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660,571 | [
"https://physics.stackexchange.com/questions/660571",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/311337/"
] | I know that moving charge (such as electrons moving around nuclei) produces a magnetic field. I also know that moving charge (again, such as electrons in atoms) can produce electromagnetic waves, which are just disturbances in magnetic and electric fields. So, what is the microscopic explanation of the electrons' motio... | In the above question, <span class="math-container">$n=2,3....$</span> doesn't imply that there is more than <span class="math-container">$1$</span> electron.
In the above problem, <span class="math-container">$n$</span> represents the principal quantum number. It tells you in which state, is that one electron. In term... | The hydrogen atom has 1 electron. The electron configuration, 1S1, refers to the ground state, <span class="math-container">$\Psi_{100}$</span>, or <span class="math-container">$n=1$</span>, <span class="math-container">$l=0$</span>, <span class="math-container">$m=0$</span>. Any other quantum numbers indicate an excit... | https://physics.stackexchange.com |
218,455 | [
"https://physics.stackexchange.com/questions/218455",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/15845/"
] | Example problem:
<blockquote>
"A sled has an initial velocity up a ramp of 5 m/s, the ramp has an angle of 20 degrees to the horizontal, and the coefficient of dynamic friction between the sled and the plane is 0.5. Find the maximum height the sled will travel to."
</blockquote>
So this is a problem I gave my stud... | The word "strength" actually means a lot of different things in different contexts. Some people will use it (incorrectly) to be synonymous with "stiffness." Sometimes it means the ability to resist permanent deformation when subjected to shearing forces ("yield strength" or "shear strength"). Sometimes it means the abi... | Graphene is a single atom thick. Some groups have made multi-layer graphene but it's still very thin. It's generally printed on a board so that it doesn't fall apart. Thicker layers are just graphite which is pencil lead.
| https://physics.stackexchange.com |
219,945 | [
"https://mathoverflow.net/questions/219945",
"https://mathoverflow.net",
"https://mathoverflow.net/users/65800/"
] | Let $A_n$ be the alternating group of $\{1,2,\cdots,n\}$.
(1). What is the cohomology ring
$$
H^*(A_4;\mathbb{Z}/3)
$$
and its Steenrod operation $P^i$'s?
(2). Are there general results about the cohomology ring
$$
H^*(A_{p+1};\mathbb{Z}/p)
$$
for general primes $p\geq 3$?
(3). What is the cohomology ring
$$
H^*... | An easier way for the first case
Consider $P$, a $3$-Sylow subgroup of $A_4$. For example, take the cyclic group generated by the cyclic permutation (123). It is self normalizing, so the double coset formula for the compositions $BP\rightarrow BA_4 \stackrel{tr}{\rightarrow}BP$ where $tr$ denotes the transfer, reduc... | Regarding your first question, you have a group extension
$$1\rightarrow (\mathbb{Z}/2)^2\rightarrow A_4\rightarrow \mathbb{Z}/3\rightarrow 1.$$
Then we can use the Lyndon-Hochschild-Serre spectral sequence
$$E_2^{p,q}=H^p(\mathbb{Z}/3,H^q((\mathbb{Z}/2)^2,\mathbb{Z}/3))\implies H^{p+q}(A_4,\mathbb{Z}/3)$$
a priori the... | https://mathoverflow.net |
266,296 | [
"https://math.stackexchange.com/questions/266296",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/36016/"
] | give an example of a complete metric space $(X,d)$ and a mapping $T: X \rightarrow X$ which does not have a fixed point in X and satisfies;
$$ d(T(x),T(y)) < d(x,y)$$
$\forall x,y \in X, x\neq y$
i thought first that this was impossible by the fixed point theorem, but then figured with the final constraint it must ... | == Take the space $\,K:=[1,\infty)\,$ with the inherited euclidean topology from $\,\Bbb R\,$ , and remark that this is a complete metric space. (hint: it is a closed space)
== Define $\,f(x):=x+x^{-1}\,$ on the above space.
== For $\,x,y\in K\,\,,\,x\neq y\,$, check that
$$|f(x)-f(y)|=|x-y|\left|1-\frac{1}{xy}\righ... | Try $X = [0,\infty )$ , $(X,d)$ is complete metric space, where $d(x,y) = |x-y|$
$T(x) = x + e^{-x} $
$$\sup_{x\neq y} = \frac{d(T(x),T(y))}{d(x,y)} = 1$$
| https://math.stackexchange.com |
11,581 | [
"https://scicomp.stackexchange.com/questions/11581",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/8138/"
] | I try to solve a system of coupled PDEs using FEM. Unfortunately, the originating matrix has very poor condition. After days of double checking and thinking, I suspect the following reason:
Given a PDE
<pre><code>a * Laplacian(u) + b * u = 0
</code></pre>
For FEM, one has to calculate two operator matrices, one for ... | No, a different unit will not alter the condition of the system. Say your FEM system is
$$
Au + \beta Mu = 0. \quad (*)
$$
Then the parameter $\beta$, here something like $b/a$ from your example, will depend on the units in a way that only allows you to add "$A$" and "$M$" in terms of units. A rescaling will then mean ... | No. It is the ratio of the scales of these two operators that will drive the condition number not their absolute magnitude. You can multiply the whole equation through by any arbitrary constant without changing the condition number.
| https://scicomp.stackexchange.com |
289,659 | [
"https://softwareengineering.stackexchange.com/questions/289659",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/187165/"
] | I'm currently interning at a company where I've been tasked with building an application from scratch. I've been working about 8 weeks, with 4 left to go. I've written a lot of code in that time, but now as I go over it, I'm realizing that it's really quite inefficient, ugly, and going to be hard to maintain for whoeve... | We're the wrong people to ask.
You're writing this code for the company; essentially it is your customer. Someone in that company knows who's going to work on it next; someone has an idea of whether more features or more maintainable code have greater value for them.
<em>You</em> are your customer, too, in some ways... | <h1>DELIVER</h1>
This is your priority. This is all they care about. This is what you've got to do.
If you get to deliver something that you feel has <strong>a sense of quality</strong> to it, you'll fell better and work better, and see a future for yourself in that company.
But you have to be <strong>realistic about t... | https://softwareengineering.stackexchange.com |
739,459 | [
"https://physics.stackexchange.com/questions/739459",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/305256/"
] | Suppose an irreversible adiabatic expansion process and a reversible adiabatic expansion process are starting from the same initial state, say, P1V1. Now, let both of these processes have equal pressure in their final state. My teacher said that the magnitude of the work done in the reversible process will be more than... | It is better to think of it the other way around and understand/derive the "2nd law" from the observation that in an adiabatic process the work done is maximum if it is reversible. When I say "derive" the 2nd law I mean making equivalent statements to that for this is at the heart of it.
Take that s... | Although at the time of your post your teacher hadn't yet taught you the second law, you can, based on the first law alone, show why the final temperature of the gas is higher for the irreversible process in the case of an ideal gas and the <em>assumption</em> that more work is done for the reversible process for the s... | https://physics.stackexchange.com |
119,006 | [
"https://softwareengineering.stackexchange.com/questions/119006",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/26304/"
] | This is an Agile development project and I do not have the ability to change that.
The design that will be the fastest and most obvious for the first phase of our project will not be compatible with the needs of our second phase. The change would not be difficult to implement now but it would take a little more time ... | If you are truly doing agile, then your team should be fully empowered as to the implementation details and your PM shouldn't have a say in it.
On one hand, agile is all about delivering some value quickly, rather than waiting until every wanted feature is perfectly in place. This occasionally means reducing short te... | You're practicing Scrumerfall. The reference to phases, PM's, etc... leads me to believe that the team has embraced Agile where it feels like it fits, versus changing previous notions and conceptions on how the process works.
In either case, do what you need to do to complete the backlog item. You're theorizing that p... | https://softwareengineering.stackexchange.com |
299,320 | [
"https://physics.stackexchange.com/questions/299320",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/136931/"
] | We are given a string of length $L$ tied to massless rings at both ends so as they can move freely in the transversal direction. The linear density of the string is $ρ$ and the tension at rest (where $y=0$ for the whole string) is $T$.
I found that the normal modes of the string are:
$$y_n(x,t)=A\cos(k_nx)\cos(\omeg... | I saw this question in a textbook, and it got the answer wrong.
The speed of the turntable does NOT change as the dry ice sublimates.
Here's how to think about it: what if you had a spinning metal turntable and cut it in half horizontally producing two thinner turntables? Each is still spinning around the same axis.... | When particles exit the surface, they would continue in the direction they were headed prior to release. That is, tangent to the rim, in the direction of rotation. So their momentum would be subtracted from the disk, slowing it down.
| https://physics.stackexchange.com |
165,612 | [
"https://electronics.stackexchange.com/questions/165612",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/72683/"
] | <img src="https://i.stack.imgur.com/gurdn.jpg" alt="LED driver">
This is an LED driver circuit, but what is the use of the transistor in it?
| The 7805 regulator is setup as an adjustable regulator as adjusted by the 10K pot. The transistor is connected as an emitter follower to increase the load current available to the LED load. Supposedly the 7805 is not able to supply the load current needed for the LEDs and so the transistor acts as a current booster.
... | The use of an external transistor is to allow for a linear regulator IC to deliver more current than usual. A 1.5A 7805 5V regulator can be made to drive loads of 3A+ using an external transistor like shown. It can also be used to make the external transistor take the heat during dissipation rather than the regulator I... | https://electronics.stackexchange.com |
58,000 | [
"https://cs.stackexchange.com/questions/58000",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/41205/"
] | In preparation for my design and algorithms exam, I encountered the following problem.
<blockquote>
Given a $2 \times N$ integer matrix $(a[i][j] \in [-1000, 1000])$ and an unsigned integer $k$, find the maximum cost path from the top left corner $(a[1][1])$ and the bottom right corner $a[2][N]$, given the followi... | (I use the symbol $\oplus$ here because $\wedge$ is mathematically used for conjunction ("and") instead of exclusive-or)
First we rearrange the terms,
\begin{align}
x_1 \oplus x_2 \oplus x_3 \oplus x_4 &= 0 \\
x_1 \oplus x_3 \oplus x_2 \oplus x_4 &= 0 \\
x_1 \oplus x_3 &= x_2 \oplus x_4
\end{align}
Then... | Xor means when we get two same variables answer is 0. That is 0^0=0 and 1^1=0. it is possible to get x1^x2^x3^x4=0 if and only if x1^x2==x3^x4
| https://cs.stackexchange.com |
58,028 | [
"https://cs.stackexchange.com/questions/58028",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/2529/"
] | Is the number of possible programs usually finite or infinite? I'm playing with the idea of generating all possible programs for a language - is that even a finite number or must we be more specific, finite RAM etc?
| When considering such questions we usually disregard limitations of real computers and think about a programming language theoretically.
A general-purpose programming language (any language used in practice falls into this category) has infinitely many programs. Furthermore, all programs can be generated systematicall... | <strong>The number of programs of any given length is finite.</strong> You can get an upper bound to the number rather simply: if the program's source code is $n$ bits long, then there are at most $2^n$ programs of that length. The real number will be far, far less, because of the need for programs to be syntactically ... | https://cs.stackexchange.com |
396,104 | [
"https://electronics.stackexchange.com/questions/396104",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16018/"
] | The watchdog of an ATMEL ATXMega128 should have been enabled with fuses. It triggers a reset, if the timer was not reset within the configured time span.
I want to be sure, that it is <strong>enabled</strong> and <strong>working properly</strong>.
What is a good method to verify that the watchdog is enabled and workin... | AtMega MCUs have a watchdog with dedicated 32kHz oscillator, so yes: putting the main oscillator on pause will trigger it. Writing a test software which intentionally fails to service the watchdog is another possibility, and it will enable you to validate not only the fact that the watchdog in enabled, but easily measu... | You can test through a sequence. Use an existing non critical output like an led as a test signal. Program the board with a test sequence that will toggle the led and loop,
And does not pet the watchdog. Test for the loop. Then program it to do a second loop, where it will not reach if the specified watchdog timer do... | https://electronics.stackexchange.com |
13,905 | [
"https://electronics.stackexchange.com/questions/13905",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/3817/"
] | For my exam I need to calculate the apparent power, active power and reactive power.
