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noise, power-spectral-density, snr I go into more details of the Allan Variance and Allan Deviation for this particular application here: What determines the accuracy of the phase result in a DFT bin?
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forces, acceleration, friction, velocity 0 & \text{else} \end{cases} The equation of motion in the region $0 \le x \le L$ is then $$ M \ddot{x} = - \mu_k Mg\frac{x}{L} $$ In this region, the solution is $$ x(t) = A \cos(\omega t + \delta), \quad \omega^2 = \mu_k g/L, $$ with constants $A, \delta$ to be fixed by the...
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fft, ifft Since my understanding is still fairly low, is DFT and FFT really the solution to my problem? Would it be logical to take the FFT , filter out outliers that are generated and cause noise, and re-construct the time domain signal back ( with the results that were acceptable ) using iFFT? That should, in theor...
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cc.complexity-theory, graph-theory Are there evenly many 3-edge-colorings? (Should be $\oplus P$-complete) Who wins at strings-and-coins? (Might be PSPACE-complete) What is its list coloring or list edge coloring number? (Might be $\Pi^p_2$-complete) Is it a unit disk graph? A unit distance graph? (Might be $\exists \...
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c#, object-oriented, parsing /// this would be used as system default. // then you can define another custom requirement // that the consumer can customize, and use the default instance // if the consumer did not provide any custom requirement. public class DefaultPasswordRequirement : IPasswordRequirement { priv...
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organic-chemistry, alcohols, stability, carbocation Title: Does 2,2-dimethylpropan-1-ol give a positive Lucas test? I learnt that the Lucas test involves the formation of a carbocation and it gives a positive test based on the stability of the carbocation formed, and hence primary alcohols do not show turbidity (condi...
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and improves students standardized test performance. 2 Domain: Geometry Theme: Solve real-world and mathematical problems involving area, surface area, and volume Description: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge le...
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everyday-chemistry, food-chemistry contains little water which leaves a large amount of very soluble sugar behind when it is baked off. Sugar is very soluble and is structurally weak, (unless caramelized). Salt, while also very water soluble and not very strong, need only be present in small quantities to give a cooki...
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compilers, parsers, lr-k Conceptually, lookahead sets are created during the itemset closure operation. Closure (recursively) creates new items with the • at the beginning for every non-terminal $\mathit{N}$ which follows the • in some item in the state. The new items are precisely the productions for $\mathit{N}$. Ea...
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$$4D_{h/2} f(x)-D_h f(x)=3f^\prime(x)-\frac{f^{(5)}(x)}{160}h^4+\dots$$ and we have after a division by $3$: $$\frac{4D_{h/2} f(x)-D_h f(x)}{3}=f^\prime(x)-\frac{f^{(5)}(x)}{480}h^4+\dots$$ Note that the surviving terms after $f^\prime(x)$ are (supposed to be) much smaller than either of the terms after $f^\prime(x)...
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quadcopter, battery Title: Estimation of Battery Life Time From PWM Signals in a Quadrotor Is there any way of estimation the battery life from pwm outputs which goes to motors in microcontroller level. I'm planning to estimate path range with this. Microcontroller, sensor and other electronic device should be neglect...
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A. x4 ≥ 1 B. x3 ≤ 27 C. x2 ≥ 16 D. 2≤ |x| ≤ 5 E. 2 ≤ 3x+4 ≤ 6 The key words in the stem are: "a single line segment of finite length" Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus c...
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java, hash-map eventually an index value is calculated - this index value represents the index of the internal array that the key-value pair will exist under. Thus, the logic for getting a value for a particular key would be to translate the key into an index value, and then to get the first Entry for that index value...
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electrostatics, electric-fields, potential, potential-energy, voltage Title: Electric Field Strength vs Electric Potential This is the simple thing I’m confused about. As I understand it, the electrostatic force from a charge out to a certain distance is inversely proportional to the distance squared (and electric fi...
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experimental-realization, noise, superconducting-quantum-computing Again the authors do not rule out the use of filters! Paper #3: Cavity Attenuators for Superconducting Qubits "This coupling opens a channel for auxiliary components in the microwave wiring to affect the temperature of the cavity mode. Examples of suc...
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molecular-biology, molecular-genetics, gene-expression, gene-regulation, operons Title: Are the subordinate genes of a repressed operon really "turned off"? Operons are often described using all or nothing language. A repressor binding to the operator is usually presented as "turning off" the regulated genes. Case in ...
