performe... | You can’t calculate any runtime except for some very simple model of a CPU. You can calculate the exact number of comparisons, or the exact number of operations moving array elements of a particular implementation of an algorithm, but it’s practically impossible to predict how many seconds or microseconds the algorithm... | https://cs.stackexchange.com |
51,032 | [
"https://security.stackexchange.com/questions/51032",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/39583/"
] | (Sorry if this isn't in the right SE / is not relevant for security.stackexchange - seemed like the best choice)
<strong>Is there a way for two anonymous parties to establish that they are <em>not</em> previously known to each other, before revealing their identities?</strong>
Suppose that Alice and Bob are able to c... | If you're assuming that either Alice or Bob could be malicious and would actively try to subvert the process (e.g. by lying about their identity or their list of "known identities") then it would seem likely that you would need a trusted third party involved.
I'd suggest that the way to go is to have the TTP involved ... | Assuming you can't trust the other party, you need a third party to identify both people, but even then, it's going to be a less than accurate process. If one party is not behaving in good faith, then there will be no intersection on the other person's list other than their actual identity.
Since the average person k... | https://security.stackexchange.com |
267,794 | [
"https://security.stackexchange.com/questions/267794",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/288148/"
] | Accidentally opened my personal email on company wifi. Had received a message with a suggestive but not graphic image in it, but still what I'd consider inappropriate use of wifi.
It was mail from a personal non-company outlook account using the iOS mail app to view it. This is not a company device either, totally pers... | What you're asking for isn't really possible with high security in the lengths you want, though if you relax the length limits a bit it's not too bad. S generates a challenge (should be at least 128 bits), P appends some metadata (username, timestamp, permissions, whatever) to the challenge and then signs it with a 256... | If you want to avoid pre-shared secrets and use PKI, at least in one direction you have to transfer relatively much data to be typed in.
You can do following. The offline application can encrypt the data for the prover and represent them as a QR code. The user should scan it, the app should transfer the data to the pro... | https://security.stackexchange.com |
693,245 | [
"https://physics.stackexchange.com/questions/693245",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/324377/"
] | I am confused whether Voltage depends on current or the vice versa. I always thought that the vice versa was correct. I tried to find the answers of some of my other conceptual doubts on the web but I was not able to understand the answers as people were saying things beyond school level. But the answers made me confus... | Ohm's law, like many (most?) physical laws, does not involve the idea of cause and effect.
I admit that I usually think of <em>V</em> as causing <em>I</em>, but an electronics engineer might put a resistor in a current-carrying circuit in order to produce a pd which can be applied across (say) a voltmeter. The current ... | They both depend on each other.If you have the IV diagram of a circuit element you can find the current for some voltage across the element and you can find the voltage for some current through the element.
| https://physics.stackexchange.com |
416,838 | [
"https://softwareengineering.stackexchange.com/questions/416838",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/376513/"
] | I'm currently trying to make a simple program with UI where a user can add, select and remove different objects inherited from an abstract common interface with a mouse.
What I plan to do is use a <code>set<unique_ptr<Concrete_class*>></code> to store collections separately for each type of all the objects ... | How do you break up <em>any</em> method that's gotten too big?
<strong>By dividing it into submethods</strong> that each do a small contained subset of the whole algorithm. Whether we're talking about dependency registration or any other kind of logic is irrelevant.
In the case of dependency injection, <em>unless there... | Why is that a problem? The lines of code are needed, it’s just sequential code, no benefit from splitting it up.