I know I get the active power from the real part and reactive power from imaginary part of the apparent power. However, I can't find any formulas for my specific problem.
I have
\$ U = 82.58 e^{j31.89°} \$ and \$ I = 1.65 e^{j31.89°... | Use these identities :-<br /><br />
\$z = R.e^{j\theta}\$<br />
\$Re(z) = R\cos(\theta) = a\$<br />
\$Im(z) = R\sin(\theta) = b\$<br />
\$z = a + jb\$<br />
\$R = |z| = \sqrt{a^2 + b^2}\$<br />
\$\theta = Arg(z) = \arctan(\frac{b}{a})\$<br /><br />
For example:<br /> \$56.e^{j40} = 56\cos(40) + 56j\sin(40) = 42.9 + 36.... | Euler's Formula: \$ e^{j \theta} = cos(\theta) + j * sin(\theta) \$
<strong>edit</strong><br>
Euler helps you to separate the complex power of \$e\$ into its real and imaginary parts. These agree with your active and reactive power resp.
| https://electronics.stackexchange.com |
133,638 | [
"https://softwareengineering.stackexchange.com/questions/133638",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/27417/"
] | We are a small team of 4 devs rather green in Scrum. Coming from all over the country, we often take odd days off or whole weeks off to go home. Therefore our team capacity changes dramatically from one iteration to another due to annual leaves, which leads to very different velocities from one iteration to another. Ho... | It might be a simple approach, but why don't you calculate your velocity as <code>completed story points * capacity</code> or <code>completed story points / capacity</code>, depending on how measure capacity. If you measure capacity in man-hours, use the second. If you measure capacity as a percentage of a 40-hour week... | Velocity can vary even if capacity remains same.
So just trust your velocity it will take care of varying capacity itself i.e. assuming you are into 3rd sprint, take average of the last two completed sprints to commit to the next sprint. do not worry about variance in capacity.
| https://softwareengineering.stackexchange.com |
248,482 | [
"https://electronics.stackexchange.com/questions/248482",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/118103/"
] | I've seen several circuit diagrams having a 0.1 microfarad capacitor connected to the supply voltage.
How do capacitors work to prevent fluctuations in DC source voltage? Why don't they completely block DC and act as a sort of break in the circuit
| The power distribution network (PDN) in a PCB is not ideal. It has non zero resistance and inductance.
Let's say an IC needs a sudden increase on supply current. The resistance and inductance of the PDN could cause that such a sudden increase in current consumption generates a temporary voltage drop (a local drop, clo... | Capacitors "block DC" in the sense that in a steady state DC system the current through a capacitor is zero.
But we aren't typically dealing with a steady state DC system. We are dealing with components that are performing some time-varying task. The power supply demands of those components will in turn be time-varyin... | https://electronics.stackexchange.com |
39,516 | [
"https://security.stackexchange.com/questions/39516",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/28687/"
] | I'm currently a web developer for a company with lots of different remote clients. There are lots of usernames and passwords that I need to know so that I can do my job. When I first started, I was able to obtain a good chuck of credentials by reading them off my boss's computer. I stored them on my computer, in 1Passw... | First, you can't e-mail over HTTPS. HTTPS is a web site protocol, not an e-mail protocol. Encrypted e-mail exchanges require the mail servers to communicate using TLS or SSL. The best way to exchange credentials, if you absolutely have to do it, is to encrypt them with a secure, long password or better yet, a pre-sh... | I second the suggestion from AJ Henderson of some non-email, web-based, HTTPS messaging application that your clients can use.
In the absence of that, you could just change the password every time you are sent credentials insecurely, storing the new, strong password in your password manager.
You can take this opportu... | https://security.stackexchange.com |
320,023 | [
"https://physics.stackexchange.com/questions/320023",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/118053/"
] | I was given the following question a while back :
An empty utility vehicle weighs 16.5 kN. Each of its tires has a gauge pressure of 205 kPa. What is the total contact area of the four tires with the pavement (assume that the tire walls are flexible so that the pressure exerted by the tire on the pavement equals the a... | You should be fine as long as you are consistent. If you use total pressure, as they do, then you also need to include the effects of the air pressure on top of the tire pushing down on it with 1 atmosphere of force!
As a thought experiment let's use some really fancy spherical-cow materials. Let's make a <em>gigant... | An open tube mercury manometer is used to measure the pressure in an oxygen tank. When the atmospheric pressure is 1040 mbar, what is the absolute pressure in Pascal in the tank if the height of the mercury in the tube is
A) 28.0 cm higher
B) 4.2 cm lower, than the mercury in the tube connected to the tank.
| https://physics.stackexchange.com |
307,653 | [
"https://electronics.stackexchange.com/questions/307653",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/150359/"
] | I am a newbie to embedded systems design so this question might seem very fundamental in nature.
I have been working as part of an Avionics team to develop an on board computing device for a unmanned aerial vehicle which would need to interact with various subsystems like camera, ir sensors, actuators, etc. We will b... | Yes, you can replace an embedded solution with standard parts. However, you might not be able to.
For example, you listed specs such as:
<ul>
<li>mil environment, temperature, vibration, reliability.</li>
<li>real time software</li>
<li>avionics (weight and size restrictions?)</li>
</ul>
You won't get a standard pc ... | It seems you are looking for something called a <i>single board computer</i>. These things exist in many varieties and tradeoffs, and the industry is quite competitive. You can get something beefy enough to run Windows 10 IOT, for example, for $350, including the Windows license and 0-70°C operating temperature. ... | https://electronics.stackexchange.com |
15,249 | [
"https://electronics.stackexchange.com/questions/15249",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/4277/"
] | I tried connecting the GPIO1_0 pin of LPC1114 to the input pin 1 of the ULN2003a IC. And I connected a 9V supply to the COM pin of ULN2003a. For whatever the logic level at pin1 (i/p) of ULN2003a, its corresponding output is always 0.57V. The logic high of the MCU at the o/p gives around 3.1V. What is wrong here?
<str... | You need pull-up resistors on the outputs (or whatever load you want to drive).
Inside the ULN2003 there are darlington transistors with an open collector, so without some external circuit the output will not be pulled up to some higher voltage.
The COM pin is connected to a freewheeling diode for each transistor, so... | The ULN2003 can only sink 500ma as you stated. It will not handle the 600ma required by the motor. You can parallel the inputs and outputs however on the ULN2003 to increase the current. For example if you were to tie two inputs to the micro output, then tie their respective outputs to the motor connection then the cur... | https://electronics.stackexchange.com |
45,776 | [
"https://mathoverflow.net/questions/45776",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10775/"
] | Given a toric ideal, say $J$, in a polynomial ring $k[x_1,...,x_n]$ we can find a finite
generating set for $J$. Is it possible, perhaps under additional assumptions on the structure of $J$, to give a finite minimal generating set for $J$ such that every subset of generators also generates a toric ideal.
If not, are... | I believe this is a counterexample. Toric ideals are prime by definition (assuming that I am remembering correctly). Then I think that the ideal of the twisted cubic $C\subseteq \mathbb P^3$ ought to do it.
$J=\langle xz-y^2, xw-yz,wy-z^2\rangle$.
Any two of the three generators will intersect in the union of $C$ a... | What is going on can be explained completely in terms of exponent vectors. To do so we can map each generator $x^u -x^v$ of $J$ to the exponent vector $u-v \in \mathbb{Z}^n$. Conversely, for each integer vector $s\in \mathbb{Z}^n$ we can form a binomial $x^{s^+} - x^{s^-}$ where $s^\pm_i = \max(\pm s_i, 0)$ are the pos... | https://mathoverflow.net |
36,985 | [
"https://softwareengineering.stackexchange.com/questions/36985",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/13312/"
] | When just starting a project, you have nothing---no UI, no data layer, nothing in between. Thus, a single story like "users should be able to view their foos" will entail a lot of work. Once you have that story, one like "users should be able to edit their foos" is more realistic, but that first story will involve sett... | This is a good question and there are probably several good answers to it. My take is this:
A story is a <strong>user story</strong> so it must be defined in terms that describe how it benefits the user.
If Agile and stories are going to work for you, then they should work even in the beginning stages. The first bu... | What you are asking is essential "how do you think about the problem space" in order to break it up into sensible pieces, from which you can do a design.
Whether you call this the user story, or analysis, or decompostion, or specification, or requirements gathering... in the end it comes down to several things which n... | https://softwareengineering.stackexchange.com |
65,589 | [
"https://stats.stackexchange.com/questions/65589",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/28466/"
] | I am currently implementing a Kmeans clustering algorithm in R. I am not using any packages and I wrote it from scratch. I am using only one set of initial guesses, and my action upon finding an empty cluster is to select a new data point randomly and use that as the new mean for the empty cluster.
I have gathered fro... | From the actual objective, K-means does <strong>not optimize the sum of total distances</strong>.
K-means optimizes the sum of squares, i.e. $SSQ:=\sum_o \min_\mu \sum_i |x_i - \mu_i|^2$.
$i$ iterates over all dimensions, and $\mu$ are the cluster centers.
Technically, this means assigning each point to the closest ... | Although this question already has an accepted answer, I would like to address the yet unadressed problem of a possible non-convergence of k-means.
This can indeed occur due to ties and cyclical assignemnt of ties to different clusters. To avoid this issue, you must always use the same deterministic tie breaking, e.g.,... | https://stats.stackexchange.com |
4,565,003 | [
"https://math.stackexchange.com/questions/4565003",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/929966/"
] | I'm working on the following problem:
The holomorphic <span class="math-container">$1$</span>-form <span class="math-container">$\frac{dz}{1+z^2}$</span>,
defined on <span class="math-container">$\mathbb{C}\setminus\{\pm i\}$</span>, can be extended to a
holomorphic <span class="math-container">$1$</span>-form <span cl... | I find your notation (using <span class="math-container">$\tan$</span> and <span class="math-container">$\sec$</span>) slightly confusing, so let me just work it out in the way that I consider to be "clean". We take the standard open cover <span class="math-container">$\{U_0,U_1\}$</span> for <span class="mat... | You also asked how one can find the pullback of the <span class="math-container">$1$</span>-form <span class="math-container">$\omega$</span> (on <span class="math-container">$\mathbb{P}^1\setminus\{\pm i\}$</span>) by the tangent function <span class="math-container">$\operatorname{tan}\colon \mathbb{C}\rightarrow \ma... | https://math.stackexchange.com |
71,264 | [
"https://mathoverflow.net/questions/71264",
"https://mathoverflow.net",
"https://mathoverflow.net/users/14541/"
] | If I have a quasiprojective variety $X$, and a subscheme $Z$, then the blowup
$$f:Y = Bl(X,Z)\rightarrow X$$
is projective over $X$, since it is constructed by a relative Proj construction. Can I find a relatively ample bundle on $Y$ that is trivial on
$$f^{-1}(X\backslash Z)?$$
At first I thought the construction ... | This can be done if $X$ has $\mathbb Q$-factorial singularities (but this is not a necessary condition!): Let $H$ be a relative ample effective divisor (not a bundle, divisor!). Then $f_*H$ is a Weil divisor on $X$ and if $X$ has $\mathbb Q$-factorial singularities, then some multiple of $f_*H$ is Cartier. Replacing $H... | anon, is your definition of relatively ample local over the base? (There are some different definitions out there, but most people seem to use the one that is local over the base now, compare for instance Ravi Vakil's notes with Hartshorne).
If your definition of relatively ample is local over the base, then there ... | https://mathoverflow.net |
154,642 | [
"https://security.stackexchange.com/questions/154642",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/-1/"
] | Lets say that you have they encryption key, but you don't have the entire cipher-text. You just have a part of it, say 60%.
