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electromagnetism, special-relativity, magnetic-fields, quantum-electrodynamics, maxwell-equations Title: Explanation of Lenz's Law phenomena If we drop a magnet through a copper pipe (without it touching any of the sides), it would fall slower than it would if there were no pipe. Having the pipe otherwise accelerate t...
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an orthonormal basis for a space given any set of vectors which span the space. ^y is called the orthogonal projection of y onto W. 2 Computing Orthogonal Complements. Orthogonal matrices 138 8. Find the kernel, image, and rank of subspaces. It can be used to reduce the dimension of the data from d to k. This calculato...
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the-sun, gas, solar-flare, solar-storm If not a causal mechanism, maybe something you can think of that current science/ scientists could have missed/ aren't taking into account in their models that, if true, would mean the sun is going to be much hotter, much sooner than we thought. Thank you so much for your help! I...
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electricity, electric-circuits, electrons, electric-current Ions do, by the way, not move alone. An ion is usually surrounded by a solvent shell: https://en.wikipedia.org/wiki/Metal_ions_in_aqueous_solution, so the dynamics would be even more complex than that of electrons in metals. In general, electrochemistry is a...
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59 Maybe this simple example will help. I use it when I teach conditional expectation. (1) The first step is to think of ${\mathbb E}(X)$ in a new way: as the best estimate for the value of a random variable $X$ in the absence of any information. To minimize the squared error $${\mathbb E}[(X-e)^2]={\mathbb E}[X^2-2eX...
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python, object-oriented, design-patterns, django, mongodb self.starttime, self.endtime = map(datetime.fromtimestamp, (int(data["starttime"]), int(data["endtime"]))) \ if {"starttime", "endtime"} <= data.keys() else self._get_day_range() This line is way too packed. I can see how you would get to it, but it ne...
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machine-learning, text-mining Title: How to create ROC - AUC curves for multi class text classification problem in Python I am working on a multiclass text classification problem and trying to plot ROC Curve but no success so far. Tried many solutions available but didn't work. Kindly please someone help me out with t...
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thermodynamics, kinetics, stability The deeper valley to the right is the global minimum (at least as far as we can tell). It has the same mathematical properties, but the magnitude of the energy is lower – the valley is deeper. If you put all of this together, (and can tolerate a little anthropomorphization) you coul...
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c++, bitwise Title: Bitwise comparison of any structure What I tried to do is compare arbitrary structures independent of the == operator implementation. template<typename T> bool bitWiseCompare(T a, T b) { size_t size = sizeof(T) / sizeof(char); char* array_a = (char*)(&a); char* array_b = (char*)(&b); for(si...
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logic, propositional-logic, natural-deduction Title: Formal Logic - Natural deduction: Problem with assumptions about exists-negation I'm stuck on how to progress with this proof, despite I have tried, I cannot see the next move. Given this proof without predicate: So far what I've accomplished: My idea is, as I can...
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c++, algorithm, comparative-review, random ASSERT(dist1.size() == 0); ASSERT(dist2.size() == 3); dist1 = dist2; ASSERT(dist1.size() == 3); ASSERT(dist2.size() == 3); ArrayProbabilityDistribution<int> dist3(dist1); ASSERT(dist1.size() == 3); ASSERT(dist2.size() == 3); ASSERT(dist3.si...
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ros, bagfile, hokuyo-laser Title: .bag file error by Hokuyo laser scanner I am new to ROS. I tried to use " rosbag record -O mylaserdata /base_scan /tf " to record the distance data. But after I finish the recording, there is no message recorded to the ".bag" file. Does anyone know the solution? Thanks in advance. Is...
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c++, performance, multithreading, thread-safety, multiprocessing std::vector<int> get = thread.get(); I would want to use it like: std::vector<int> get = mthread::execute_processes({[](std::pair<int, int> x) { return x.first + x.second; }, [](std::pair<int, int> x)...
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quantum-mechanics, wavefunction-collapse Title: A particle in a box is measured to not be on the right hand side of the box. How does the wave function collapse? Starting with initial wave function of a particle in a box with width $2\pi$.
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php, object-oriented, validation Throwing an exception is the right thing to do here. It allows the code that called rule to decide how to handle it. rule should only responsible for saying "Hey, ummm, something wen't horribly wrong," not deciding how to handle it. (In fact, an uncaught exception is basically an exi...