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arduino, rosserial, laserscan Originally posted by Stefan Kohlbrecher with karma: 24361 on 2014-08-01 This answer was ACCEPTED on the original site Post score: 0 Original comments Comment by Kent Williams on 2014-08-01: Thanks for the response Stefan! So if the vector is of type float*, should I be declaring and init...
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python, python-3.x, tkinter There's really no reason to use an intermediate value (regulardata) if you're immediately appending the data to a list. You also have the potential for a bug, since this function assumes that the lists are empty (which they are now, but bugs in other parts of your code might forget to rese...
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quantum-field-theory, special-relativity, quantum-spin, fermions, classical-field-theory $$ \Lambda: \quad \psi_l(x) \mapsto \sum_{m }S_{lm}(\Lambda) \psi_m (\Lambda^{-1} x) , $$ i.e. as a field. The $a_\alpha(p)$ transform according to a rule which is a little more convoluted to write down. Essentially one defines...
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filters, transform, hilbert-transform In short: $$y[n]=\sum_ky_k[n-kL],\qquad y_k[n]=(x_k\star h)[n]$$ where $h[n]$ is the impulse response, $x_k[n]$ is the $k^{th}$ input block, $y_k[n]$ is the convolution of $h[n]$ with $x_k[n]$, and, finally, $y[n]$ is the output signal.
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wheeled-robot, raspberry-pi GPIO.setup(Motor2A, GPIO.OUT) GPIO.setup(Motor2B, GPIO.OUT) GPIO.setup(Motor2E, GPIO.OUT) print("ON") GPIO.output(Motor1A, GPIO.HIGH) GPIO.output(Motor1B, GPIO.LOW) GPIO.output(Motor1E, GPIO.HIGH) GPIO.output(Motor2A, GPIO.HIGH) GPIO.output(Motor2B, GPIO.LOW) GPIO.output(Motor2E, GPIO.HIG...
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machine-learning, deep-learning, reinforcement-learning Title: Quick question on basic Basic concept of experience replay Due to my admitted newbie's understanding on the field, I'm about to ask a dummy question. While sampling batches, for example experience replay buffer which contains number of samples, after getti...
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Now this looks like Clement C's hint. • $\frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}$ and $H_{n+2}-H_{n+1}=\frac{1}{n+2}$, hence summation by parts converts such series into an elementary (telescopic) one. – Jack D'Aurizio Feb 25 '18 at 16:47 • For gosh sakes, the asker has been suspended for their low quality posts th...
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fft, matlab Title: Which FFT algorithm does Matlab use? Exactly which FFT algorithm does Matlab use for the fft function? I though originally it was the Cooley-Tukey Decimation in Time algorithm but the Matlab documentation does not give a reference to exactly which algorithm is used. It does however reference to this...
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newtonian-gravity, atoms Title: Are individual atoms affected by gravity? If we could place individual atoms in the vacuum, would it fall towards earth just like a bowling ball in the vacuum? Yes. Gravitation holds for all massive objects, no matter how tiny the mass be be. The only caveat is, the force is directly p...
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python, python-3.x, validation while True: try: test = str(input("What test do you want to take? Computer Science, History or Music? ").strip().lower()) is_it_correct(test, "computer science", "history", "music", """\nSorry, you didn’t input valid settings. Please enter (without the quotes) either ...
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I assume that the coordinate system origin is at the center of the curve. (1) Parametric Cubic in Bézier Form This is the obvious choice because the symbols on your picture look like the control points of a cubic Bézier curve. These control points are $\mathbf{P}_0 = (-60,20)$, $\mathbf{P}_1 = (0,20)$, $\mathbf{P}_2 =...
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turing-machines, computation-models Title: Does the amount of symbols a turing machine has affect what computations it can perform? Do additonal symbols on a turing machine actually change what is computationally possible on a machine, or do they just make them easier to work with? For example is there anything a 3 sy...
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Making the subs and expanding gives: $\frac{1}{2}+\frac{1}{4(w-1)}-\frac{1}{4(w+1)}$ Now, it is just a matter of ln. This is one possible approach. Resubbing we get $\frac{ln(\sqrt{1+4e^{4x}}-1)}{2}+\frac{\sqrt{1+4e^{4x}}}{2}-x$ Just to satisfy my curiousity, I have always when seeing a nested exponential defined u...