Is there a way to possibly decrypt that part of the cipher-text? Does it depend on the specific algorithm or mode? Does it depend on the specific forms of data like text and not image form?
| First, regarding the encryption algorithm, there are two general types of algorithms, blocks and chains. A block algorithm applies the key to each block of data (e.g. 256 bit blocks), while a chained algorithm uses the previous block to decode the current block, with the key serving as the first block in the chain. For... | To add to Phyrfox's answer, it also depends on the data. If the data has any forward error correction (like a hamming code) included in it then some missing parts of the data can be re created. If it was something like a plain text password, or a part of a shared secret you would have to guess the missing parts. And if... | https://security.stackexchange.com |
2,478,229 | [
"https://math.stackexchange.com/questions/2478229",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/492343/"
] | The matter of interest is
$$\int_{0}^{1/2} \frac{1}{|\sqrt{x}\ln(x)|^p}\, dx$$
I am aware that this integral converges for $p=2$ (that's not too hard to show). I also believe that this integral diverges for $p>2$...but how can I show that using elementary calculus and related techniques (comparison test etc)?
| By enforcing the substitution $x=e^{-z}$ we get
$$ \int_{0}^{1/2}\frac{dx}{\left(-\sqrt{x}\log x\right)^p} = \int_{\log 2}^{+\infty}\exp\left[\left(\frac{p}{2}-1\right)z\right]\frac{dz}{z^p} $$
and we clearly need $p\leq 2$ to ensure the (improperly-Riemann or Lebesgue)-integrability of $\exp\left[\left(\frac{p}{2}-1\r... | A simple change of variables does the trick: $y=1/x$
$$\int_0^\frac12\frac1{(-\sqrt x\log(x))^p}dx = \int_2^\infty\frac1{-y^{-p/2}\log(\frac1y)^p}\frac1{y^2}=\\
=\int_2^\infty \frac{y^{\frac p2-2}}{\log(y)^p}dy$$
The last integral converges iff $\frac p2-2\leq-1$, which is equivalent to $p\leq2$.
| https://math.stackexchange.com |
17,904 | [
"https://dba.stackexchange.com/questions/17904",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/6562/"
] | In SQL Server, I have a varchar column with value such as:
<pre><code> 07/May/2012:00:06:22
07/May/2012:00:06:22
07/May/2012:00:06:22
07/May/2012:00:06:22
07/May/2012:00:06:22
</code></pre>
<ul>
<li>How do I convert this column to a datetime column with real datetimes?</li>
<li>If this is not possible, how do I j... | Assuming dates in other months are truncated to 3-char months:
<pre><code> ALTER TABLE dbo.tablename ADD newcol DATETIME;
UPDATE dbo.tablename
SET newcol = CONVERT(DATETIME,
REPLACE(LEFT(varchar_col, 11), '/', ' ')
+ ' ' + RIGHT(varchar_col, 8), 113);
</code></pre>
Once you've verified, you can dro... | Likely you have some data that doesn't fit the datetime column somewhere in the file. Insert to a staging table with a varchar or navachar field for the column and look at the data. You may need to adjust some of it (or null out bad records) before loading to the real table.
| https://dba.stackexchange.com |
358,538 | [
"https://physics.stackexchange.com/questions/358538",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/169923/"
] | Would the total potential energy of a spring with uniformly distributed mass be equal to the sum of the potential energy possessed by every infinitesimally small point along the spring? If so, would PE be equal to the integral of force times distance and therefore $U=(1/2)kd^2$.
| Good question. Short answer is that it is not ignored but that both positive and negative amplitudes provide the same physics.
<hr>
<strong>Long answer</strong>: In physics, certain assumptions often seem unintuitive until one works things out. Suppose that
$$A=-\sqrt{C^2+D^2}$$
then the position would be
$$x(t)=-|... | Taking the negative sign of $A$ is totally equivalent to redefining the phase $\phi$ to $\phi'=\phi+\pi$,
$$A\cos(\omega t+\phi')=-A\cos(\omega t+\phi)$$
This just means you are redefining where you start measuring the angle from. Or you can think of this as a change in the initial condition.
| https://physics.stackexchange.com |
431,186 | [
"https://physics.stackexchange.com/questions/431186",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/135297/"
] | I have a system consisting of N distinguishable particles. Each particle has two states, one with energy E and the other with energy 0. The number of particles in the state with energy 0 is <span class="math-container">$n_{0}$</span> and the number of particles in the second state is <span class="math-container">$n_{1}... | I figured my problem now out maybe it is also of interest for others. I have in total N labeled particles and hence I can arrange them in <span class="math-container">$N!$</span> ways. Now I distribute the particles in two boxes. The boxes dont't have any drawers or anything and hence in the end I am not able to discri... | Since the particles are distinguishable, the answer is simply the number of possible combinations of <span class="math-container">$n_1$</span> elements drawn from a set of <span class="math-container">$N$</span> elements:
<span class="math-container">$$
\Omega (U,N) = \binom{N}{n_1}
$$</span>
Where <span class="math-... | https://physics.stackexchange.com |
592,684 | [
"https://math.stackexchange.com/questions/592684",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/93509/"
] | Suppose that $U$ and $V$ are two independent uniform $(-1,1)$ random variables.
Any hints on how I can show that their conditional distribution, given $U^2 +V^2<1$ is given by the uniform distribution over the unit circle, namely
$$f_{U,V|U^2+V^2<1} (u,v|w<1) =1/{\pi}, \quad u^2+v^2<1$$
Both an intuitiv... | use the conditional probability formula $P(X \in A| X \in B) = \frac{P(X \in A \cap B)}{P(X \in B)}$ when $P(X \in B) > 0$.
Now take $X = (U, V), B = \{(u,v): u^2 + v^2 <1\}$. Let A be a measurable subset 0f $(-1, 1) \times (-1,1)$, since $P(X \in B) = \frac{m(B)}{4} = \frac{\pi}{4}$, we have $P(X \in A | X\in B... | The original density of $(U,V)$ is constant on $\left(-1,1\right)^{2}$. Actually it equals $\frac{1}{4}$ since integration over that area must result in
$1$. The density of $(U,V)$ under condition $U^{2}+V^{2}<1$ is constant as well. There is only one choice then: $\pi^{-1}$. This because integration over that area ... | https://math.stackexchange.com |
3,248,354 | [
"https://math.stackexchange.com/questions/3248354",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/429931/"
] | I'm having a hard time constructing an explicit degree <span class="math-container">$2$</span> map <span class="math-container">$$C \rightarrow \mathbb{P}_k^1$$</span> where C is given by cutting out the elliptic homogeneous equation <span class="math-container">$$X^3+Y^3-Z^3=0$$</span> in <span class="math-container"... | Assuming <span class="math-container">$\operatorname{char}k\neq 2,3$</span>.
If we have a cubic in, for example, Weierstrass form
<span class="math-container">$$
Y^2Z+a_1XYZ+a_3YZ^2=X^3+a_2X^2Z+a_4XY^2+a_6Z^3
$$</span>
then it is obvious <span class="math-container">$(X:Y:Z)\mapsto(X:Z)$</span> is a degree <span class... | I think that the map is
<span class="math-container">$\phi: C\to \mathbb{P}^1$</span> such that
for each <span class="math-container">$[X,Y,Z]\in C$</span> you have that
<span class="math-container">$\phi([X,Y,Z])=[X,Y]$</span>
It’s well defined because <span class="math-container">$X,Y\neq 0$</span> otherwise a... | https://math.stackexchange.com |
22,090 | [
"https://scicomp.stackexchange.com/questions/22090",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/9506/"
] | In the the Finite Element Method (FEM), we attempt to obtain the Weak Form of the described equation. I understand that this is an attempt to reduce the <strike>order</strike> regularity of the equation, but what are the actual benefits and disadvantages of using the Weak Form? What does regularity mean in this sense?
... | The weak form of the PDE means that you have, in some sense, "fewer constraints on the kinds of functions that you can use" to construct a solution.
To put it into perspective, recall that in FEM, you look for a solution of the form:
$$\sum_{j}u_j*\phi_j(x)$$
where $u_j$ are the unknown scalar coefficients (which ... | It's precisely the opposite of what you had. You use the weak form to increase the regularity (or alternatively, allow you to solve problems with less regularity). Integration always smooths.
The intuition is actually quite simple: For "most" functions, if you take an integral, then its derivative exists (its derivati... | https://scicomp.stackexchange.com |
49,144 | [
"https://mathoverflow.net/questions/49144",
"https://mathoverflow.net",
"https://mathoverflow.net/users/33841/"
] | Let $\Gamma\subset\mathbb{P}^2$ be a singular plane curve and let us consider $f:C\to\Gamma$ the normalization map. Given $L\in\mathrm{Pic}(\Gamma)$, is it always true that $h^0(\Gamma,L)=h^0(C, f^*L)$? If not, can you exhibit a counterexample?
| Alternately, for any such $\Gamma$ and $C$, we always have a short exact sequence $$0 \to O_{\Gamma} \to f_* O_C \to F \to 0,$$
where $F$ is a finite length $\mathcal{O}_{\Gamma}$-module supported where $\Gamma$ is non-smooth.
Twisting by a very positive (ie, high multiple of an ample) Cartier divisor $L$ and taking... | Here is a concrete counterexample.
Let $X$ be a degree $4$ plane curve with a unique node $r \in X$. The normalization $f \colon \tilde{X} \to X$ is a genus $2$ curve, hence hyperelliptic. Let $p, q \in \tilde{X}$ be two points that are conjugate under the hyperelliptic involution and do not map to $r$ under the norm... | https://mathoverflow.net |
186,453 | [
"https://physics.stackexchange.com/questions/186453",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/82296/"
] | That is to say, is there a word that picks out protons, neutrons, AND electrons, rather than just saying "nucleons plus electrons"?
| You may be able to call them elemental particles. If you're looking for a single word, maybe even elementals.
| You may address all of them as Sub-atomic Particles
| https://physics.stackexchange.com |
388,016 | [
"https://math.stackexchange.com/questions/388016",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/75116/"
] | Let $P(x)$ be a polynomial of degree $101$. Then $x\mapsto P(x)$ cannot be a one-one onto mapping, i.e., bijective function from $\Bbb{R}$ to $\Bbb{R}$. True or false?
I think is when we take $P(x)=P(y)$, we get :
$$
ax^{101}+bx^{100}+\ldots+cx+d = ay^{101}+by^{100}+\ldots+cy+d
$$
or
$$
a\left(x^{101} - y^{101}\right)... | $P(x) = x^{101}$ is a bijective polynomial of degree $101$. $Q(x) = x^{101}-x^2$ is of degree $101$, too, but it's not injective. So unless there's more to the question, an arbitrary 101st degree polynomial can be bijective, but not all of them are.
| A polynomial $P:\mathbb{R}\to\mathbb{R}$ is bijective if and only if $P'(x)$ never changes sign.
In less mathematical language, we need the polynomial to always go up, or always go down, and it's only allowed to level out momentarily.
With this in mind, it is fairly easy to write down a polynomial of odd degree that ... | https://math.stackexchange.com |
440,932 | [
"https://softwareengineering.stackexchange.com/questions/440932",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/157676/"
] | Let’s say that we want to encode recipes or dishes for <code>x</code> days in the form of a <strong>string</strong>. There can be an arbitrary number of days. Each day, we can have 0–3 of the following: breakfast, lunch, dinner. For each meal, there are multiple possible options ordered by preference (preferred option,... | Sorry but this
<blockquote>
eggs,muesli-fish,lentils,pasta-veggies;-burger-
</blockquote>
is a train wreck of noise. It's far to difficult to see the structure here.
This is data. You need a data language. I'm a fan of JSON.
<blockquote>
There can be an arbitrary number of days. Each day, we can have 0–3 of the followi... | If you want to make this accessible to non-programmers, I think it's best to use something that they're familiar with: parentheses. You don't have to document anything new or surprising, just let parentheses do what they do:
<pre><code>((eggs muesli) (fish lentils pasta) (veggies))
(() (burger) ())
</code></pre>
If you... | https://softwareengineering.stackexchange.com |
16,257 | [
"https://bioinformatics.stackexchange.com/questions/16257",
"https://bioinformatics.stackexchange.com",
"https://bioinformatics.stackexchange.com/users/9448/"
] | I have a big single-cell RNA seq data
<pre><code>> dput(head(new.dat[,1:10]))
structure(list(cell1 = c(0.793763840992639, 0, 1.96843530982957,
0.461736429639991, 0.717968540649498, 0), cell2 = c(3.61741696702738,
0.231662370550224, 0, 0, 0, 0), cell3 = c(4.14348883366621, 0.118161316317251,
0.08074552209482, 2.27... | <pre><code>WhichCells(seurat_object made by this matrix, slot = 'counts', expression = PTPRC > 0 )
</code></pre>
By Seurat R package this is possible
| This is basic R subsetting operation. Most subset operations give you a subset of rows based on a column, while you're doing the opposite here - but the logic is the same.