I don’t like a giant main() so I would have a method “injectDependencies”. <em>Maybe</em> if there are clearly separate areas I would split it up, but there’s no huge benefit from it.
| https://softwareengineering.stackexchange.com |
70,155 | [
"https://mechanics.stackexchange.com/questions/70155",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/29678/"
] | So I'm having this issue with my car and it only happened after I left it for around 2 months without driving. There is check engine code P171 saying System running too lean. I connected OBD2 reader and managed to get some test results, everything passed except this:
<blockquote>
MID: $3c TID:$81
EVAP Monitor (0.040&qu... | Since you have a scan tool, check the fuel trims to see if the ECM is adding fuel to compensate for a vacuum leak. ECM can add up to 25% more fuel, which would indicate a fairly large leak in the intake. Also check the O2 sensor reading to make sure it's switching rapidly between rich and lean.
| Check the rubber intake hose for cracking. I had several tears in mine that were causing a major vacuum leak in the intake and triggering the P0171 code. The reason for the cracking was the cycles of the rubber bending back and forth during acceleration and deceleration combined with engine heat and so on. Prior to rea... | https://mechanics.stackexchange.com |
316,036 | [
"https://softwareengineering.stackexchange.com/questions/316036",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/184971/"
] | I have a requirement for a service that does the following.
Take a block of text and identify the server names in it (by name or ip address). So given:
<blockquote>
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Donec libero felis, accumsan in nunc id, lacinia rutrum libero. <strong>Server1</strong> Prae... | If your current code is simple and fast enough for your needs, do nothing. Just to optimize because "it seems a bit brute force" is not a good reason, it will mostly complicate things for no benefit. Do not fall into the trap of premature optimization.
However, if your current code really is too slow for your purposes... | One option would be to use regular expressions: build one regular expression that matches any of the servers (in your case, it would be <code>Server1|Server2|192\.168\.0\.2</code>, you can build that by using something like <code>string.Join("|", servers.Select(Regex.Escape))</code>).
Don't forget about the option to ... | https://softwareengineering.stackexchange.com |
2,472,824 | [
"https://math.stackexchange.com/questions/2472824",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/373393/"
] | I am asked to show that the sequence $$\left\{\frac{e^n-e^{-n}}{e^n+e^{-n}}\right\}$$ converges using the definition of convergence. Thus, I am trying to do this by using the definition of convergence, i.e., I am looking for a value for $n$ that will make this true. However, I am having some trouble since this involves... | Note that as @carmichael561 said, you really need to find what this tends to in order to figure out an $n$ for which
$$
\bigg|\frac{e^n-e^{-n}}{e^n+e^{-n}} -L\bigg|<\epsilon
$$
fortunately it's not too hard to figure out $L=1$. Then we work backwards as usual
$$
\bigg|\frac{e^n-e^{-n}}{e^n+e^{-n}} -1\bigg|<\eps... | The limit is $1$. Let's try to solve, for $m> 0$:
$$\bigg|\frac{1-e^{-2n}}{1+e^{-2n}} -1\bigg|< 10^{-m}$$
I don't really know but if I remember correctly if $x > 0 $
$$-2x(1-x) <\frac{1-x }{ 1+x } - 1 = \frac{-2x }{ 1+x } <
-2x
$$
So if we set $2x = e^{-2n}<10^{-m}$ we are done.
| https://math.stackexchange.com |
488,367 | [
"https://physics.stackexchange.com/questions/488367",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/97459/"
] | As the title says: why don't we add Wilson loops to common Lagrangians such as the Standard Model? They're gauge invariant and (correct me if I'm wrong, not sure on that) are renormalizable.
Suppose they are indeed renormalizable, one answer I can think of is that they are not per-se a function of spacetime. But then ... | The reason Wilson loops are excluded from the lagrangian density (in the continuum limit) of a quantum field theory is simply because it is a nonlocal operator. Many nice properties of a quantum field theory are lost when the lagrangian density is built out of nonlocal operators, the most important being causality. Uni... | The kinetic term for a gauge field is a sum of infinitesimal Wilson loops. In this sense, the Lagrangian for a typical gauge theory <em>already</em> has Wilson loops.
In lattice gauge theory, this is completely explicit. In classical lattice gauge theory, a gauge field is described by assigning an element of the gaug... | https://physics.stackexchange.com |
116,542 | [
"https://softwareengineering.stackexchange.com/questions/116542",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/38994/"
] | Is there a duration limit for FDD Project when those projects are likely to fail due external and internal factors?