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python, pyranges The data I am working with: a pyranges covering hotspots in the human genome (all chr1 for the moment) +--------------+-----------+-----------+-----------+ | Chromosome | Start | End | Score | | (category) | (int32) | (int32) | (int64) | |--------------+-----------+-----------+...
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object-oriented, ruby 5) Use a linter. Check out RuboCop. You will be surprised by all of the style rules you break! Here is an example of how I might write this class: class RateLimit def initialize(maximum_requests, time_limit) @maximum_requests = maximum_requests @time_limit = time_limit @user_request...
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fourier-transform, wavelet, signal-detection The DWT is representing the signal to be detected (in this case a periodic signal) with a set of non-periodic functions, so this requires lots of components (bands as you refer to them – but DWT really works with scale not frequency) to follow the periodic nature of the sig...
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ros, ros-kinetic, service, server And i have the following error : /home/user/omniROS/omniROS_ws/src/total_torque/src/totalTorque.cpp: In member function ‘void Torque::initialisation()’: /home/user/omniROS/omniROS_ws/src/total_torque/src/totalTorque.cpp:17:108: error: no matching function for call to ‘ros::NodeHandle:...
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we calculate the sum of natural numbers? Well, the sum is clearly 1 + 2 + 3 + 4 + 5. 4. In mathematics, summation is the addition of a sequence of any kind of numbers, called addends or summands; the result is their sum or total. But of course, we don’t want the total area (the number of x’s and o’s), we just want the ...
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quantum-mechanics, operators, wavefunction, hamiltonian, heisenberg-uncertainty-principle Where there is a "sudden" change in Hamiltonian: $$ H \to H' $$ However, since the universe cares only about relative position and not actual position (insert general relativity philosophy here), it should be impossible to distin...
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ds.data-structures, tree For storing data in the leaves (by which I assume you mean that each key is stored in a leaf, or that value (in a map structure) are all stored in leaves), views of skip-lists as trees may have this property. I mentioned some tree-views of skip lists on another question at this site. Others th...
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quantum-gate, superposition $=CNOT\frac{1}{\sqrt{2}}\left(|0\rangle|0\rangle+|1\rangle\right|0\rangle)$ (here I have just multiplied out the $|0\rangle$ into the brackets) $=\frac{1}{\sqrt{2}}\left(CNOT|0\rangle|0\rangle+CNOT|1\rangle\right|0\rangle)$ (here I have used the fact that the operator is linear, so I can ba...
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c++, performance SpriteBuffer<spriteRenderer, spriteSheet> spriteBuf; struct FXParticle { Vec2 position{0, 0}; Vec2 delta{0, 0}; u32 idx{0}; i32 life{100}; FXParticle* Init() noexcept { position.Set(Vec2::Rnd(200.0f, 200.0f)).Sub(100.0f, 100.0f); delta.Polar(Rnd(TAU), Rnd(1.0f, 2.0f...
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c#, winforms sf.Alignment = StringAlignment.Center; sf.LineAlignment = StringAlignment.Center; g.FillEllipse(new SolidBrush(Background), rc.Left + 1.5f, rc.Top + 1.5f, rc.Width - 4.0f, rc.Height - 4.0f); g.DrawEllipse(new Pen(new SolidBrush(BorderColor), 3.0f), rc.Left + 1.5f, rc.Top + 1.5f, r...
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Consider the set $X = \mathscr L − \{ (\phi \land \psi) \}$; we have that $P_i \in X$ and that if $\sigma \in X$, then $\lnot \sigma \in X$; thus, rules 1 and 2 are satisfied by $X$. Consider now $\sigma_1, \sigma_2 \in X$; then $\sigma_1, \sigma_2 \in \mathscr L$ and thus, by rule 3 : $(\sigma_1 \land \sigma_2) \in \...
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ChaCha Ingal Cortez our prof. gave the same question but the ans. he gave is different from your ans. in no 2, his answer is (y')^3 + 2ay"=0 are they the same with your answer sir ? Jhun Vert They are different. I made a mistake in $y - k$ of the above solution. $(y − k)^2 = \pm 4a(x − h)$ $2(y - k) \, y' = \pm 4a$...
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arduino, rosserial Title: Arduino DUE + CMake with rosserial_arduino Hello all, What is the board name I should use for BOARD? The following does not work. generate_arduino_firmware(due_project SRCS due_project.cpp ${ROS_LIB_DIR}/time.cpp BOARD due PORT /dev/ttyACM0 ) I have installed DUE related stuff in IDE ...