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newtonian-mechanics, special-relativity, forces, mass, mass-energy there exists energy and momentum , even with mass 0. These questions arises from me because E=mc2 and F=ma does not relate and one does not agrees with other. E=mc^2 is a description of the total energy of a system in relativistic mechanics. F=ma i...
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classical-mechanics, magnetic-fields, fluid-statics, perpetual-motion For simplicity replace the magnets with an ideal spring (ie there are no losses due to hysteresis). Initially the chamber is at the surface with the spring in its relaxed state. The weight of the chamber is greater than the buoyant force on it so it...
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$$\Pr(x_{ti}, x_{tj}) \,\propto\, (1-p_i-p_j)^{-(x_{ti}+x_{tj})}\,p_i^{x_{ti}}\,p_j^{x_{tj}}.$$ Proceeding from day to day, again assuming independence, these probabilities continue to multiply. Thus, for each pair $$\{i,j\},$$ we may once and for all collect our counts $$x_{ti}$$ and $$x_{tj}$$ over all the days $$t$...
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ruby, ruby-on-rails, hash-map Title: Refactoring if statement based on a hash key I have to call Article.to_draft/to_archive/publish method depending on the presence of the corresponding key in the params hash. I do, however, have no idea to implement it properly. def update_state method = if params[:draft].present?...
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python, performance, serialization, file-structure, cryptocurrency Title: Parsing Bitcoin binary data file with Python The script parses Bitcoin database (blkXXXXX.dat) files directly from raw binary to txt human readable view. And I think about how to encrease the speed of processing. Can anyone suggest how to improv...
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slam, navigation, laser, ros-kinetic, scan Now, the problem is that data is being published on the topics (/plato1/scan and /plato2/scan). But somehow this error is causing me problems. I am running it in Gazebo simulation. (((Below is the pdf file of the tf tree. Please download it))) https://drive.google.com/file/d/...
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java, tree, inheritance Expression (minus the parser) Expression.toInOrder calls toString while BinaryExpression.toString calls toInOrder. This works, but it's very confusing. Is there a better way? (Maybe not) Should evaluate return a Number instead of a raw double? Number To go with evaluate and differentiate it ...
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python, oauth, jwt import tornado.web from tornado import gen import logging from cosmos.rbac.object import COSMOS_USERS_OBJECT_NAME from cosmos.auth.oauth2 import get_token from cosmos.rbac.object import SYSTEM_USER try: import urlparse # py2 from urllib import urlencode import urllib as urllib_parse e...
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java, beginner, array The better step could be to just stick with either arrays or ArrayList, if that's feasible. Converting between them is adding complexity to your code. If studentScores was defined as List<List<Double>>, you could use the existing Collections.max and .min methods: for (List<Double> scores : studen...
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# Deriving summation formulas I'm working through Spivak's Calculus (Fourth Edition). In chapter 2, problem 6: The formula for $1^2 + ... + n^2$ may be derived as follows. We begin with the formula $(k+1)^3 - k^3 = 3k^2 +3k +1$ Writing this formula for $k = 1, ... , n$ and adding, we obtain $(n+1)^3 - 1= 3 (1^2 + .....
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ShivaniGillon: Feb. 6, 2015, 11:40 p.m. I also got the same answer :) weisbart: Feb. 7, 2015, 11:36 a.m. Good job! Thanks also for posting the questions, AZobi. I really do want you guys to all work together. It helps everyone, including me. You guys learn from each other and learn by explaining and I can see what your...
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inorganic-chemistry Borazine, with boron rather than aluminum in the six-membered ring, is known as an aromatic ring and even called "inorganic benzene". Like its benzene counterpart, the borazine ring can be fused to give polymeric structures ultimately leading to hexagonal boron nitride. But with aluminum nitride,...
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homework-and-exercises, thermal-conductivity I know the equation is $\frac{dQ}{dt} = -kA \frac{dT}{dx}$ but I still cannot get the right answer. Here, in the case of your question, the brass rod and the steel rod are connected in parallel combination in between the hot reservoir and the cold reservoir. So the therma...