For example XP projects should kept short due the openess of the concept and dependents on the individuals in the team and lack of documentation which is vulnerable to disturbances like losing team membe... | You pretty much nailed the most important ones. I have a few minor additions, plus the disadvantage of tests actually succeeding - when you don't really want them to (see below).
<ul>
<li>Development time: With test-driven development this is already calculated in for unit tests, but you still need integration and sys... | Having just started trying automated tests in our team, the biggest disadvantage I've seen is that it's very difficult to apply to legacy code that wasn't designed with automated testing in mind. It would undoubtedly improve our code in the long term, but the level of refactoring needed for automated testing while ret... | https://softwareengineering.stackexchange.com |
272,684 | [
"https://physics.stackexchange.com/questions/272684",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/93783/"
] | I'm reading J. Schwinger's book "Quantum Kinematics and Dynamics" and I'm trying to make sense of his formulation of his famous quantum action principle. In essence, he starts from considering <em>arbitrary</em> variations of the the quantum amplitude $\langle a, t_1 |b, t_2 \rangle$, where $|a, t_1 \rangle$ is an eige... | A short answer would be that because states are transformed via unitary transformations, infinitesimal transformations would be given by i times a hermitian operator.
For a longer answer one can use some model for the states where one expresses an arbitrary state $|a,t\rangle$ as a corresponding unitary operator $U(a,... | It is natural to endow any time-evolution of isolated systems with the natural abelian group structure of reals, i.e. $E(t)E(s)=E(t+s)$, $E(t)^{-1}=E(-t)$. This is because we want our mathematical definition of evolution to behave accordingly like a reversible physical time evolution that can be applied step-by-step.
... | https://physics.stackexchange.com |
148,466 | [
"https://security.stackexchange.com/questions/148466",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/136438/"
] | I had a personal wiki set up with mediawiki on my server with nginx.
Recently I noticed that all my sites that used php (Mediawiki and all Wordpress sites) were not responding or timing out.
Then I found a lot of requests in my /var/log/nginx/error.log like this :
<pre><code>request: "GET /index.php?title=Benutzer:M... | If you have a server on the public internet, it will be scanned and probed. This is just a fact of life, and should inform the base of your security policy.
You are most likely going to primarily see three types of attacks:
<ul>
<li>Spammers will try to make comments on blogs, edit pages on wikis, and in general do ... | There is another risk.
In past years an open MediaWiki could be used to boost SEO as spam would then link back to pages hosted on your Wiki, which could be deleted after growing to some arbitrary size. You would then have broken links coming back to you for years to come as old email or forum spam is reviewed.
Goog... | https://security.stackexchange.com |
205,012 | [
"https://dba.stackexchange.com/questions/205012",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/124721/"
] | How to count, how may true and false for the field public in postgresql user table
i have tried this query
<pre><code>select
sum(case when false then 1 else 0 end) as false,
sum(case when true then 1 else 0 end) as true
from public.user;
</code></pre>
but am not getting any value and if i remove public from query... | Use the <code>filter()</code> clause:
<pre><code>select count(*) filter (where "public") as public_count,
count(*) filter (where not "public") as not_public_count
from public."user";
</code></pre>
Note that <code>user</code> is a reserved keyword, you have to use double quotes in order to use it as a table na... | Other ways, that work in older versions that don't have <code>FILTER</code>, using <code>CASE</code> expressions or subqueries:
<strong><code>SUM</code> and <code>CASE</code> expression</strong>
<pre><code>select
sum(case when not public then 1 else 0 end) as false,
sum(case when public then 1 else 0 end)... | https://dba.stackexchange.com |
260,545 | [
"https://stats.stackexchange.com/questions/260545",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/143028/"
] | Suppose you observe vector $X_i$ of independent variables, and $y_i$ dependent variables, with likelihood $l\left(\theta;X_i,y_i\right)$. Assume the $y_i$ are independent. Furthermore assume you are given positive <em>weights</em>, $w_i$ which are arbitrary, and compute the weighted Maximum Likelihood Estimator (WMLE?)... | Hamilton shows that this is a correct representation in the book, but the approach may seem a bit counterintuitive. Let me therefore first give a high-level answer that motivates his modeling choice and then elaborate a bit on his derivation.