This gives you a subset of rows when the expression is based on a column
<pre><code>df[logical_expression_that_subsets_rows,]
</code></pre>
Why not ... | https://bioinformatics.stackexchange.com |
84,250 | [
"https://cs.stackexchange.com/questions/84250",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/80541/"
] | I need to prove whether the language $ L = \{w \in \{0,1\}^* \mid |w|_0 = |w|_1 \}$ can be written as a regular grammar. Obviously it can, but how do I prove it?
| Let's consider a simpler recursion:
$$ T(n) = T(n-1). $$
Using back substitution, we get $T(n) = T(n-2)$, $T(n) = T(n-3)$, $T(n) = T(n-4)$, and so on.
What you do is go first to $T(n) = T(n-2)$, and then substitute this equation into itself to get $T(n) = T(n-4)$. So you're skipping a step.
| What you get is correct, but you haven't gone further one more step, but two more steps.
T(n) = 2T(n - 1) + n
First :
T(n - 1) = 2T(n - 2) + (n - 1)
T(n) = 4T(n - 2) + 2(n - 1) + n
Second :
T(n - 2) = 2T(n - 3) + (n - 2)
T(n) = 8T(n - 3) + 4(n - 2) + 2(n - 1) + n
Third :
T(n - 3) = 2T(n - 4) + (n - 3)
T(n) = ... | https://cs.stackexchange.com |
98,949 | [
"https://dba.stackexchange.com/questions/98949",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/37398/"
] | I have user called <code>test_user</code> created under <code>MySQL 5.5.17</code> under MS Windows 2008R2, I want to grant this user select privileges on all databases except MySQL database, note I have around 200 database inside this instance.
EDIT:
<img src="https://i.stack.imgur.com/mAnlx.png" alt="enter image des... | Run the output of the following query:
<pre><code>SELECT CONCAT("GRANT SELECT ON ",SCHEMA_NAME,".* TO 'test_user'@'localhost';")
FROM information_schema.SCHEMATA
WHERE SCHEMA_NAME NOT LIKE 'mysql';
</code></pre>
| Since you have 200 databases and you do not want to grant one by one. Fastest way to do that would be
<pre><code>GRANT SELECT ON *.* TO 'test_user'@'localhost';
FLUSH PRIVILEGES;
</code></pre>
And then just revoke the privilege in mysql db
<pre><code>REVOKE SELECT ON mysql.* FROM 'test_user'@'localhost' ;
FLUSH PRIV... | https://dba.stackexchange.com |
2,748 | [
"https://scicomp.stackexchange.com/questions/2748",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/1740/"
] | Generally speaking, I've heard numerical analysts utter the opinion that
<blockquote>
"Of course, mathematically speaking, time is just another dimension, but still, time <em>is</em> special"
</blockquote>
How to justify this? In what sense is time special for computational science?
Moreover, why do we so often... | Causality indicates that information only flows forward in time, and algorithms should be designed to exploit this fact. Time stepping schemes do this, whereas global-in-time spectral methods or other ideas do not. The question is of course why everyone insists on exploiting this fact -- but that's easy to understand: ... | While there are some exceptions (e.g. fully discrete finite element methods), temporal discretization generally implies an inherently sequential dependence in flow of information. This dependency restricts semi-discrete algorithms (BVP in space, IVP in time) to compute solutions to subproblems in sequential manner. T... | https://scicomp.stackexchange.com |
487,449 | [
"https://stats.stackexchange.com/questions/487449",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/296388/"
] | *sorry if this isn't the right SE community, maybe it's more philosophical*
You often hear this refrain in games like Poker or Hearthstone. The idea is that making play A this game resulted in a loss, but always making play A in the long run/limit is the best odds/EV.
My question is: Why does this idea seem to require ... | I do not believe that this is a question of Bayesian vs. frequentist frameworks. It is a question of having the correct (predictive) distribution and minimizing the expected loss with respect to this distribution and a specified loss function. Whether the predictive distribution is delivered by a Bayesian or by a frequ... | I don't think either that this is a question about frequentist vs bayesian.
There is someone, in fact, that argue that frequentist approach to the case of once-only experiments is not solid enough: what interest do I have on what happens to an experiment if I repeat it indefinitevely, if I actually don't have the possi... | https://stats.stackexchange.com |
144,246 | [
"https://mathoverflow.net/questions/144246",
"https://mathoverflow.net",
"https://mathoverflow.net/users/30412/"
] | I proved the following facts by unenlightening calculations. Since the statements are quite clean, I think there should be a conceptual explanation for them, which my proof certainly is not.
Let $q$ be a prime power, and let $\mu_{q+1}$ be the set of $(q+1)$-th roots of unity in the finite field $\mathbf{F}_{q^2}$. ... | Let $E$ be a curve defined by a singular Weierstrass equation over $\mathbb{F}_q$, where the singularity is a node, say at the origin. Then, Silverman says (Arithmetic of Elliptic Curves, page 46) that $E$ may be written as
$$
E: y^2 + A_1 xy - A_2 x^2 - x^3 = 0,
$$
where $A_1^2 + 4 A_2$ is not zero.
If the two tangent... | The question and the analog to the Cayley map in complex numbers pointed out in the comment by Jyrki Lahtonen is not only an <em>analog</em>, but in fact both are special cases of this more general observation: Let $z\mapsto\bar z$ be an involutory automorphism of a field $F$, and let $E$ be the subfield fixed by $\bar... | https://mathoverflow.net |
1,949,475 | [
"https://math.stackexchange.com/questions/1949475",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I used the method to find the square root of complex numbers and it did work for $0 + i \times i^3$.
$$x + iy = \sqrt{i^4}$$
$$x^2 - y^2 + 2xyi = i^4$$
equating the components,<br>
$$x^2 - y^2 = 0$$
$$2xy = 1$$
using,
$$(x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2$$
$$(x^2 + y^2)^2 = 1$$
$$x^2 + y^2 = 1$$
$$x^2 = {1\ov... | From $x^2 - y^2 + 2xyi = i^4$, remember that $i^4=1$, so $$x^2-y^2=1,\quad 2xy=0$$
| You wish to solve $(re^{i\theta})^2 = r^2e^{i2\theta} = i^4 =1$. Taking the modulus gives $r=1$,
and the solutions to $e^{i2\theta} =1$ are given by
$2\theta = n 2 \pi$, from which we get the solutions $\pm 1$.
| https://math.stackexchange.com |
1,511,178 | [
"https://math.stackexchange.com/questions/1511178",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <blockquote>
Solve the equation $z^7=-1$
</blockquote>
<strong>My attempt:</strong>
$$z=x+yi$$
$$(x+yi)^7+1=0$$
$$(x^2+2yi-y^2)^3(x+yi)+1=0$$
but now it's start to look ugly.
I'm sure that there is a simple way
| $$z^7=-1\Longleftrightarrow$$
$$z^7=|-1|e^{\arg(-1)i}\Longleftrightarrow$$
$$z^7=1\cdot e^{\pi i}\Longleftrightarrow$$
$$z^7=e^{\pi i}\Longleftrightarrow$$
$$z=\left(e^{\left(\pi+2\pi k\right)i}\right)^{\frac{1}{7}}\Longleftrightarrow$$
$$z=e^{\frac{1}{7}\left(\pi+2\pi k\right)i}$$
With $k\in\mathbb{Z}$ and $k:0-6$
<... | We can say that $$z^7=-1$$
or,$$z^7=\cos\pi+i\sin\pi$$
or,$$z^7=\cos(4n+2)\pi+i\sin(4n+2)\pi \,\ \text{where} \,\ n=0,1,2,3,4,5,6$$
or,$$z=\left[\cos(4n+2)\pi+i\sin(4n+2)\pi\right]^{\frac{1}{7}} \,\ \text{where} \,\ n=0,1,2,3,4,5,6$$
or,$$z=\cos(\frac{4n+2}{7})\pi+i\sin(\frac{4n+2}{7})\pi \,\ \text{where} \,\ n=0,1,2,... | https://math.stackexchange.com |
273,906 | [
"https://electronics.stackexchange.com/questions/273906",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/114979/"
] | If the open circuit voltage of a 3V CR2450 Battery is at 2.95 Volts: is it at end of life?
I have a CR2032 3V that could fit in the device and I could use a nickel to compensate to fill the gap in the device: is there any foreseeable problem in doing this?
Update: installed a CR2032 as a temporary measure until a CR... | For CR2450 with a capacity of >600mAh at a 0.4mA rate;
If ESR is < 20 Ohms then you have at least 50% capacity left.
If ESR is > 50 Ohms then there is not much life left (20%?)
Use a 1K load and measure voltage before after and compute voltage drop in % and multiply percent of 1K as your ESR.
<ul>
<li>Capacity ... | I have a MyQ garage door sensor it says replace on my phone the new CR2450 3.380 volts the one I am replacing reads 2.980.I will be installing a AA battery pack next to it with 2 AA lithium batteries so the batteries don't have to be replaced as often
| https://electronics.stackexchange.com |
1,355,905 | [
"https://math.stackexchange.com/questions/1355905",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/253588/"
] | <blockquote>
State the coordinates of the vertex and the number of $x$-intercepts for the following function:
$$
y = -4x^2 + 1
$$
</blockquote>
I am not really asking for a straight-up answer. If you could please tell me HOW you found the vertex and the number of $x$-intercepts (or how many times it intersects t... | It suffices to show that both $A\subset B$ and $B\subset A$.
Fix $x \in A$. Then we can write $x=2k$ for some $k$, which means we could also write $x=2k=2k-2+2=2(k-1)+2$. Thus $x\in B$, because for $k'=k-1$ we can write $x=2k'+2$.
This proves one direction, that $A\subset B$. The other direction is nearly identical.
| You need to show us some effort in the future.
First, to show two sets are equal, we normally pick an element of the first set, show it is contained in the second, then pick an element in the second, and show it is contained in the first.
If we suppose $x \in A$, then $x=2k$ for some integer $k$. Since $x = 2k$, $x =... | https://math.stackexchange.com |
236,014 | [
"https://electronics.stackexchange.com/questions/236014",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/111022/"
] | I'm confused about the sizing of the battery cables for a UPS system,
When the battery is discharging the voltage decrease and current increase to a maximum value (which depend on the end of discharge value of the battery)
Should I size the cables according to this maximum current value (end of discharge) , or accordin... | You should size your cables for the worst operating conditions possible. For cables that mean the highest possible current and the highest ambient temperature. If the highest current occurs at the end of the discharge, then you should size your cables for that.
You didn't mention charging currents, so I assume they ar... | You should always size your cables for the maximum expected current, and also use a fuse or circuit breaker to protect the cables for excessive current.
Especially in your case, if you are concerned with higher currents at lower voltages, you would absolutely want the largest cables possible to minimize the voltage dr... | https://electronics.stackexchange.com |
434,194 | [
"https://softwareengineering.stackexchange.com/questions/434194",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/361708/"
] | When writing platform independent software in C++, can I nowadays safely<sup>1</sup> assume that a byte has a size of 8 bits? Or do I have to calculate it like this, for example:
<pre><code>#include <climits>
std::size_t byteSize = sizeof(char) * CHAR_BIT;
</code></pre>
<hr />
<sup>1</sup> In the sense it is sta... | Nowadays, a byte is indeed an octet of 8 bits on most of the current computers. But the C++ standard doesn't guarantee that:
<blockquote>
<strong>[intro.memory]/1:</strong> The fundamental storage unit in the C++ memory model is the byte. A byte is at least large enough to contain any
member of the basic execution cha... | sizeof(char) is always 1, because a char is the smallest data word. But there's no guarantee that a char is 8 bits. It is on most platforms, but there may still be some obscure specialist processors where it's not.