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quantum-mechanics, condensed-matter, hamiltonian Title: (Altland-Simon) Deriving ferromagnetic interaction term from interacting tight-binding Hamiltonian Below is a part of the book "Condensed Matter Field Theory" by Altland and Simon.
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the spring is mass-less, and the force in either end equals the force of the others, but in the opposite direction (Newton’s 3rd. The simplest model for mechanical vibration analysis is a MASS-SPRING system: Mass m Mass m k k with m = mass, and k = spring constant k is defined as the amount of force required to deflect...
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complexity-theory, time-complexity, np-complete, reductions Yes, of course. If your reduction function $f$ has running-time function $T_f \in O(n^k)$, then $|f(x)| \in O(n^k)$ -- a Turing machine can not write to more than one cell per execution step. Let's say problem A is NP and problem B is NP-complete. I've found...
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c#, object-oriented, .net, interface I would convert the list properties Documents and Pages to getter-only properties. public interface IPortfolio { string FirstName { get; set; } string LastName { get; set; } string Name { get; set; } int Id { get; set; } List<IDocument> Documents { get; } }
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terminology-and-notation There are more special cases in Dirac notation, which might not be the most sensible notation from a general point of view (they are the equivalent of "irregular verbs") but which are in heavy use and which are useful shorthand:
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quantum-mechanics, homework-and-exercises, momentum, conservation-laws, symmetry Title: How to show that translational invariance in $y$ of implies that it's an eigenstate of $p_y$? Let us consider a particle on a plane with uniform magnetic field $B=B\hat{z}$, and hence with the Hamiltonian $H=\frac{1}{2m}(\vec{p}+e\...
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## 4 Answers Following the comment and your own implementation with Root it is better to define this: nthtri[t_] := Root[#^2 + # - 2 t &, 2] nthtri[28] 7 This has no unlocalized Symbols as your own version had. With your code if you set x = 5 before using it it will fail. f is the function you are looking for: ...
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python, performance, array, numpy lst.append(max(ABC.sum(), 1e-10)) return lst # Time function. func_time = timeit.timeit(func, number=10000) print func_time I couldn't make much improvement on this, sorry. Since you didn't explain what the code is supposed to do, there was no opportunity for algorithmic insight...
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discrete-signals, z-transform, transfer-function $$H(z)=\frac{A}{z-z_0}+\frac{A^*}{z-z_0^*}+B\tag{1}$$ where $^*$ denotes complex conjugation. The reason why your expansion doesn't work is that the given function $H(z)$ is improper, i.e., the degree of its numerator is greater than or equal to the degree of the numera...
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control, ros, matlab, simulation, troubleshooting Question I cannot explain how the input command gets that value. And as a result how ros_control calculates the input signal. Any help, hint or idea about what causes this difference will be of great help. Update Without the derivate term, and only $K_p = 15$ the initi...
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java, beginner, object-oriented, game, android } }); } @Override public void onRestart() { super.onRestart(); pause = false; mediaPlayer.seekTo(stopMediaplayer); mediaPlayer.start(); } @Override public void onPause() { super.onPause(); pause = true; mediaPlayer.stop(); mediaPlayer...
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formal-languages, context-free, pushdown-automata Title: Can a DPDA decide if two letters appear the same number of times mod 5? $ L = \{ w ∈\{0,1\}^* \mid |w|_0 = |w|_1 \mod 5 \}$ So i tried figuring out why this is CFL and whether its DCFL or not but i couldn't come up with any PDA! I'm studying for my exam a...
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electromagnetism, electricity, electric-circuits There are a lot of different types of ports for chargers: USB, USB-C, ecc. And people, myself included, touch the port, the metal conductive end of the cable by mistake all the time, while the charger is connected to the electric socket! Why am I not dead? What are the ...
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black-hole, gravity, space-time, special-relativity, horizon Thus, the usual result of "infinite gravitational time dilation makes the image of the infalling object hover forever near the horizon" is also straightforwardly deducible from the diagram, and so is completely consistent with the infalling object being able...
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java, object-oriented, inheritance, interface, constructor } } (Since you're still a student, I might go over the top with some explanations.) Code Style Always format your code. Always. (CTRL+SHIFT+F in eclipse and CTRL+ALT+L in intellij). There's also the possibility to activate the formatting for save actions. Use...