<em>Motivation</em>:
As should become clear from reading Chapter 13, there ... | This is the same as above, but I thought I would provide a shorter, more concise answer. Again, this is Hamilton's representation for a causal ARMA($p$,$q$) process, where $r=\max(p,q+1)$. This $r$ number will be the dimension of the state vector $ (\xi_t, \xi_{t-1},\ldots, \xi_{t-r+1})'$, and it is needed to make the ... | https://stats.stackexchange.com |
110,621 | [
"https://security.stackexchange.com/questions/110621",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/96933/"
] | I am calling an HTTPS URL through a Java program. Does my Java client need to provide a certificate to the server to establish this connection? In other words, do I need my own certificate or is the server's certificate (which contains its public key) enough?
| Depends what you are doing, and what you want to verify. If you are accessing data, and want to be sure that the server which knows the corresponding private key is the one sending you data (e.g. you're accessing a web page), you don't need your own certificate.
If the server wants to be able to verify that the client... | Generally, most web servers running HTTPS do not require the client to have a certificate. If the server requires the client to authenticate, this is often done through credentials (e.g. username and password).
However, the converse is generally not true - i.e. most clients DO require web servers to have a valid cert... | https://security.stackexchange.com |
399,318 | [
"https://softwareengineering.stackexchange.com/questions/399318",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/106553/"
] | TL;DR - When designing classes for MVC use, is there "best practice" for how classes should be structured to eliminate property duplication and/or redundancy? I'm trying to avoid large (one-size-fits-all) classes with many (redundant) properties, but am also concerned about having too many isolated classes.
I've been... | <blockquote>
<strong>TL;DR</strong><br>
If you duplicate too much, you violate DRY/YAGNI. If you reuse too much, you (may) end up having to rewrite core parts of your domain logic later on.
Never abstract for abstraction's sake, never duplicate just for duplication's sake. Always look at your situation and pic... | Make sure you don't blur the responsibilities between views and models.
You're talking about inheritance but a view has a totally different responsibility to a TodoItem and changes for different reasons.
If you just want to show for example PersonName in your view without duplicating it then simply creates a proxy pro... | https://softwareengineering.stackexchange.com |
45,892 | [
"https://security.stackexchange.com/questions/45892",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/10714/"
] | There is a lot of security related products for home users and it is becoming unclear what the difference is between them.
What is the difference between antimalware, antispyware, antiadware and antivirus and are all of them necessary? Are other security products such as firewall and anti-spam necessary, as they ofte... | Here are some to think about, mainly from the "home user" perspective. The enterprise environment is unlikely to use a single vendor for all security needs. If they do, the setup and support package usually eliminates all common mistakes.
<strong>Good:</strong>
<ul>
<li>More integration/less administrative work to do... | For me, a big downside is bloat. For a while I used Comodo firewall on my windows home machines, but gradually updates started including some stuff that really should have been optional, like live chatting and such.
Also, over time, I'd accumulated a large amount of images to make up the gui that weren't really neces... | https://security.stackexchange.com |
2,594,249 | [
"https://math.stackexchange.com/questions/2594249",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/448693/"
] | <blockquote>
Question: Among the complex numbers $z$ satisfying $|z-25i|\le15$, the number having lowest argument is:<br>
a)$10i$<br>
b)$-15+25i$<br>
c)$12+16i$<br>
d)$7+12i$
</blockquote>
All the numbers so satisfy the condition.