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2º) Draw the height from $$Q \ to \ \overline{PR}$$, getting the point $$O$$ $$\sin 30º=\dfrac{1}{2} \ then \ \overline{QO}=\overline{QD}=\overline{DR}$$ 3º) $$\angle PDO=60º-45º=15º$$ 4º) For 1º) $$\overline{OP}=\overline{OD}=\overline{QO} \rightarrow{} \angle PQO=\angle QPO=45º$$ 5º) For 4º): $$\angle QPD=45º-15º...
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The hyperbola xy = 3 notation gives an upper bound for a function f, there is a need describe... At infinity is, when considering a function f ( n ) to a! For machine-independent calculations, vertical and oblique check the algorithm efficiency before it! That draws increasingly nearer to a curve without ever meeting i...
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quantum-mechanics, quantum-information, quantum-spin, eigenvalue, rabi-model $$ \frac{\hbar}{2} \begin{pmatrix} \delta & \omega_R \\ \omega_R & -\delta \end{pmatrix} \begin{pmatrix} a \\ b \end{pmatrix} = i\hbar \begin{pmatrix} \dot{a} \\ \dot{b} \end{pmatrix} $$ But when I try to solve this, I end up getting some no...
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black-holes Of course it's always possible that this is wrong: either the black holes we know about could be charged for some reason, or there could be whole other populations of charged black holes. So we'll have to do observations and experiments to check. People are always trying to improve our observations of blac...
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estimation, climate-science, solar-cells Title: Why don't solar panels contribute to global warming? I've been wondering this for a while but I have not yet encountered an explanation. This is from my understanding of physics, which is by no means expert, so sorry for my crude explanation: Energy within earth can be...
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javascript, beginner, google-apps-script Other Relevant Code: function emailAttachmentRetrieval(emailSubject, attachmentNumber){ var msgs = GmailApp.getMessagesForThreads(GmailApp.search('subject: ' + emailSubject,0,1)) for (var i = 0 ; i < msgs.length; i++) { for (var j = 0; j < msgs[i].length; j++) { v...
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python, python-3.x Title: USB stick condition check and file deleting function I have a function called USB(), that will observe a USB stick's insertion and delete files inside of it, if there are some: import os import shutil # 1. Check and clean USB def USB(): usb_inserted = os.path.isdir("F:") # <-- returns b...
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monte-carlo-tree-search, function-approximation, alphazero, alpha-beta-pruning Regardless, these position evaluations are linear: they are composed of a bunch of if-else statements, e.g. 'if I have a Pawn, adds 1 point', 'if I have no card in a suit, adds 4 points'. This is what the paper means by linear function appr...
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molecular-genetics, human-genome, hiv, experiment, gene-therapy That out of the way lets get into the potential problems that could be caused by removing the CCR5 gene from human embryo using the CRISPR-cas9 system. These can mainly be grouped into two classes: off-target or side effects of the procedure itself and a...
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c++, multithreading Performance nitpick: I've heard that it is useful to put one cache-line's worth of padding in between your two atomic variables, to eliminate false sharing. Of course if you do that then your shared_spinlock class gets much bigger. But if you don't do that, then all this fiddling with memory orders...
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fasta, python, refseq, blastp, makeblastdb Title: makeblastdb creating multiple files of unexpectedly large sizes I have a set of 100 amino acid sequences and I want to perform a BLASTP sesrch against the refseq_protein database. Accordingly I had set up the standalone version of BLAST (Version 2.11.0+) and downloaded...
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Shell sort aims to mitigate this by doing the following: 1. pick a large number $H$ some constant factor less than the length of the sequence 2. consider every $H^{th}$ element in the sequence and apply insertion sort to those elements 3. now consider every $(H + 1)^{th}$ element and do the same 4. repeat incrementing...
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logic, proof-techniques, lambda-calculus, semantics, term-rewriting $$ y \{x := 1\}\{y := x\} = y\{y := x\} = x, $$ whereas $$ y \{y := x\}\{x := 1\{y := x\}\} = x\{x := 1\} = 1. $$ Now let's do the base case more carefully. The term $t$ is just a variable. We have to consider three possibilities: $t=x$, $t=y$, $t \ne...