Many years ago, I had to write code for a DSP chip that only had one word size for all integer types.
| https://softwareengineering.stackexchange.com |
590,209 | [
"https://electronics.stackexchange.com/questions/590209",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/281803/"
] | I have a circuit that dissipates 0.4 watts through a 1/2 watt resistor. It gets quite hot to the touch. Every other component in the system is cool. I am just trying to make sure this is safe in a circuit in a closed box with minimal venting.
| <strong>You should never choose resistors</strong> to operate > 50% of rated power for THT parts to allow for ambient rise above 25'C. Using 100% rated power at 25'C means the resistor is operating at 125'C and heating up nearby components or a 100'C rise. Using 50% of Pmax means the internal temp will rise 50'C a... | If it is a reputed make resitor, it will not fail unless the ambient temperature of the resistor goes very high. I have seen some low cost resistors where rated wattage is 3W and they smell and getty pretty hot anything above 2W.
An engineer would check the temperature of resistor in actual application (enclosed) and s... | https://electronics.stackexchange.com |
352,801 | [
"https://mathoverflow.net/questions/352801",
"https://mathoverflow.net",
"https://mathoverflow.net/users/141953/"
] | Suppose we have the following data:
1) A group ring <span class="math-container">$\mathbb{Z}[G]$</span>, where <span class="math-container">$G$</span> is a torsion free group.
2) <span class="math-container">$M_{\bullet}$</span> a bounded (above and below) chain complex of <span class="math-container">$\mathbb{Z}[G]$... | No way. Let <span class="math-container">$G={\mathbb Z}$</span> so that <span class="math-container">${\mathbb Z}[G]={\mathbb Z}[x,x^{-1}]$</span>. Then use the complex
<span class="math-container">$$\ldots \rightarrow 0 \rightarrow 0 \rightarrow {\mathbb Z}[x,x^{-1}] \xrightarrow{1-x+x^2} {\mathbb Z}[x,x^{-1}] \righta... | Let <span class="math-container">$G$</span> be infinite cyclic, generated by <span class="math-container">$x$</span>.
Let <span class="math-container">$M_\bullet$</span> be a free resolution of the <span class="math-container">$\mathbb{Z}[G]$</span>-module <span class="math-container">$U=\mathbb{Z}/3\mathbb{Z}$</span>... | https://mathoverflow.net |
121,668 | [
"https://cs.stackexchange.com/questions/121668",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/-1/"
] | <blockquote>
Say that a graph, <span class="math-container">$G = (V, E)$</span> has 2 minimum spanning trees (MSTs).
Given this condition stipulated, prove that any cycle formed by all
the edges in both the MSTs (i.e., the union of the edges in of the 2
MSTs) that at minimum, 2 of the edges in the set which is ... | <strong>Lemma:</strong> Let <span class="math-container">$C$</span> be a cycle of <span class="math-container">$G$</span> that contains an unique edge <span class="math-container">$e$</span> of maximum weight. Edge <span class="math-container">$e$</span> does not belong to any MST of <span class="math-container">$G$</s... | Consider the typical MST algorithms. You get exactly two MST if at some step you have to choose between two edges of equal weight, and that will happen only if they are part of a cycle. And they have to be cheap enough to get included in the MST, but that is harder to characterize...
| https://cs.stackexchange.com |
498,790 | [
"https://physics.stackexchange.com/questions/498790",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/25292/"
] | I have <span class="math-container">$N$</span> pure, but nonorthogonal, states <span class="math-container">$|\psi_n\rangle$</span> with density matrix <span class="math-container">$\rho_n=|\psi_n\rangle\langle\psi_n|$</span>.
Say we call the the total density matrix <span class="math-container">$\rho=\frac{1}{N}\sum_... | Let us denote the overlap matrix by <span class="math-container">$O$</span>, this is, <span class="math-container">$O_{nm}=\langle\psi_n\vert\psi_m\rangle$</span>. Then,
<span class="math-container">$$
S_{\mathrm{vN}}(\rho)=S_\mathrm{vN}(O)\ .
$$</span>
More generally, <span class="math-container">$O$</span> has the ... | In such situations it is common to calculate the linear entropy instead of the full VN entropy. The linear entropy comes from the first term approximation in the expansion of <span class="math-container">$\log(\rho)$</span> as Taylor series around <span class="math-container">$\rho= I$</span>, which is <span class="mat... | https://physics.stackexchange.com |
3,794,783 | [
"https://math.stackexchange.com/questions/3794783",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/551838/"
] | <blockquote>
If <span class="math-container">$\triangle ABC$</span> is a triangle and <span class="math-container">$\angle CAB = \frac{\pi}{2}$</span>, with height <span class="math-container">$AD$</span> and median <span class="math-container">$AK$</span>; suppose that <span class="math-container">$D$</span> is betwee... | You cannot differentiate the equation simply as the equality does not hold for all <span class="math-container">$x$</span>. Instead let <span class="math-container">$$f(x)=\int_{0}^x\frac{t^2}{1+t^4}\mathrm{d}t$$</span>
Then,
<span class="math-container">$$f'(x)=\frac{x^2}{1+x^4}\quad, \ g(x)=2x-1 ,\quad g'(x)=2$$</spa... | Another idea to solve it :
<span class="math-container">$x \in [0,1]\to \frac{t^2}{1+t^4}=\frac{t^2}{1-(-t^4)}=t^2(1-t^4+t^8-t^{12}+...)$</span> so <span class="math-container">$$\int_{0}^{x} \frac{t^2}{1+t^4} dt=2x-1\\
\int_{0}^{x} t^2(1-t^4+t^8-...) dt=2x-1\\
\frac{x^3}{3}-\frac{x^7}{7}+\frac{x^{11}}{11}-...=2x-1$$</... | https://math.stackexchange.com |
101,484 | [
"https://electronics.stackexchange.com/questions/101484",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/24055/"
] | I have a capacitive sensor connected to a 555 timer wired as an astable multivibrator and the free running frequency is 60kHz. When the capacitance of the sensor changes, the frequency of the 555 also changes. The maximum frequency deviation from the center frequency is 20kHz, i.e lowest frequency (60kHz-20kHz) is 40kH... | One simple method is to add a single-shot / monostable vibrator that is triggered by the oscillator. If the mono time is slightly shorter than the period time of the highest frequency (\$T = \dfrac{1}{60\text{kHz}}\approx 16.7\text{ms}\$), you effectively have a PWM signal that is proportional to the input frequency.
... | Try this one using the PLL IC565.
<img src="https://i.stack.imgur.com/zZxJK.png" alt="enter image description here">
| https://electronics.stackexchange.com |
341,041 | [
"https://electronics.stackexchange.com/questions/341041",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/107608/"
] | I would like to ask if packet loss in p2p LAN is a normal behavior in LAN.
And now in more details:
I am connecting PC to target board with TI's chip and LAN9221 controller.
I am doing a ping-pong test, with udp protocol:
<ol>
<li>PC is sending the first packet.</li>
<li>target wait for packet, and on receive, it se... | No. There is no collision or packet loss in p2p Ethernet network. We have not had collisions/packet loss since the introduction of Ethernet switches. If you are connected point to point Tx/RX with no switch in-between ...there simply cannot be packet loss on the wire (it's typically a software problem).
If you are co... | Collision failures yes, but you haven't any of those in a p2p or switched setup.
I test with flood pings usually and any connection with a single dropped ping within a minute or so at least isn't good. It would work, though, as dropped packets should be resent by upper layers.
| https://electronics.stackexchange.com |
324,024 | [
"https://softwareengineering.stackexchange.com/questions/324024",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/236000/"
] | Sometimes we meet a situation where we should iterate (or map) over a collection, applying the same procedure (function) for all elements except the first one. The simplest example is finding the max element of collection, but is not a good one: the operation here is idempotent. More realistic example is table dumping ... | I would try something like that in Scala for mapping differently the first element :
<pre><code>def apply[T,X](f: T=>X, g: T=>X, l: Seq[T]): Seq[X] = l match {
case Nil => Nil
case head :: tail => f(head) +: apply(g,g,tail)
}
> apply((x: Int)=> x*x, (x: Int)=> -x, List(5,4,3,2,1))
res1: Seq... | Just split the list into a scalar value to process separately, then work on the rest.
<pre><code>val first = list.head
val rest = list.tail
val firstResult = firstFunc(first)
val restResult = rest.map(restFunc)
</code></pre>
| https://softwareengineering.stackexchange.com |
237,004 | [
"https://electronics.stackexchange.com/questions/237004",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/111485/"
] | After Google searching "Do Fibre Optic Cables attract any noise", most results return that they attract virtually no noise. Is this the case or are there some exceptions?
| You are right, this is the case but fiber optics can still have problems that can be perceived as noise that lead to incorrect data:
<strong>Intersymbol interference:</strong>
This is a kind of noise because the previous symbol that was sent will interfere with the actual symbol that is being sent. Thus the previous ... | To make proper comparisons between fibre and cable you have to consider the photodiode at the end of the fibre to be part of the fibre and this is the weak link in terms of noise. Typically the Hamamatsu S5973 photodiode produces a noise equivalent power (NEP) of \$1.5 \times 10^{-15}\$ watts per Hz and given that the ... | https://electronics.stackexchange.com |
540,834 | [
"https://electronics.stackexchange.com/questions/540834",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/272996/"
] | I’m new to electricity, and I’ve got a question about electrons flow inside a Li-on battery. A lot of articles and videos show us only Li+ ion flows from anode to cathode through electrolyte during discharging of battery. But there is no info about e- flow from cathode to anode inside battery. As I know, there must be ... | Always there must be a complete circuit: a closed loop of <em>flowing charges</em>. But no electrons flow in electrolytes. The amperes inside the battery-electrolyte are composed of flowing charged atoms; the lithium ions.
Flows of positive charge are opposite that of electrons in wires. Of course this means that, ... | There does need to be a closed loop for electrons to flow, but it doesn't need to be inside the battery.
The electrons flow through the external circuit, "forced" by the battery. The current flow inside the battery is in the form of Li+ ions.
| https://electronics.stackexchange.com |
70,076 | [
"https://electronics.stackexchange.com/questions/70076",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | Normally vias are made with through hole plating. In the past they used to make vias by soldering a piece of wire to connect the top and bottom layers (like a short piece of 24 gauge copper wire). Could the same be done with solder?
Question: Can a VIA in a double sided PCB be connected with solder? Is there any prece... | In your excerpted schematic, you left out the rest of the receiver input, which includes a DC path to ground through the coil L4 and the primary of the transformer T5. That's why you can assume the source of Q10 is at DC ground.
Depending on its value, C27 is probably there to provide an AC impedance that helps to iso... | When Q10 is off, Q9 is also off. Q9 is part of an inverting stage; that pull up resistor drives Q11 on. So with Q10 off and Q11 on, the receiver input is isolated from the transmit signal, and pulled to ground.
Without knowing the particulars of the transmitter final and the receiver input, it's hard to say for certai... | https://electronics.stackexchange.com |
377,356 | [
"https://electronics.stackexchange.com/questions/377356",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/101286/"
] | Whenever I seach for radar implementations, independently of application (weather, military, autonomous vehicles, speed limiters, etc) it always comes in many flavours: huge antennas, small antennas, high power, low power...but never low frequencies. They are offen in the GHz area. Why one’s not able to create a radar ... | To a first order approximation, you get directivity by making the aerials large with respect to the wavelength.
It is much easier to make a moderately directive antenna at say 24GHz then it is at 24MHz where the thing would need each dimension to be 1000 times as large for the same beam pattern (Or course you may not... | Any measurement or imaging system using electromagnetic waves has trouble resolving features smaller than the wavelength of that feature - smaller features "fall in between the waves" and/or create erratic effects like aliasing. This is also the case with microscopes, cameras etc. - a normal optical microscope will not... | https://electronics.stackexchange.com |
193,510 | [
"https://electronics.stackexchange.com/questions/193510",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/88137/"
] | I need to trigger a 555 timer IC in astable mode as soon as it has power. It CAN NOT be done manually through a negative pulse like it usually is. The solution must be compact as space in my project is certainly at a premium. I either need a method of converting a constant high to a negative pulse, however this would r... | 60 s is too long a time for a old analog timer like the 555. Use a microcontroller.