The answer given is c) but i think the answer should be b) since it has the... | For any definition of integral, you have $f\leqslant g\implies\int_B f\leqslant\int_B g$ and $\int_B-f=-\int_Bf$. Therefore\begin{align}-|f|\leqslant f\leqslant|f|&\implies\int_B-|f|\leqslant\int_Bf\leqslant\int_B|f|\\&\iff-\int_B|f|\leqslant\int_Bf\leqslant\int_B|f|\\&\iff\left|\int_Bf\right|\leqslant\int_... | Preassume that integral $\int g$ is defined for any nonnegative measurable function $g$. This with $\int g\in[0,\infty]$ and $\int g_1+g_2=\int g_1+\int g_2$.
Function $f:B\to\mathbb R$ induces nonnegative functions $f_+:B\to\mathbb R$ prescribed by $x\mapsto\max(f(x),0)$ and $f_-:B\to\mathbb R$ prescribed by $x\mapst... | https://math.stackexchange.com |
64,610 | [
"https://softwareengineering.stackexchange.com/questions/64610",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/7452/"
] | This was my experience at a previous company. As it was a small startup company, some of the normal software development procedures were not followed strictly. One of my colleagues was a senior programmer with the company for 2 years. His skills were quite lacking. He would allocate his tasks to me and then take cr... | You already did what I think many would have advised, which is to leave the company and find new management.
Had you stayed, source control would be one way to build evidence. The other would have been to not finish his tasks, which it sounds like did happen. At some point management (well, competent management anyway... | I would say there's nothing you can do, once it has happened, unless you have evidence. And it sounds like you've come out of the situation ok.
I would suggest that this kind of thing is pretty uncommon but certainly not unheard of in the industry, so I would take a lesson from this and protect yourself in future.
Th... | https://softwareengineering.stackexchange.com |
14,836 | [
"https://chemistry.stackexchange.com/questions/14836",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/7317/"
] | Why are the two molarities multiplied and not added, and why is each raised to the power of the coefficient rather than multiplied by it? What is the reasoning behind this form? Was it simply determined that the probability of reaction was proportionate to both and thus they are multiplied together? I'd like to know wh... | After much research and work, I wrote a little explanation (not that the other answers weren't good, they just weren't well written for someone who didn't know about thermodynamics and other concepts …):
The below results were determined experimentally but this explanation gives some insight into why they are the way ... | Equilibrium is also the state in which the forward and reverse reactions are proceeding at equal rate. Consider a hypothetical reaction
$$\ce{aA + bB} \overset{k_1}{\underset{k_{-1}}{\ce{<=>}}}\ce{ cC + dD}$$
If we assume that the forward and reverse processes are elementary reactions (a <strong>big</strong> a... | https://chemistry.stackexchange.com |
142,509 | [
"https://mathoverflow.net/questions/142509",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2264/"
] | Suppose we have a collection of exactly $N$ points (say $N=1000$), with each point belonging to 2-dimensional Euclidean space $\mathbb{R}^2$, but we don't know the coordinates of the points. Suppose that we instead have, for some pairs of points, an approximation for the Euclidean distance between them.
<strong>Quest... | If $x$ and $y$ are two commuting idempotents, then $(x+y)^3 = x+y+6xy$, $(x+y)^2=x+y+2xy$, so $z=x+y$ satisfies the equation $z^3-3z^2+2z=0$. Plugging $z=3$ into the equation, we obtain $6=0$. So the ring is a product of a ring of characteristic $3$ and a ring of characteristic $2$.
In the ring of characteristic $2$, ... | <strong>The trivial/elementary proof (in particular, it does not use the axiom choice).</strong>
A ring $R$ satisfies your condition iff it satisfies the identity $x^3=x$.<br>
Pf.