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quantum-mechanics, quantum-information, harmonic-oscillator, quantum-optics, coherent-states \langle 0|e^{-i t\hat{H}}|0\rangle&=\sum_{n_i,n'_j}\langle 0|\{n_1,\dots,n_N\}\rangle\langle\{n_1,\dots,n_N\}|e^{-i \hat{H}}|\{n_1',\dots,n_N'\}\rangle\langle\{n_1',\dots,n_N'\}|0\rangle\\ &=\prod_i\sum_{n_i}|\langle 2n_i|0\ra...
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Series Example Consider the signal • Find the Fourier series coefficients, ; which harmonics are present? • For the periodic waveform shown below find the Fourier series coefficient and also find the waveform period, xt 516 2 500 t 4 – --- 10 2 5000 t 8 + --- = + cos + sin ak a0 T0 5 4 –4 t. For this example, all the F...
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thermodynamics, temperature, molecules, gas Note that the diatomic gas does not have a heat capacity of $\frac72 R$ as you would expect if rotation about its axis or vibration along its axis were involved in storing energy. The reason is that these modes are quantized - and that the thermal energies are insufficient t...
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computer-networks the frame time because if transmission of another frame were started in the frame time of the current frame, collision would occur. a time interval (equal to the frame time) before the frame time because if transmission of another frame were started in this time interval, collision would still occur...
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ros, ros-melodic, catkin-make Original comments Comment by asps946701 on 2022-10-13: Hi , I used apt install "ros-melodic-webrtc" and "ros-melodic-webrtc-ros" but it got same error. When I go to path : "/opt/ros/melodic/include/webrtc/media/base/" , I found .h file name is :"adaptedvideotracksource.h". Should I mod...
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mysql, bash relocate_item () { while true; do clear # check if mode and location are none # for first scan if [[ -z $mode ]]; then input=$(return_scanner_input) mode=$(check_input_for_scanmode $input) elif [[ -z $location ]]; then printf "...
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c++, linked-list It's not wrong. Node<T> *head = NULL; But in C++ (unlike C) the * is usually placed as part of the type. Node<T>* head = nullptr; In C++ the type information is very important so keeping it all together is useful in reading. Also NULL is C code. In C++ we use nullptr - it is type safe (unl...
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operating-systems, memory-management, virtual-memory, security, filesystems Title: How pictures and videos are usually loaded in Memory? Lets assume I'm talking about Jpeg and Mp4 and a general video player(not sure if different ones load it differently, if they do please tell) So do video players (process) usually lo...
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java private <T> boolean isFullyInitialized0(T object) { Set<Object> memorizedObjects = new HashSet<>(); for (Field field : object.getClass().getDeclaredFields()) { field.setAccessible(true); Object fieldValue = ReflectionUtils.getField(field, object); if (fieldValue...
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javascript, jquery Title: Am I on the right track with JavaScript/jQuery? I've been trying to learn how to develop jQuery plugins but have little guidance on the matter. I see lots of code on the web, of course, but am not sure what exactly constitutes best practices due to the level of variability in style. $.notify...
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rviz Title: Updating RViz display without clock being published (use_sim_time is true) I am playing back a bag file and need to be able to move things around while the bag is on pause. I have an interactive marker that broadcasts its pose as a transform. I also have a laser scan in the frame of the marker's transform...
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javascript, node.js, promise, async-await, timeout As you suggest doing the await every so many iterations will improve the ratio. But without knowing the time per iteration you can not be sure of a reasonable count. A suggested improvement. The await can be improved using a object to handle the promises based on time...
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temperature, greenhouse-gases Title: In the past, why did the levels of individual greenhouse gases rise and fall at the same time? According to ice core samples from Vostok in Antarctica, methane and carbon dioxide levels seem to have risen and fallen at around the same time over a 450 thousand year period. I was una...
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javascript // typo: letover, should probably be left over. Again this variable name could be clearer var letover = xp - generated_xp if (letover == 0) return level if (letover < 0) return level if (letover > 0) return get_level(xp - generated_xp, level + 1) } If I fixed a few issues but left the structure in ...
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ros, c++, catkin, jenkins, message-generation And although I'm not sure the correlation, Jenkins has also started returning similar error (with my latest commit): In file included from /tmp/test_repositories/src_repository/rqt_common_plugins/rqt_marble/include/rqt_marble/marble_plugin.h:42:0, from /tm...