This can be done by the cheap and tiny PIC 10F200. It has only 6 pins and comes in the same package individual transistors do. All it needs is power and a bypass cap. The oscillator is built in, which is good to a few percent. Thi... | While what you need can be easily accomplished using a 555, in this instance - because of your space constraints - it seems a cheap 8 pin microcontroller might be a better fit.
In order to get the astable duty cycle you want, the 555 circuit will need two resistors and two capacitors and, if you need to use the bipol... | https://electronics.stackexchange.com |
3,406,894 | [
"https://math.stackexchange.com/questions/3406894",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/610712/"
] | Let <span class="math-container">$H=L^2(\mathbb{R})$</span>, we define the multiplication operator with a function <span class="math-container">$h\in H$</span>, (<span class="math-container">$0\leq h)$</span> and <span class="math-container">$||h||_1>0$</span>
.
We have <span class="math-container">$$T_h: H \righta... | So If we suppse that <span class="math-container">$||h||_1>0$</span> then we can find the inverse operator for <span class="math-container">$(T_h-\lambda I) $</span> for selected <span class="math-container">$\lambda \in \mathbb{R}$</span>.
So since, <span class="math-container">$||h||_1>0$</span>, there exists <... | If <span class="math-container">$T$</span> is compact, then every <span class="math-container">$\lambda\in \sigma(T)\setminus\{0\}$</span> is an eigenvalue of finite multiplicity. So it suffices to show that <span class="math-container">$T_h$</span> cannot have eigenvalues of finite multiplicity (if <span class="math-c... | https://math.stackexchange.com |
29,612 | [
"https://stats.stackexchange.com/questions/29612",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/11691/"
] | I am doing multiple linear regression. I have 21 observations and 5 variables. My aim is just finding the relation between variables
<ol>
<li>Is my data set enough to do multiple regression?</li>
<li>The t-test result revealed 3 of my variables are not significant. Do I need to do my regression again with the signific... | The general rule of thumb (based on stuff in Frank Harrell's book, <em>Regression Modeling Strategies</em>) is that <em>if you expect to be able to detect reasonable-size effects with reasonable power</em>, you need 10-20 observations per parameter (covariate) estimated. Harrell discusses a lot of options for "dimensi... | The answer to the general question is that it depends of many factors with the main ones being (1) number of covariates (2) variance of the estimates and residuals.
With a small sample you do not have much power to detect a difference from 0. So I would look at the estimated variance of the regression parameters. From... | https://stats.stackexchange.com |
65,850 | [
"https://mathoverflow.net/questions/65850",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3757/"
] | The most elementary way to define $p$-adic modular forms is via limits of classical modular forms.
More precisely $f \in \mathbb{Z}_p[[q]]$ is called a $p$-adic modular form
if there are modular forms $f_n$ with integral coefficients such that
$f \equiv f_n \mod p^n$ (as $q$-expansions). Note it does not really make se... | There is such a theory, but the analytic object that the forms live on is an analytified modular curve, not simply $\mathbb{C}_p$ (though there is a "$p$-adic upper-half plane" that can be used to uniformize some similar moduli spaces, but as far as I know not the usual modular curves).
Basically, if $f$ is a classica... | I personally would say that the root of the problem is the absence of a globally defined exponential map on $\mathbb{C}_p$. In the complex world $z \mapsto q(z) = \exp(2 \pi i z)$ is an isomorphism between $\mathbb{C} / \mathbb{Z}$ and $\mathbb{C}^\times$; but $\mathbb{C}_p / \mathbb{Z}$ is a horrible mess, and has not... | https://mathoverflow.net |
444,404 | [
"https://electronics.stackexchange.com/questions/444404",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/220456/"
] | Please excuse me if my question is very naive or broad. I just wanted to get some direction. I didn't know how else to ask for help.
I am working on Analog electronics and MCUs. It seems to be manageable with my knowledge. I am looking for a job change but many companies are asking if I have experience in High Speed d... | You learn as much as you can, and learn how to learn. Find out what works for you. The best thing is by doing. Get a dev board, then find tutorials on it. When I started messing with electronics early on, the most I could do is make an LED light up. I burned a few up and learned to use resistors to limit the current.
... | Personal projects are the best way to get experience in something that your current work doesn't involve. They have specific success criteria, it gives you something to talk about in the interview, and shows you have initiative. There are low cost FPGA boards (I recommend those made by Digilent) and shields to get you ... | https://electronics.stackexchange.com |
2,535,767 | [
"https://math.stackexchange.com/questions/2535767",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/403529/"
] | The shortest distance of points of on $y^2 =2x+10$ from the origin of the coordinates .(W<strong>ithout derivative use</strong> )
I can use the derivative to solve the question but Without derivatives I can not . please help me !
| <strong>Hint</strong>: The distance is given by $$d=\sqrt{x^2+y^2}=\sqrt{x^2+2x+10},$$
and the radicand can be written as $$x^2+2x+10=x^2+2x+1-1+10=(x+1)^2+9.$$
| The shortest distance is obtained when the circle $x^2+y^2=d^2$ is tangent to the parabola $y^2=2x+10$.
<em>Because if $d$ is smaller, there is no intersection and if $d$ is greater there are multiple intersections meaning the curves cross each other and that contradicts the fact the $d$ is the minimal distance to ori... | https://math.stackexchange.com |
39,003 | [
"https://datascience.stackexchange.com/questions/39003",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/56922/"
] | On my dell core i7 - 16GB RAM - 4gb 960m GPU laptop, I am working on a project to the classify lung CT images using 3d CNN. I'm using the CPU version of tensorflow. The images are prepared as numpy array size (25,50,50).
My CNN model had 2 conv layers, two maxpool layer, one FC layer and output layer. With this archi... | If you add ‘continent’ or ‘location’ as a feature for the model, then you will be able to control for potential bias while getting the results of the additional data.
| Yes, <em>usually</em> with ML, more data you have, better the results! Of course mixing data from different population is risky, but if it works you are on the right path.
Using more data helps generalise during the training of your model. So, if you are able to test your model over sample from both population and you... | https://datascience.stackexchange.com |
403,673 | [
"https://softwareengineering.stackexchange.com/questions/403673",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/310179/"
] | I sometimes end up with services encapsulating the responsibility of doing some sort of business process for which there are several possible outputs. Typically one of those output is success and the others represent the possible failures of the process itself.
To fix the idea consider the following interfaces and cl... | <h2>The problem</h2>
The purpose of having these result classes derive from the same interface is so that the interface becomes what the consumer knows and works with. The consumer doesn't care about the specific implementing classes.
However, your interface doesn't contain anything. You're using it as a marker inter... | It seems to me that you are massively over complicating your life in this example by not using Exceptions instead of your <code>IOperationResult</code> interface.
Simply throw a <code>ValidationException</code> or <code>APIErrorException</code> in your Service and handle with try catch as usual.
Furthermore, say you ... | https://softwareengineering.stackexchange.com |
49,620 | [
"https://dsp.stackexchange.com/questions/49620",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/36088/"
] | The filter impulse response is [1/9 1/9 1/9;1/9 1/9 1/9;1/9 1/9 1/9].
how do i determine whether it is an Low pass filter or a high pass filter. If this is a low pass filter how do i convert it to a high pass filter or the opposite.
| <h2>General</h2>
We assume 2 modes of filters: LPF or HPF.
<h2>Classifying Filter Type</h2>
Usually, if it is a well planned LPF and well Planned HPF a simple test will do.<br>
Calculate the sum of all coefficients.<br>
The sum of the coefficients is the first element of the DFT of the signal.<br>
It means it is the... | The other answer gave a rule of thumb to determine if a filter is low pass or high pass.
A simple way to convert a low pass to high pass for an even length filter is to multiply every other coefficient term by -1. The coefficients of this filter are orthogonal to the original filter.
The sum of coefficients are now... | https://dsp.stackexchange.com |
509,865 | [
"https://stats.stackexchange.com/questions/509865",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/311624/"
] | I have a presentation about ML vs DL. A basic one at that. I had a project about CNN and Robotic manipulator, which I finished, so let's say I know a thing or two about AI.
So, before I start ML vs DL, I want to start with classification, what is it etc. I am planning to say that, "ML and DL, in basic, are classif... | DL is a subset of ML, so I'll comment on ML particularly. You'd be wrong because classification, although an important one, is only one of the tasks we perform. Some other problems addressed by ML methods can be listed as follows:
<ul>
<li>Regression (many classification algortihms also do regression)</li>
<li>Clusteri... | This is too coarse. A classification algorithm maps an input to a discrete category prediction, or a predicted probability distribution over discrete categories. I can think of at least three other common uses of deep learning models:
<ol>
<li><strong>Regression models</strong> map inputs to continuous predictions, lik... | https://stats.stackexchange.com |
1,044,329 | [
"https://math.stackexchange.com/questions/1044329",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/161221/"
] | Let $A,B,C$ be the three angles in the a triangle (with length $a,b,c$). Can we show that
$$x^2+y^2+z^2\geq 2x y \cos A+2xz\cos B+2yz\cos C?$$
for all $x,y,z\in\Bbb R$.
I do not see whether it is true, but I find it in some book.
I suspect it is false. My idea is that if $x=a$, $y=b$, $z=c$, then the cosine theorem ... | Notice that
$x^2+y^2+z^2- 2x y \cos A-2xz\cos B-2yz\cos C=$
$$(x,y,z)\begin{pmatrix}1&-\cos A&-\cos B\\-\cos A&1&-\cos C\\ -\cos B&-\cos C&1\end{pmatrix}\begin{pmatrix}x\\ y\\ z\end{pmatrix}.$$
Now, since $A+B+C=\pi$ then $(\pi-A)+(\pi-B)+(\pi-C)=2\pi$.
Thus, we can consider three normali... | The matrix is positive semidefinite. Its characteristic polynomial is
$$
(1-X)^3-(1-X)(\cos^2A+\cos^2B+\cos^2C)-2\cos A\cos B\cos C.
$$
If $A+B+C=\pi$, it's easy to prove that
$$
2\cos A\cos B\cos C=1-(\cos^2A+\cos^2B+\cos^2C)
$$
(start from $\cos^2A+\cos^2B+\cos^2C$ and consider $C=\pi-(A+B)$). Set $k=\cos^2A+\cos^2B+... | https://math.stackexchange.com |
556,391 | [
"https://physics.stackexchange.com/questions/556391",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/254920/"
] | My QM text defines the position operator as follows:
<blockquote>
The position operator <span class="math-container">$X= (X_1,X_2,X_3)$</span> is such that for <span class="math-container">$j=1,2,3: \ X_j \psi(x,y,z)= x_j \psi(x,y,z)$</span>.
</blockquote>
To me this can mean two things.
1) <span class="math-con... | This is quite an odd way to introduce the position operator, I have to admit. Both definitions you have used are correct, they're just used in different ways in quantum mechanics.
In the the first one, <span class="math-container">$X$</span> is what is technically called a vector operators, in this case it's a little ... | The Hilbert space can be seen as a direct product of three independent Hilbert spaces.
<span class="math-container">$$|x,y,z\rangle=|x\rangle\otimes|y\rangle\otimes|z\rangle$$</span>
When expressed as such, the position operator is also seen as a direct product of three operators each acting on their corresponding spa... | https://physics.stackexchange.com |
93,163 | [
"https://math.stackexchange.com/questions/93163",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/16998/"
] | The question in the book was "What percentage of a $35\%$ solution of alcohol in water should be replaced by pure alcohol to give a solution containing 75% alcohol? Assume that the original solution contains 100 units."
Here's how I answered it:
$35\%(100) + 100\%(x) = 75\%(100 + x)$
after solving, I got $x = 160$ a... | It's a bit simpler, in my opinion, to solve the problem more directly:
Let $x$ be the amount of the original solution replaced.
The new amount of alcohol is $$\underbrace{\vphantom{(}.35}_{35\% \text{ of}}\cdot\underbrace{ {(100-x) }}_{\text{remaining amount}}+\underbrace{\vphantom{(} x}_{\text{amount}\atop\text{ ad... | You start with 35 units of alcohol.<br>
When you remove $x$ units of liquid, the number of alcohol units drops by $\frac{35x}{100}$,<br>
and when you replace it with $x$ units of pure alcohol, the number of alcohol units increases by $x$, such that the alcohol content is now 75%.
