text:
# Check if a number can be expressed as power in C++

C++Server Side ProgrammingProgramming

Here we will check whether we can represent a number as power, like ab or not. Suppose a number 125 is present. This can be represented as 53. Another number 91 cannot be represented as power of some integer value.

## Algorithm

isRepresentPower(num):
Begin
if num = 1, then return true
for i := 2, i2 <= num, increase i by 1, do
val := log(a)/log(i)
if val – int(val) < 0.0000000001, then return true
done
return false
End

## Example

Live Demo

#include<iostream>
#include<cmath>
using namespace std;
bool isRepresentPower(int num) {
if (num == 1)
return true;
for (int i = 2; i * i <= num; i++) {
double val = log(num) / log(i);
if ((val - (int)val) < 0.00000001)
return true;
}
return false;
}
int main() {
int n = 125;
cout << (isRepresentPower(n) ? "Can be represented" : "Cannot be represented");
}

## Output

Can be represented
Published on 27-Sep-2019 08:31:32


text:
# Axiomatic proofs in propositional logic

I have to use these three axioms

(A1) $$P \to (Q \to P)$$

(A2) $$(P \to (Q \to R)) \to ((P \to Q) \to (P \to R))$$

(A3) $$(\neg Q \to \neg P) \to ((\neg Q \to P) \to Q)$$

along with Modus Ponens to prove :

1. $$(\neg\neg P \to \neg Q) \vdash (Q \to \neg P)$$

2. $$\neg(\neg \neg P \to \neg Q), (\neg \neg P \to \neg Q) \vdash P$$

I understand the process of creating the proof, but I have tried many things and have racked my brain to no avail. Any help would be appreciated, thanks.

• 1. is simply Contraposition : $(\lnot \beta \to \lnot \alpha) \to (\alpha \to \beta)$. You can find a proof of it in this post. – Mauro ALLEGRANZA Sep 17 '19 at 12:32
• 2. is an instance of Ef Falso : $\lnot \alpha \to (\alpha \to \beta)$. You can find a proof of it in this post. – Mauro ALLEGRANZA Sep 17 '19 at 12:37
• @MauroALLEGRANZA Thanks for the links, however I think my question differs in that I have a non-empty set of premise propositions. This would make the proofs different, no? As opposed to proving a theorem without any assumptions. – asilentfrog Sep 17 '19 at 13:06
• Use Modus Ponens. – Mauro ALLEGRANZA Sep 17 '19 at 13:10
• Oh as an additional last step. Is the proof the exact same though? Having the additional assumption doesn't make them any simpler? – asilentfrog Sep 17 '19 at 13:19

For the first one: If you are allowed to use the Deduction Theorem, it's pretty straightforward. First, let's prove $$\neg \neg P \to \neg Q, Q \vdash \neg P$$:

$$1 \ \neg \neg P \to \neg Q \ Assumption$$

$$2 \ Q \ Assumption$$

$$3 \ Q \to (\neg \neg P \to Q) \ Axiom \ 1$$

$$4 \ \neg \neg P \to Q \ MP \ 2,3$$

$$5 \ (\neg \neg P \to \neg Q) \to ((\neg \neg P \to Q) \to \neg P) \ Axiom \ 3$$

$$6 \ (\neg \neg P \to Q) \to \neg P \ MP \ 1,5$$

$$7 \ \neg P \ MP \ 4,6$$

OK, so now that we have $$\neg \neg P \to \neg Q, Q \vdash \neg P$$, we just use the Deduction Theorem, and we get $$\neg \neg P \to \neg Q \vdash Q \to \neg P$$

If you are not allowed to use the Deduction Theorem, then this one gets a good bit nastier:

$$1 \ \neg \neg P \to \neg Q \ Assumption$$

$$2 \ (\neg \neg P \to \neg Q) \to (Q \to (\neg \neg P \to \neg Q)) \ Axiom \ 1$$

$$3 \ Q \to (\neg \neg P \to \neg Q) \ MP \ 1,2$$

$$4 \ Q \to (\neg \neg P \to Q) \ Axiom \ 1$$

$$5 \ (\neg \neg P \to \neg Q) \to ((\neg \neg P \to Q) \to \neg P) \ Axiom \ 3$$

$$6 \ ((\neg \neg P \to \neg Q) \to ((\neg \neg P \to Q) \to \neg P)) \to (Q \to ((\neg \neg P \to \neg Q) \to ((\neg \neg P \to Q) \to \neg P))) \ Axiom \ 1$$