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• :Would you please tell me how $MN=1+\cos 2x$ in \begin{align} HN &= \cos x \\ ON &= 1\\ NP &= 2\cos x\\ NM &=1+\cos 2x \end{align} ? – Khosrotash Dec 24 '17 at 19:06 the same diagram also gives an easy demonstration of the fact that $$\sin 2x = 2 \sin x \cos x$$ as @Sawarnak hinted, with the help of this result, you...
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semiconductor-physics When carbon or silicon surfaces are prepared under clean room conditions, the dangling bonds can persist. In the semiconductor industry this clean room preparation technique is followed by bringing in a doping gas in order to purposefully alter the electronic band structure of the substrate mater...
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sum of basic components. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Current time: 0:00 Total duration: 24:15. The motivation for this work is to develop a deeper unde...
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c, exception, c11 /** * @def sgl_catch(exception) * * Catches an exception and execute the following bloc * of code if it corresponds to the thrown exceptions */ #define sgl_catch(exception) \ } ...
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tables in references such as Gere, Lindeburg, and Shigley. Derivation of expression for Young’s modulus Let us consider a beam initially unstressed as shown in fig 1(a). Because computing moments of inertia directly can be quite laborious, people have worked out indirect ways of computing unknown moments of inertia fro...
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• @TerrenceTown Since $\log$ is the inverse of $\exp$, the conversion between multiplication and addition goes in the other way. $\exp$ converts addition into multiplication, therefore its inverse converts multiplication into addition. – Daniel Fischer Oct 9 '14 at 18:09
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thermodynamics, time Title: First Law of Thermodynamics as a rate equation In a standard engineering thermodynamics textbook (Fundamentals of Thermodynamics, Sonntag, et. al, 6th ed) the First Law of Thermodynamics is differentiated with respect to time, and written as a rate equation. It is stated (p. 141): "In so do...
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classical-mechanics, lagrangian-formalism, differential-geometry, mathematical-physics, constrained-dynamics There's actually no problem with what I said after my last equation in the OP. The first term vanishes because each $\frac{\partial r}{\partial q _i}$ is separately a tangent vector. The second term vanishes be...
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filters, digital-communications, matched-filter "does the matched filter maximize the SNR only at the sampling instant, or everywhere?" has the answer that the SNR is maximized only at the sampling instant $t_0$. At other times, other filters could give a larger SNR than what the matched filter is providing at time $...
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entropy, correlation-functions, molecular-dynamics Third: If, for example, I want to compute CF for relative distance $\vec r=\vec r_2-\vec r_1$, where $\vec r_1, \vec r_2$ are the absolute positions of two atoms, what will be $X$ and $Y$? I'm sorry if I've written something unclear, I'm always ready to clarify the q...
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roslaunch started roslaunch server http://hostname.local:35062/ SUMMARY ======== PARAMETERS * /rosdistro: indigo * /rosversion: 1.11.21 NODES / env_test (test_package/environment_reader.py) auto-starting new master process[master]: started with pid [11449] ROS_MASTER_URI=http://localhost:11311/ setting /r...
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java, algorithm, search return tentativeValue; } else { // Here, 'initialPlayer == minimizingPlayer'. double tentativeValue = Double.POSITIVE_INFINITY; for (S child : state.children()) { double value = makePlyImpl(child, ...
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quantum-mechanics, wavefunction, dirac-equation, singularities, hydrogen So why is Dirac equation's solution allowed to be unbounded? What are the boundary and smoothness conditions on the wavefunction? I suspect that Dirac equation simply doesn't admit S states with bounded wavefunction in Coulomb potential. Can it t...
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• @StevenStadnicki thanks. Your calculations confirm what I wrote above but I am looking for something more powerful and accurate so that I can enumerate the points lie between circles as detailed in my question. Unfortunately, your calculations will not provide an upper and lower bounds. In fact I thought there is a r...
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forces, magnetic-fields, metals I have read that bismuth is the most diamagnetic element, eg is about 8x more diamagnetic than silver. So if I cast a round (ie, a coin) about the size of a quarter out of 99.99% bismuth should it slide slowly down a magnetic ramp? No. The eddy current breaking effect is very weak for b...