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javascript, performance, ecmascript-6, cellular-automata const update = () => { let int = rand(0, 7) let row = cellularAutomaton[0] row[int] = row[int] ? 0 : 1 // now, how to update the remaining rows? for (let i = 1, n = cellularAutomaton.length; i < n; i++) { row = cellularAutomaton[i] for (let k =...
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filters, gaussian, gmsk $f_s$ such that the Nyquist frequency $f_s/2$ was at $2/T$ (at $f=0.1$ in the plot below), we can see in the plot that all aliasing components that are above $f_s/2$ would be lower than 80 dB. This is likely sufficient to meet any practical distortion target for GMSK and suggests that $f_s=4/T$...
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python, strings, programming-challenge, python-2.x if(len(word) > 0): currentLength = 1 longest = 1 dict = {word[0] : 0} i = 1 while i < len(word): if (dict.has_key(word[i])): i = dict[word[i]]+1 dict.clear() if (longe...
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robotic-arm, actuator, dynamics, torque Title: Why do series elastic actuators have more accurate and stable force control? The other day, somebody was telling me about a robot in their lab, and they mentioned that it has "series elastic" actuators. But after doing a bit of Googling, I'm still not sure as to what this...
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physical-chemistry, bond, hybridization, valence-bond-theory Thus, my question is how the hybrid argument that was presented works and how would one be able to realize the different hybridized states of an atom in a molecule (as an approximation). Older textbooks decided to use a d-orbital formalism for elements of t...
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c++, asynchronous, thread-safety, c++20, boost saved_async_completion_handler(executor_type ex, completion_handler_type && handler) : m_ex(asio::get_associated_executor(handler, ex)) , m_handler(std::forward<completion_handler_type>(handler)) , m_work_guard(asio::make_work_guard(m_ex)) {} ...
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python, beginner # returns dealers removed aces dealer_hand = [card if card != 'x' else 'A' for card in dealer_hand] return dealer_hand, dealer_total, dealer_result Victory checking Before I take a look at handling the player's turn, I'm going to zoop down to the bottom and look at comparing our victories. Y...
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python, algorithm, python-3.x, sorting Rework the algorithm to not modify the container you're looping over: def subset_of(long_groups, group): return any(lg[0] <= g[0] and g[1] <= lg[1] for long_group in long_groups for lg in long_group for g in group) ... longest_groups = [] for group in groups:...
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c++, c++11, tree, template, heap First of all, it doesn't have a default constructor. I tried to write Tree<int> tree; and got a compile-time error. Consider making your tree default-constructible and thus consider the fact that some trees can be empty, which means that they could also have an empty or is_empty method...
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homework-and-exercises, newtonian-mechanics, rotational-dynamics For B1.3, (a) appears to be the most logical choice. It is my understanding that an object whose shape is asymmetric about the spin axis will result in an angular momentum vector not aligned with the spin axis which makes (c), (d) nonviable answers. Addi...
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speech-recognition, mfcc, visualization, feature-extraction For example, here is an MFCC plot of a very simple signal. What signal is that? If you are ready then please hover the yellow space.
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symmetry, metric-tensor, field-theory, action, variational-calculus $$ \frac{\delta S}{\delta g_{(\mu \nu)}}=0 , \qquad \frac{\delta S}{\delta T_{[\mu \nu]}}=0 \tag{2} $$ But I don't see these symmetrizations (in books, articles, etc.) explicitly. I have always believed that the objects $\frac{\delta S}{\delta g_...
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python, python-3.x Title: Computing the total property management fee for properties My goal was to create a "calculator" to compute the monthly property management fee for two vacation rental condos my wife and I own. My purpose was to take user input for name, dates and rental rate and compute the total property man...
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pair parametric.. Point on the sphere are careful in calculating the values, point-plotting is highly dependable we... Get the free a parametric graph '' widget for your website, blog, Wordpress, Blogger, orientation!, but with a faster speed and an opposite orientation that of the parametric equations =... Expressions...
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$D(f \times g) = R(f) \times D(g) + D(f) \times g$ where $R$ is the right-shift operator defined as: $R = ( \text{function$f$on$\zz$} \mapsto ( \text{int$n$} \mapsto f(n+1) ) )$ Namely for any function $f$ on $\zz$ and $n \in Z$, $R(f)(n) = f(n+1)$. For convenience we also define the summation operator: $S = ( \te...