We can write all this as
$$35 - \f... | https://math.stackexchange.com |
72,363 | [
"https://mechanics.stackexchange.com/questions/72363",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/53116/"
] | How long will the air conditioner last if it is making a loud squealing noise. I want to know if I have to replace it right away.
| Usually it will either be the belt is slipping on the AC pulley because the serpentine belt is worn out, the tensioner pulley is no longer providing the amount of tension on the serpentine belt, or the belt needs adjustment. You can try belt replacement first or check the tensioner to see if it is where it should be (a... | Check what Paulster2 said and if that doesn't fix the problem it could be the bearings in the AC clutch..... spray some WD-40 in there and if the problem lessens, then it's a good sign the clutch needs replacement. The WD-40 won't be a fix. Good luck.
| https://mechanics.stackexchange.com |
160,319 | [
"https://physics.stackexchange.com/questions/160319",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/45504/"
] | According to wikipedia,
<blockquote>
A rainbow is an optical and meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets...
</blockquote>
Given that we require reflection, refraction and dispersion to take place, I was quite intrigued when I saw that the reflect... | I think the regular pattern of pixels in your LCD screen acts like a diffraction grating, almost like the surface of a CD. I'm not suggesting that it is the pixels themselves but perhaps some finer, repetitive structure.
| There is glass there and probably many other materials that disperse the light, a high percentage of light gets reflected not in the surface but in a deeper zone, therefore the ligth will come across different layers of materials, suffering from refraction and dispersion.
| https://physics.stackexchange.com |
163,964 | [
"https://electronics.stackexchange.com/questions/163964",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/57198/"
] | Why is HV kept open in OC test of transformer? Also, why is LV shorted in SC test of the transformer? (Generally this is preferred - why?)
| By definition, an OC test of a transformer is an Open Circuit test. Why would you connect the HV windings? The open circuit test primarily is used to determine the core (magnetic) losses of the transformer, as with no load, you don't have to worry about copper (winding) losses.
For an SC test, the low voltage side i... | <ol>
<li><strong>Short Circuit</strong>
<ul>
<li>In short circuit test we have to pass rated current through the short circuited side. </li>
<li>Therefore we select High Voltage (HV) side normally for short circuiting, because it's rated current is less and therefore it is easy to short.</li>
<li>Since the winding are... | https://electronics.stackexchange.com |
434,276 | [
"https://mathoverflow.net/questions/434276",
"https://mathoverflow.net",
"https://mathoverflow.net/users/494497/"
] | Consider a function <span class="math-container">$h$</span> defined on real numbers, which is not of the form <span class="math-container">$kx+b$</span> i.e. a linear function. If <span class="math-container">$h$</span> maps rational numbers to rational numbers and it maps irrational numbers to irrational numbers, coul... | Answering a question of Erdos, Barth and Schneider proved that for every countable dense sets <span class="math-container">$A$</span> and <span class="math-container">$B$</span>
in the complex plane, there exists an entire function such that <span class="math-container">$f(z)\in B$</span> if and only if <span class="ma... | Let <span class="math-container">$q_n$</span> be a numbering of the rationals, with <span class="math-container">$q_1=0$</span>. We can define a non linear, analytic function <span class="math-container">$F:\mathbb{R}\to\mathbb{R}$</span> which is strictly increasing and that maps <span class="math-container">$\mathbb{... | https://mathoverflow.net |
174,018 | [
"https://security.stackexchange.com/questions/174018",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/164314/"
] | My question is really simple, are HttpOnly or Secure flags needed if a website doesn't have a private part accessible with login?
| These flags are useful if the cookies you're working with contain sensitive information (such as session cookies). They help to protect your cookies against being compromised in <em>some</em> attack scenarios.
To recap:
<ul>
<li>A cookie flagged <code>Secure</code> is only sent to the server if the connection is secu... | It depens on whaty ou use cookies for.
HttpOnly makes the cookie unacessible from JavaScript. This is good for session cookies since it means that an attacker exploiting XSS can not steal them. However, in most situation you need to read the cookies with JS, and then setting the HttpOnly flag isn't really an option. S... | https://security.stackexchange.com |
63,088 | [
"https://cs.stackexchange.com/questions/63088",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/23833/"
] | I'm working on an algorithm and I'm trying to figure out its time complexity given the operations it takes to complete a input set of specific length, I have been testing the algorithm with varying input lengths.
The results shows that every time I double the input length, it takes 4 times more operations than before ... | Recurrent equation:
$$T(n) = 4 \cdot T(\frac{n}{2})$$
$$T(1) = O(1)$$
Its solution:
$$T(n) = \Theta(n^2)$$
| Unless you are promised that this pattern continues ad infinitum, you can not conclude anything. Asymptotic properties can not be inferred from finite samples, ever.
| https://cs.stackexchange.com |
262,238 | [
"https://electronics.stackexchange.com/questions/262238",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/125288/"
] | Section 13.4 of the STM32 Reference Manual (for my STM32F303RE board) states:
<blockquote>
The DMA controller performs direct memory transfer by sharing the system bus with the
Cortex-M4 ® F core. <em>The DMA request may stop the CPU access to the system bus for some
bus cycles, when the CPU and DMA are targetin... | What this means is that if the DMA and CPU are both targeting RAM, depending on whose turn it is in the bus matrix scheduler, the CPU may be forced to wait for the DMA's turn to be finished.
e.g. If the DMA is doing a ram-ram copy and the CPU is reading/writing to a peripheral register, then they are using two separa... | The DMA here is interfacing hardware to memory ports designated for exclusive access.
The DMA can be used with the main peripherals: SPI, I2C, USART, general-purpose timers, DAC and ADC with exclusive access to the DMA memory mapped
<ul>
<li>0x4002 0400 - 0x4002 07FF (1K) DMA2</li>
<li>0x4002 0000 - 0x4002 03FF (1K) ... | https://electronics.stackexchange.com |
414,593 | [
"https://physics.stackexchange.com/questions/414593",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/102243/"
] | This question I want to deal with the basics of modelling a physical theory: Let's say we start with observing in the world (be it little bubbles in the water, a particle moving, a pattern in the traffic jam, whatever), and we want to build a theory to describe what we see, that is capable of making predictions about f... | <blockquote>
At the moment I identify an observed object from my surrounding nature with a mathematical object, is this already considered an assumption.
</blockquote>
Yes.
When you take into account that the ordering of operators is not set in stone, then we introduce a new pathway for "natural consequences"
| <blockquote>
The <em>first step</em> in building a physical theory is translating observed objects into mathematical objects: For example translating the perceived position of a particle into an element of R3
My question stems from the case of quantum mechanics, where observables <em>are identified</em> with ope... | https://physics.stackexchange.com |
40,576 | [
"https://stats.stackexchange.com/questions/40576",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/14888/"
] | We have a small dataset (about 250 samples * 100 features) on which we want to build a binary classifier after selecting the best feature subset. Lets say that we partition the data into:
Training, Validation and Testing
For feature selection, we apply a wrapper model based on selecting features optimizing performanc... | i think it is biased. What about applying FS in N-1 partition and test on last partition. and combine the features from all fold in some way(union/intersection/ or some problem specific way).
| The simple answer is that you should do feature selection on a different dataset than you train on (you're doing this already, so don't change this)---the effect of not doing this is you will overfit your training data. You must also not do feature selection on your test set, as this will inflate estimates of your mode... | https://stats.stackexchange.com |
155,717 | [
"https://mathoverflow.net/questions/155717",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2937/"
] | In 'Foundations of Constructive Analysis', in the notes at the end of the first chapter, Bishop poses an apparent paradox as an exercise for the reader:
<blockquote>
Since every sequence of rational numbers can presumably be described
by a phrase in the English language, and since the phrases in the
English lang... | A similar "paradox" occurs if you replace "describable in English" with computable. I'll show how the paradox is resolved in this case. Also, I'll do this for Baire space (the set of functions from $\mathbb{N}$ to $\mathbb{N}$) to make life simple.
The set of all computable (possibly partial) functions is countable. H... | <blockquote>
Consider the first (in lexicographic, say) sequence of rational numbers not describable in the English language...
</blockquote>
It is safe to say that in order to actually describe a sequence, one must provide a canonical algorithm for generating it. Thus, this is equivalent to providing a Turing machine... | https://mathoverflow.net |
262,172 | [
"https://softwareengineering.stackexchange.com/questions/262172",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/75034/"
] | I always wondered what are the effects of including not needed headers to the final executable once compiled. In my code some times I may included many different headers that I do not need (or I used to need but now I don't and forgot to remove them). Now before compiling the final executable I always clean up my heade... | Importing in Java, C# and the like is fundamentally different from including in C and C++:
The former will add the named modules to those considered for symbol resolution, the latter inserts the named headers content literally into the translation unit.<br>
Which means a header can contain anything the source-file can... | If you are not using precompiled headers then each include means that the header is included fully into each compilation unit. That means reading the file and putting it through the same pipeline of the rest of the code and filling the symbol table.
So yeah unused includes will slow down compilation.
Some compilers w... | https://softwareengineering.stackexchange.com |
3,454,440 | [
"https://math.stackexchange.com/questions/3454440",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/294594/"
] | How to simplify the following?:
<span class="math-container">$(a-b)^2(y-x)+(b-a)(x-y)^2-(b-a)(x-y)$</span>
I have performed the following, but I think what I have arrived at is not the final step:
<span class="math-container">$(b-a)((b-a)(y-x)+(x-y)^2-(x-y))$</span>
<span class="math-container">$ (b-a)((b-a)(y-x)+(... | <span class="math-container">$\int |g(x^{-1}y)|dy=\int |g(y)|dy$</span> since you are integrating w.r.t. Haar measure. Hence, By Fubini/Tonelli Theorem we get <span class="math-container">$\int \int |g(x^{-1}y)|dy|f(x)|dx=\|f\|_1\|g\|_1$</span>.
| <span class="math-container">$$\int \int |f(x)g(x^{-1})|dxdy=^{TONELLI}\int|f(x)|(\int|g(x^{-1}y|dy)dx=||f||_1||g||_1$$</span>
by a simple change of variables(exploiting the fact the <span class="math-container">$G$</span> is a group with a Haar measure)
| https://math.stackexchange.com |
127,144 | [
"https://chemistry.stackexchange.com/questions/127144",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/87284/"
] | We have seen that, when we pour salt in water then it gets dissolved, that means it is soluble in water. But when we pour sand into water then it doesn't dissolve in water, that means it is insoluble, but still sand gets wet. But there are certain substances which doesn't get wet by water for example, sulfur particles ... | Polar/hydrophilic soluble substances get dissolved, like table salt or sugar.
Polar/hydrophilic insoluble substances get wet, as they attract water, like sand, or limestone.
Nonpolar/hydrophobic insoluble substances do not get wet, as they repulse water, like wax, teflon or silanized glass.
| The water molecules undergo a sort of attraction between them. This attraction is due to <span class="math-container">$\ce{H}$</span> atoms being attracted by the oxygen atoms of neighboring water molecules. At the surface of the water this attraction produces a sort of "skin" due to the attraction of the molecules bet... | https://chemistry.stackexchange.com |
507,374 | [
"https://physics.stackexchange.com/questions/507374",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/196864/"
] | I was learning about black body radiation and the explanations given by Max Planck and Albert Einstein when a thought crossed my mind.