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proteins, amino-acids, thermodynamics Why is enthalpy change positive? You made a bond between the two amino acids. That is exothermic. The energy used to catalyze the peptidyl transferase reaction is from the breakage of the bond between the amino acid in question, and the aminoacyl-tRNA it's attached to. The two rea...
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ros Title: TF_REPEATED_DATA warnings Hello, I am trying to run two turtlebot3s in Gazebo. When I try doing anything related to tf, for example run rqt, I get the warning message: Warning: TF_REPEATED_DATA ignoring data with redundant timestamp for frame base_footprint at time 91,695000 according to authority /gazebo ...
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size, astropy not I = Sersic(x) (Alex is also correct that you have almost no resolution near the value of r_eff that you are trying to find.)
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homework-and-exercises, electromagnetism, plasma-physics, magnetohydrodynamics \mathbf{k} \times \left( \mathbf{k} \times \delta \mathbf{E} \right) & = - \left( \frac{ \omega }{ c } \right)^{2} \left( \frac{ c }{ V_{A} } \right)^{2} \delta \mathbf{E} - \left( \frac{ \omega }{ c } \right)^{2} \delta \mathbf{E} \tag{4c}...
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imu Title: ROS Answers SE migration: IMU Sensor I have a cheap 10-DoF IMU and would like to bring this data into ROS for use in the best way possible. I have it publishing the raw values from the device as an Imu message, but would like to be able to calibrate the biases and convert the data to SI units per the Imu m...
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ros, motion-planning, moveit Original comments Comment by Mike Scheutzow on 2023-04-15: It is poorly documented, but compute_cartesian_path() does much less than you might think. All it does is linearly interpolate between eef waypoints that you provide to it. Determining good waypoints is the difficult task. If the f...
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antimatter, explosions Antimatter annihilation from anti-hydrogen is surprisingly messy: it will not be pure gamma rays. The positrons will meet electrons and produce 0.511 MeV gammas, but the protons meeting antiprotons will initially have a quark annihilate an antiquark, producing a gluon that then gets involved in ...
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energy, potential, dipole Title: Will dipole be restored to its Initial position after removing uniform electric field from it? Potential Energy is the amount of energy which gets stored in the system when external Force is applied on the system. And the system can give us back that energy in any energy form. Keeping ...
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thermodynamics, physical-chemistry, plasma-physics Such a device would be physically possible, but ridiculously uneconomic for the purpose of trash recycling.
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fl.formal-languages, automata-theory Please let me know if you need more detail in the preceding description. Otherwise, we will continue our construction.
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temperature, thermal-radiation Title: How does the physical motion of atom lead to photon emission? It's known that what we call a temperature is in fact molecular motion at microscopic scale. But at which point the emission of photons happens due to this physical motion, so that we can talk about the thermal emission...
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# How to find the following derivative? Here is the complete problem but (c) is the part that I am having problems with, I have already solved (a) and (b): (a) If $t=\tan\left(\frac{x}{2}\right)$,$-\pi<x<\pi$, sketch a right triangle or use trigonometric identities to show that $$\cos\left(\frac{x}{2}\right)=\frac{1}...
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quantum-mechanics, hilbert-space, group-theory, observables The operator $\mathbf{L}^2$ cannot be written the form $\mathbf{L}^2\otimes \mathbf{1}+ \mathbf{1}\otimes \mathbf{L}^2$ (because it is quadratic in the $L_i$'s) so its eigenvalues are no additive. Finally, there are eigenvalues of finite transformations. On ...
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java String cipherText = VigenereCipherEncrypter.encrypt(message, cipherKey); System.out.println("Encrypted message: " + cipherText); String decryptedMessage = VigenereCipherDecrypter.decrypt(cipherText, cipherKey); System.out.println("Decrypted message: " + decryptedMessage); ...
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regression, encoding, labels, mlp, categorical-encoding Title: LabelEncoder with a Multi-Layer Perceptron? So we're working on a machine learning project at work and it's the first time I'm working with an actual team on this. I got pretty good results with a model that uses the following SKLearn pipeline: Data -> Lab...