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quantum-mechanics, homework-and-exercises, lagrangian-formalism, hamiltonian-formalism Start with the Lagrangian function $L(x, \dot{x})$. Compute the canonical momentum $p= \frac{\partial L(x, \dot{x})}{\partial \dot{x}}$. Express $\dot{x}$ in terms of $p$ and $x$: $\dot{x}=\dot{x}(p,x)$. Write down the Hamiltonia...
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quantum-chemistry, molecular-orbital-theory Title: What are the molecular orbitals of the hypothetical linear H₃⁺ molecule? What would be the wave function of the lowest energy molecular orbital of a hypothetical linear $\ce{H3+}$ molecule? According to the LCAO method, I feel the lowest energy MO will be $\mathrm{1...
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general-relativity, differential-geometry, geometry, models, stress-energy-momentum-tensor To begin with, which set do I choose for M? I think I can answer this question myself. I take this set to be the set of intuitive descriptions(that I can make intuitive sense of) of events in the world. For example, E:= "(a part...
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c++ return temp; } //delete function node* deleteNode(node* tnode,int val){ if(tnode==NULL) return tnode; if(tnode->value>val){ tnode->left=deleteNode(tnode->left,val); } else if(tnode->value<val){ tnode->right=deleteNode(tnode->right,val); } else{ if(tnode->l...
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thermodynamics, ideal-gas In the Boltzmann factor it is always the energy that appears, so when the relationship between momentum and energy is different (e.g. in a relativistic gas) the distribution over momentum is different. For example one gets $$ f(p) \propto p^2 e^{-E/k_B T} $$ where $p = \gamma m v$ and $E = \...
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cannot be defined in a way that makes it holomorphic. b) Find the radius of convergence of the series. The interval of convergence may be as small as a single point or as large as the set of all real numbers. EXPECTED SKILLS: Know (i. By the Ratio Test, the power series will converge provided l\,|x|1: that is, provided...
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performance, strings, homework, matlab fclose('all'); end And the driver (don't review this please): Word_Count_Speeches.m: diaryFile = 'project3Results.txt'; if exist(diaryFile) delete(diaryFile); end % Count for all speeches diary(diaryFile); fileName = 'Speeches/Abraham_Lincoln_The_Gettysburg_Address.txt'; fp...
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c++, template, logging void LogDestory(); } #if WIN32 #define LOG_INFO(format, ...) Logger::Log(Logger::LOG_LEVEL_INFO, __FILE__, __LINE__, __FUNCTION__, format, __VA_ARGS__) #define LOG_DEBUG(format, ...) Logger::Log(Logger::LOG_LEVEL_DEBUG, __FILE__, __LINE__, __FUNCTION__, format, __VA_ARGS__) #define LOG_ERROR(...
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biochemistry, kinetics, catalysis The frequent correlation is described by the Michaelis-Menten kinetics, which introduces the Michaelis constant $K_M$ as the substrate concentration at which half of all enzyme is bound to substrate $-$ and thus the reaction is running at a speed of $\frac{V_{max}}{2}$. As you can see...
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y=0,x=0,x=2,y=2 Required area = $\frac{1+\ln (2)}{2}$ =>P = 0.846 Alternatively, We can do by the integration method in two parts • first, x from zero to 1 => p = 0.5 [ valid y range here is [0,2] ] • second , x from 1 to 2 => p = 0.346 [ valid y range here is [0,2/x] ] • P = 0.846 Can you Please Explain the the I...
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aqueous-solution, ph, stoichiometry so that now we can equate conditions for both solutions and find the mass: $$\mathrm{pH}_1 - \log{m_1(\ce{KA})} = \mathrm{pH}_2 - \log{m_2(\ce{KA})}$$ $$\log{\frac{m_2(\ce{KA})}{m_1(\ce{KA})}} = \mathrm{pH}_2 - \mathrm{pH}_1$$ $$m_2(\ce{KA}) = m_1(\ce{KA})\cdot10^{\mathrm{pH}_2 - \m...
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general-relativity, differential-geometry, definition, geodesics It's also called a light-like geodesic, as opposed to time-like geodesics and space-like geodesics. For two events separated by a time-like interval, sufficient time passes between them that there could be a cause–effect relationship between the two eve...