When we heat an iron piece, its color changes gradually from red, orange, yellow to bluish white. Yet such a change is not visible in a glowing piece of charcoal obtained from wood. W... | Any black body emits radiation of all frequencies. So a hot charcoal definitely emits some blue light. It doesn't appear blue, because most of its light is red, orange, or yellow. To shift the spectrum toward perceiving the white light, you must increase the temperature to the temperature of the Sun (5,778K), but this ... | The glowing color of an object is based on its temperature. Wood Charcoal probably won't get hot enough to look blue. The sun is around 5500 degrees and emits all colors of em radiation. Wood charcoal will take a lot of help from the user (pumping air on the charcoal) to approach that required temperature and it will p... | https://physics.stackexchange.com |
379,346 | [
"https://mathoverflow.net/questions/379346",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | Let <span class="math-container">$M\subseteq B(H)$</span> be a von Neumann algebra. Is it true that the mapping
<span class="math-container">$$\psi: M \to B(H \otimes H): m \mapsto m \otimes \text{id}_H$$</span>
is <span class="math-container">$\sigma$</span>-weakly continuous? Here the <span class="math-container">$\s... | There are many ways to do this. Maybe the quickest is to notice that <span class="math-container">$\psi$</span> is a <span class="math-container">$*$</span>-isomorphism between <span class="math-container">$M$</span> and <span class="math-container">$\psi(M)$</span>, hence an order isomorphism, hence normal. (For this ... | I want to note that the final question in the OP has a simple answer. For a Hilbert space <span class="math-container">$H$</span> and <span class="math-container">$\xi,\eta\in H$</span> let <span class="math-container">$\omega_{\xi,\eta}$</span> be the trace-class operator, which gives the normal function <span class=... | https://mathoverflow.net |
2,152,708 | [
"https://math.stackexchange.com/questions/2152708",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/384880/"
] | Given is the function $f(x,y)=\frac{x^3-y^3}{x^2-y^2}$ defined for $(x,y)\in\mathbb{R^2}, \, x^2\neq y^2$
I need to find the limit of $\lim_{(x,y)\rightarrow(0,0)} \frac{x^3-y^3}{x^2-y^2}$.
I have tried a few paths, $(x,mx),\, (x,mx^2), \, (x,sin(x)), \, (x,tan(x))$ but all of them yield the same result, $0$.
So I... | The problem is that there is no limit, only pathwise limits (which of course depend on the path to zero).
To see this one could rewrite the expression:
$${x^3-y^3\over x^2-y^2} = {(x-y)(x^2+xy+y^2)\over(x-y)(x+y)} = {(x+y)x - y^2\over (x+y)} = x - {y^2\over x+y}$$
Now of course $x\to 0$, but the term $y^2/(x+y)$ can... | A method is to consider $y=mx$
<em>Note : $m=m(x,y)$ is variable, it is the ratio of converging rates of $y$ and $x$.</em>
<br/>
$$f(x,y)=\frac{x^2(1+m^2+m)}{x(1+m)}=x\frac{1+m+m^2}{1+m}$$
If $m\to\pm\infty\quad f(x,y)\sim\frac{m^2}{m}x=mx=y\to 0$
If $m\to0$ then $f(x,y)\sim x\to 0$
If $m$ is bounded let's have $... | https://math.stackexchange.com |
61,066 | [
"https://physics.stackexchange.com/questions/61066",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/23129/"
] | I have a cylinder filled with water in it at the bottom of the ocean. Say 100 meters down. In this cylinder is a piston that moves up and down. Its job is to squish the water out the bottom of the cylinder to create an air space in the top half of the cylinder. There are lots of holes to let the water move freely out o... | I think that a sketch says more than equations and words
<img src="https://i.stack.imgur.com/mT0xh.png" alt="Yoyo">
The yoyo will, in an infinitesimal sense, have to move around the red dot (but is kept from doing so by the table). The direction in which the yoyo will move, depends on the angle of the string, and thu... | If the outside radius is $r_O$ and the inside where the string attaches $r_I$ then the no-slip condition is $v + \omega r_O =0$. The string lengthening rate is $\dot{l} = \omega r_I$ so the end of the string motion is $\dot{x}=v+\dot{l} = v + \omega r_I$. Together they make
$$ v = \frac{r_O}{r_O-r_I} \dot{x} $$
$$ ... | https://physics.stackexchange.com |
396,404 | [
"https://stats.stackexchange.com/questions/396404",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/240419/"
] | I assume there are various ways of explaining it, but what's the most intuitive (yes I understand that is a relative concept)
Edit due to request:
Obvious example: There is a 1/6 chance of rolling a 6 on a 6-sided die. Expected number of rolls is 6/1.
Another example: You have 4/6 chance of rolling 1-4 on a 6 sided ... | Let <span class="math-container">$p$</span> be the probability of the event (so for you, <span class="math-container">$\frac{m}{n}$</span>), and <span class="math-container">$C$</span> be the expected number of tries,
Then <span class="math-container">$C = p + (1-p)(C+1)$</span>, since with probability <span class="m... | I think that the most intuitive explanation is to simply note that a probability of m/n means that out of n trials, the expected number of successes will be m. So if there are n/m trials, the expected number of successes will be 1. This comes down to the fact that the expected number of trials to get k successes is the... | https://stats.stackexchange.com |
2,786,598 | [
"https://math.stackexchange.com/questions/2786598",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/563052/"
] | I want to find one set of coordinates for regular polygon of n-sides. I have given one vertice(0,0). And some given lenght of side L. I don't have other n - 1 vertices coordinates. I know there might be many possibilities, but I need just one.
| You are right that the appeal to $B\in A$ in the bolded part of your quote is not necessary for the conclusion it's trying to draw.
I'd chalk it up to sloppy editing and move on.
| One way to view "There is no universe" is: "Given any set A, then exist a set B such that <span class="math-container">$B\notin A$</span>". What Halmos does is to show a contradiction from <span class="math-container">$B\in A$</span>, in this sense <span class="math-container">$B\in A$</span> is necessary.
| https://math.stackexchange.com |
111,270 | [
"https://electronics.stackexchange.com/questions/111270",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/43181/"
] | There is a parallel LC circuit with unknown values for the inductor and the capacitor. How exactly can I identify the value of the inductor and capacitor?
I know I can apply an sinusoidal function to the circuit and calculate the product of LC by identifying the resonance frequency. However I cannot figure out how e... | <ol>
<li>Identify the resonant frequency (f1)</li>
<li>Add a parallel capacitor of known value (Cx).</li>
<li>Measure the resonant frequency again (f2). If it doesn't oscillate try with other capacitor value.</li>
<li>\${f_2 \over f_1} = \sqrt{ C \over {C + C_x}}\$. The only unknown in this is C. You can calculate it.<... | A parallel combination of ideal parts would (theoretically) result in a resonant effect with zero bandwidth. Of course, you can measure the existing bandwidth, which is determined by the loss resitanc(es). But you should know how the equivalent circuit diagram looks like - that means: R(loss) in parallel to LC or in se... | https://electronics.stackexchange.com |
144,371 | [
"https://physics.stackexchange.com/questions/144371",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/35960/"
] | In the appendix of the textbook of <em>Group Theory in Physics</em> by Wu-Ki Tung, the transpose of a matrix is defined as the following, Eq.(I.3-1)
$${{A^T}_i}^j~=~{A^j}_i.$$
This is extremely confusing for me, since in the case of Lorentz transformation ${\Lambda_\nu}^\mu$ is considered in the text (eg. Ch.10) as a... | <blockquote>
Therefore it occurred to me that the definition in the book of Weinberg is not consistent with that in the book of Tung: in one of them the symbol <span class="math-container">${\Lambda_\mu}^\nu$</span> is defined as the inverse of the Lorentz transformation of contravariant vectors, while in the other cas... | In terms of $4\times 4$ matrices, elements of the representation of SO(3,1) group must obey the following relation:
$$ g\cdot A^{T} \cdot g = A^{-1}, $$
where $g = \text{diag}(1, -1, -1, -1) = g^{-1}$.
Does it answer your question?
| https://physics.stackexchange.com |
160,659 | [
"https://security.stackexchange.com/questions/160659",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/149487/"
] | I've heard that websites that download malicious data onto the user's computer without their consent <em>do</em> exist, but is this possible on an iMac <em>as well</em> as Windows and other operating systems? How about iPhones?
Basically, can websites download content onto your Apple device without your consent? I've... | The OS part is mostly irrelevant here. A web <em>page</em> is built from:
<ul>
<li>a general part containing text and global structure: the HTML file itself</li>
<li>various auxiliary files: presentation (css), images or other media files, and scripts</li>
</ul>
The browser by itself downloads the main HTML page and ... | In certain cases, yes it can, what it is usually called is a "drive by download": JavaScript exploits, Java exploits (or even you approving the download), and other exploits can indeed infect your computer, if you believe a website is risky you can download the NoScript extension or disable active plugins like Java or ... | https://security.stackexchange.com |
401,800 | [
"https://softwareengineering.stackexchange.com/questions/401800",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/352042/"
] | im working on a RPG (combat system) and have a question about a specific part of the design / code.
First I have to explain some background information about the system:
Every time a character deals damage to an other character (weapon attack, spell damage etc) the buffs / status effects of the attacker and the targe... | <blockquote>
B, It could be a non static "TakeDamage" method which is called on the target for example target.TakeDamage(baseDamage, sourceCharacter), but then the method (which is called on the target) would raise events of the source character which feels weird or am I just overthinking it?
</blockquote>
You are n... | Using events may work. But I don't think I would do it like that at all. When using events you are depending on the order in which modifiers are handled.
Instead you could create a <code>ICombatSystem</code> interface which contains a <code>HandleAttack(IDamageSource source, IDamageTarget target)</code>. <code>IDamage... | https://softwareengineering.stackexchange.com |
8,755 | [
"https://electronics.stackexchange.com/questions/8755",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1225/"
] | I am trying to design an oscilloscope/BNC input circuit for a side project and to learn more about filters.
The requirements are:
<ul>
<li>150-200 MHz -3dB bandwidth</li>
<li>1 megohm impedance</li>
<li>50 ohm termination option (I can omit this if it causes problems.)</li>
<li>Can be switched between 2x and 20x atte... | Input capacitance is significant for capturing high frequency content signals. Given that you are using discrete parts and not considering RF parasitics, this system will be restricted to the 100's of kHz for 1% accuracy.
<img src="https://i.stack.imgur.com/BlWgG.png" alt="alt text">
The goal is to maintain constant ... | For attenuation, you may consider looking at what a probe does. The factor is the same (1/10 = 2/20). Just short the additional resistor and capacitor from the probe circuit with a switch, like 1:1 and 1:10 switchable probes do.
| https://electronics.stackexchange.com |
402,642 | [
"https://electronics.stackexchange.com/questions/402642",
"https://electronics.stackexchange.com",
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] | So I have battery cells with a rated capacity of 3.5Ah and a nominal voltage of 3.5v Now, say I have a system that requires 12A for a period of 10 seconds. For this battery it is advised not to discharge beyond 2C or the efficiency hit becomes unreasonable. From my understanding, I can increase the amount of batteries ... | <blockquote>
For this battery it is advised not to discharge beyond 2C
</blockquote>
A 2C discharge rate for a 3.5 Ah battery would be 7A. So, the manufacturer is recommending that you do not draw more than 7A from a single instance of this battery.
<blockquote>
From my understanding, I can increase the amount o... | If you put two 3.5Ah batteries in parallel, you now have a 7Ah battery, and a 2C discharge current is 14A, meeting your 12A requirement.
A rated capacity of 3.5Ah probably means the 10 hour rate, which is 350mA for 10 hours. Unfortunately, as the discharge rate goes up, the actual battery capacity falls. You might get... | https://electronics.stackexchange.com |
187,414 | [
"https://dba.stackexchange.com/questions/187414",
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"https://dba.stackexchange.com/users/115390/"
] | I have <code>Message</code> table
<pre><code>DDL
CREATE TABLE [dbo].[Message](
[ID] [int] NOT NULL,
[Message] [varchar](50) NOT NULL,
[DateCreated] [datetime] NOT NULL,
CONSTRAINT [PK_Message] PRIMARY KEY CLUSTERED
(
[ID] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF... | As far as I understood it would work as a pagination, and the params you would control on the app side anyways. I'd would the following:
@SQL2012:
<pre><code>SELECT [ID]
, [message]
, DateCreated
FROM [message]
ORDER BY ID DESC
OFFSET 1 ROWS
FETCH NEXT 2 ROWS ONLY
</code></pre>
| I think this is solution for your case.
<pre><code>SELECT TOP 2 *
FROM [dbo].[Message]
WHERE ID < (SELECT ISNULL(MIN(ID),2147483647) FROM [dbo].[Message] WHERE <predicate>)
ORDER BY ID DESC
</code></pre>
For example we can use <code>DateCreated</code> column to filter rows and check examples which you provid... | https://dba.stackexchange.com |
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