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c#, linq possible multiple enumerations of IENumerable Should I change it to a List or leave it the way it is? private IEnumerable<ProductLineDto> FilterAtHighestLevel(IEnumerable<ProductLineDto> ganttData, GanttFilterDto ganttFilterDataModel) { if (ganttFilterDataModel.ProjectId == null) ...
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energy Well, if it's meaningful to talk about the total field energy contained in some box then its meaningful to compute the average density of energy by dividing out the box volume. If I take the limit of smaller and smaller boxes around a point, this average density approaches the density at that point. We can go t...
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cosmology, reference-frames, coordinate-systems, universe, observable-universe Essentially is there any way to define a fixed "central" point of the universe that isn't either entirely arbitrary, or based solely on the Observable Universe (which I assume is centered on us?) In standard cosmology, the answer to the bol...
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inorganic-chemistry, acid-base, stoichiometry, concentration, mole The answer is $\pu{50 mL}$. I have tried a bit, but the answer I get is wrong. Let volume be $V$ at the beginning, therefore, no. of moles of $\ce{HCl}$ is $0.1V~\pu{mol}$, no. of moles of $\ce{H2SO4}$ is $0.2V~\pu{mol}$. Total volume of solution after...
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Another way to do the problem would be to use the same formula with n= 10, a= 3, but then subtract off 3- to allow for the missing 3(20) term. for the GP a, ar, ar^2, ar^3 ... and so on Sum of first n terms = a(1 - r^n) / (1-r) where in the first term the power of r is 0.. whereas here it is one.. so yeah i got that.....
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sql, mysql INNER JOIN messages ON messages.id = messageid UNION SELECT messages.id, time, senderid, userid FROM messages_recipients INNER JOIN messages ON messages...
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classical-mechanics, noethers-theorem, classical-field-theory Title: Translation invariance Noether's equation In chapter 13 of Goldstein's classical mechanics, on page 591 when talking about Noether's theorem, Goldstein says we need condition 3, which is $$\tag{13.133} \int_{\Omega'}\mathcal{L}(\eta_\rho'(x^\mu),\eta...
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quantum-mechanics, quantum-field-theory, special-relativity, symmetry, poincare-symmetry $\hat{f} = f - i\hbar(X_f - \frac{i}{\hbar}i_{X_f} \theta)$, ($\theta$ is a symplectic potential whose exterior derivative equals the symplectic form) close to the centrally extended algebra because their action is isomorphic to t...
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performance, awk Title: Extract sections of a file into separate files I have a file of the form - >SDF123.1 blah blah ATCTCTGGAAACTCGGTGAAAGAGAGTAT AGTGATGAGGATGAGTGAG... >SBF123.1 blah blah ATCTCTGGAAACTCGGTGAAAGAGAGTAT AGTGATGAGGATGAGTGAG.... And I want to extract the various sections of this file into individual...
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quantum-mechanics, terminology, history, anharmonic-oscillators This energy can be also determined using the Kramers-Born approach... The fact that one obtains exactly the same result seems to me to furnish remarkable support for the quantum-mechanical equations which have been taken here as a basis
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homework-and-exercises, newtonian-mechanics, newtonian-gravity, energy-conservation, escape-velocity Title: Formula of escape velocity While establishing relation of escape velocity and radius , I confronted a problem . (i) $$v_e=\sqrt{\frac{2GM}{R}}$$ This states that $v_e$ is inversely proportional to the square r...
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filters, image-processing, image-segmentation, edge-detection The above is a scheme for a very effective edge detector. Of course we don't implement it manually but use libraries which implemented this and tweaked the implementation. You may find it in MATLAB's edge() (Under the canny method), OpenCV's cv::Canny and P...
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A very common example is “$A$ is isomorphic to $B$”, which strictly speaking means only that there exists some isomorphism between $A$ and $B$. But almost invariably, when proving such a statement, one exhibits a specific isomorphism or proves that some previously known map is an isomorphism, and it often matters later...
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If the length of $\sigma$ is $n$, then $\sigma \preceq f$ means $\sigma(i) = f(i)$ for all $i < n$, i.e. $\sigma$ is an initial segment of $f$. You can cover with countable many cylinders because the cylinders form a countable basis for $X$. Even when $A$ is countable, $A^\mathbb{N}$ has a countable basis. The part tha...
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