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the circumference of an ellipse. See Basic equation of a circle and General equation of a circle as an introduction to this topic. A Shape is a type of UIElement that enables you to draw a shape to the screen. Matrix for rotation is an anticlockwise direction. If (x, y) is a point of the new curve, transformed from (px...
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general-relativity, gravity, computational-physics, simulations, solar-system (b) the mathematical sophistication required is if anything even greater than using analytical methods. You aren't going to be doing this without a thorough understanding of general relativity, and you aren't going to be doing it on your hom...
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optics, photons Title: How does distance affect the intensity of a specular reflection? I have a specular reflection I'm capturing with a camera. I'd like to calculate the intensity of a reflecting pixel depending on the bulb distance from the reflected surface. I'm aware of the inverse square law, but my understandi...
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gazebo, simulation ...... so first 2 are working fine and when I try to do 3rd one to launch gazebo it says gazebo successfully initialized and model was shown for 2 secs and after that it says process has died as described below..... so please if anyone can help it would be of great help ..... please try to help us. ...
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c++, unit-testing, classes, c++20, overloading // Enable this function if ElementT = RGB void print(std::string separator = "\t", std::ostream& os = std::cout) const requires(std::same_as<ElementT, RGB>) { for (std::size_t y = 0; y < height; ++y) { for (...
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quantum-mechanics, optics, particle-physics, solid-state-physics, large-hadron-collider I have attached this slide from (http://meetings.chess.cornell.edu/ACABioSAS/TrackA/SAXSandSANS-Biospecifics_Trewhella_ACA_2015fin.pdf). What I don't understand is that since nucleus is much bigger than the neutron, classically, th...
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entomology, ecology, biological-control probably gone some way towards this (did you notice whether the mosquito problem got any better after the plants were removed?) Biological control: introduce predators or parasites into the environment. Plenty of species eat adult mosquitoes but there aren't really any that prim...
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$and$ 0! And they can also be negative (except for integers). = -1! We can find the factorial of any number which is greater than or equal to 0(Zero). The factorial value of 0 is by definition equal to 1. The factorial can be seen as the result of multiplying a sequence of descending natural numbers (such as 3 × 2 × 1)...
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java, bitwise, utf-8 In general, text is more likely to contain shorter UTF-8 sequences than longer ones, so you might as well handle the shorter cases first to save a few CPU cycles. Rather than setting n to be the number of trailing bytes, set it to be the expected length of the array. I'd rename n → expectedLen to...
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waves, acoustics, frequency, harmonics 1.5 sec sample: The first peak between $168-175Hz$ 2.25 sec sample:
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notation, differentiation, calculus In other words, is it correct to simply substitute numbers in to a quantity like $dt$? Could I say that at a certain instant in time, $dt$ = 4 seconds? I've seen this done before in a few books and well, frankly it irritates me because I'm seeing the $d$ operator used in many diffe...
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process is supposed to be. 1 Convolutions of Discrete Functions Definition Convolution of Vectors Mid-lecture Problem Convolution of Matrices 2 Convolutions of Continuous Functions Definition Example: Signal Processing Frank Keller Computational Foundations of Cognitive Science 2. Following is an example to demonstrate c...
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python, performance, random, matrix Title: Procedural generation of a general matrix representing a tile map The problem is to design an structure which generates "uniformly" the next one in an initially zero matrix. Taking an arbitrary index i in the range [0,m-1] for any j where a[i,j] == 0. It is, for example: \beg...
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biophysics, rocket-science, space-mission Water is even tougher nut to crack than is air. Food? What we do know is that every attempt to make a self-sustaining environment has failed miserably. Basically, we don't know how to do that. Issue #2: Humans need to come home. Given the above, sending humans to Mars permanen...
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c#, object-oriented, design-patterns, iterator The rest of the information that you attempted to provide in the name of the property should be apparent from the relationship between the classes. Iterating over collections My second problem is usage, because I will end up with an IEnumerable containing an IEnumerable...
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homework-and-exercises, symmetry, field-theory, conformal-field-theory, majorana-fermions &=\int d^2z\big(\delta\Phi\bar\partial\Phi+\bar\partial(\Phi\delta\Phi)-(\bar\partial\Phi)\delta\Phi\big)\\ &=2\int d^2z\delta\Phi\bar\partial\Phi\end{align} Since the equation has to be true for all variations $\delta\Phi$, we f...
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