Will shows above with a short computation that if $R$ satisfies the condition, then the characteristic divides $6$. So if $z=e+f$ with $e,... | https://mathoverflow.net |
8,931 | [
"https://robotics.stackexchange.com/questions/8931",
"https://robotics.stackexchange.com",
"https://robotics.stackexchange.com/users/11615/"
] | I'm working with a differential-drive robot that has odometry measurements from wheel shaft encoders and heading information from an IMU (I'm using BNO055 in IMU mode to get Euler angles, primarily the heading angle).
I'd like to use the IMU header angle to augment the odometry which is prone to slipping and other erro... | Combining two sensor outputs that should theoretically give you the same information is called "sensor fusion".
The easiest way to go about this is with a tool known as a complimentary filter. The complimentary filter uses a "blend" value, between 0 and 1, to produce the output:
<pre><code>filterOutput = blend*senso... | You're robot must be moving pretty fast for this delay to cause problems.
Use a circular buffer to store the odometry readings, so you'll have a record of the last 100ms of odometry readings.
Use the IMU and odom combined at time $T_{-100ms}$ to estimate your last known 'accurate' state. Integrate the odom forward fr... | https://robotics.stackexchange.com |
302,586 | [
"https://physics.stackexchange.com/questions/302586",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/12157/"
] | Assuming matter is more or less uniformly distributed in the Universe, what would be the net gravitational force acting on a stationary (from the reference frame of the Universe as a whole) lump of matter, from the rest of the Universe in these cases?
<ol>
<li>The Universe is infinite,</li>
<li>The Universe is finite ... | In 1st case, assuming an infinitesimal part of the lump, We consider the universe as the superposition of 1. The rest of the lump and 2. The other masses which we considered them all in a single mass density $\rho$.
The forces of the uniform infinite matter cancel on any infinitesimal part by symmetry. What remains is... | First of all your question assumes there is a universal proper inertial frame which may or may not be true. With both case scenarios the answer is it depends. Gravitational attraction is not linearly related to the distance between mass/energy in question. Because of that relationship the homogeneous distribution of ma... | https://physics.stackexchange.com |
55,958 | [
"https://dsp.stackexchange.com/questions/55958",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/34272/"
] | I saw details indicating "total energy of a Fourier-transformable signal equals the total area under the curve of squared amplitude spectrum of this signal."
I have no issue with that. But I have found pretty much no discussions about the consequence of applying the Rayleigh energy equation to the Fourier transform of... | <blockquote>
First if y[n] and x[n] were periodic, then wouldn't the ratio of their periods always be rational since each period is always integer?
</blockquote>
No. I mean. Yes.
<span class="math-container">$x(t)$</span> might be e.g. <span class="math-container">$2\pi T$</span>-periodic, and <span class="math-co... | It is a commonly understood (but not necessarily universally followed) convention that square brackets as in <span class="math-container">$x[n]$</span>
means discrete-time signals where <span class="math-container">$n$</span> is an integer (in accordance with the common convention that variables denoted by the letters... | https://dsp.stackexchange.com |
1,764,511 | [
"https://math.stackexchange.com/questions/1764511",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/333930/"
] | If I use the above statement, provided that it is right, in a question, would I have to prove it as well?
| In this case, the proof is rather trivial: since the $\cap$ operator is both associative and commutative, all the following are equivalent:
$$ (A \cap B) \cap (A \cap C) $$
$$ A \cap B \cap A \cap C $$
$$ A \cap A \cap B \cap C $$
$$ A \cap B \cap C $$
$$ A \cap (B \cap C) $$
As others said, whether or not you actuall... | Statement: $A \cap (B' \cap C') = (A \cap B') \cap (A \cap C')$
<ul>
<li>$A \cap (B' \cap C') \subset (A \cap B') \cap (A \cap C')$</li>
</ul>
$x \in A \cap (B' \cap C') \implies x \in A$ and $x \in B' \cap C' \implies x \in A, x \in B', x \in C' \implies x \in A \cap B'$ and $x \in A \cap C' \implies x \in (A \cap B... | https://math.stackexchange.com |
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