$$7 \ Q \to ((\neg \neg P \to \neg Q) \to ((\neg \neg P \to Q) \to \neg P)) \ MP \ 5,6$$

$$8 \ (Q \to ((\neg \neg P \to \neg Q) \to ((\neg \neg P \to Q) \to \neg P))) \to ((Q \to (\neg \neg P \to \neg Q)) \to (Q \to ((\neg \neg P \to Q) \to \neg P))) \ Axiom \ 2$$

$$9 \ (Q \to (\neg \neg P \to \neg Q)) \to (Q \to ((\neg \neg P \to Q) \to \neg P)) \ MP \ 7,8$$

$$10 \ Q \to ((\neg \neg P \to Q) \to \neg P) \ MP \ 3,9$$

$$11 \ (Q \to ((\neg \neg P \to Q) \to \neg P)) \to ((Q \to (\neg \neg P \to Q)) \to (Q \to \neg P)) \ Axiom \ 2$$

$$12 \ (Q \to (\neg \neg P \to Q)) \to (Q \to \neg P) \ MP \ 10, 11$$

$$13 \ Q \to \neg P \ MP \ 4,12$$

The second one is of the form $$\neg Q, Q \vdash P$$, and that is actually really easy to prove:

$$1 \ \neg Q \ Assumption$$

$$2 \ Q \ Assumption$$

$$3 \ \neg Q \to (\neg P \to \neg Q) \ Axiom \ 1$$

$$4 \ \neg P \to \neg Q \ MP \ 1,3$$

$$5 \ Q \to (\neg P \to Q) \ Axiom \ 1$$

$$6 \ \neg P \to Q \ MP \ 2,5$$

$$7 \ (\neg P \to \neg Q) \to ((\neg P \to Q) \to P) \ Axiom 3$$

$$8 \ (\neg P \to Q) \to P \ MP \ 4,7$$

$$9 \ P \ MP \ 6,8$$

So, instead of $$Q$$, use $$\neg \neg P \to \neg Q$$ in the above proof, and you're done. Here is a computer-verified proof:

format: plain


text:
It turns out that my brief soirée with reinforcement learning (RL) became a long dance. I started watching David Silver’s lectures, and seriously considered doing a pet research project in RL. Good thing, deep in my lab’s archives, I found a gem of a problem that may be solvable by reinforcement learning— protein structure prediction. In this post, I will walk you through the first step of my journey in RL-plus-bioinformatics by creating a Gym library for determining protein structures.

The main idea is that given a protein sequence, we wish to infer what it looks like. However, determining a protein structure in the molecular level is computationally-intensive. Folding@Home is a good example. It implements a distributed computing scheme to use a volunteer’s machine idle time (from PS4 to your web browser) in order to simulate thousands of protein configurations. For our case, we start with simple protein abstractions that are computationally manageable.

## The 2D Hydrophobic-Polar (HP) Lattice Model

The HP Lattice Model is a seminal work that describes proteins in the lens of statistical mechanics (Lau and Dill, 1989). Simply put, it gives us a handle to tackle the protein folding problem in a more tractable fashion. Furthermore, it has been proven that the HP Lattice problem is NP-complete (Berger and Leighton, 1998), joining the ranks of our well-loved travelling salesman and graph coloring problems.

As a result, we can apply optimization techniques such as dynamic programming to solve HP lattices. Because we are doing RL, we will attempt a solution based on markov decision processes (MDPs). First, let’s examine the characteristics of a protein lattice.

### Treat it like a game

The goal is simple. Given a protein sequence made up of H and P “molecules,” find the most stable configuration. That is, the config with the highest number of adjacent H molecules (corresponds to the configuration with the lowest energy).

We start with an initial molecule (as per the example above, it’s H), and decide where to put the next molecule: up (U), down (D), left (L), or right (R). We do this until all molecules are placed or if we accidentally trapped ourselves in the sequence.

That’s it! However, there are some rules that must be followed while playing this game:

• You cannot move diagonally (only L, R, U, or D).
• You should only put a molecule adjacent to the previous one.
• Placing a molecule on an occupied space is penalized.
• Trapping yourself and failing to finish the task incurs heavy penalty.

As you can see, the HP Lattice model is a very simple abstraction of actual proteins. We only deal with two types of molecules (not 20 amino acids nor $20^3$ codon combinations), we only work inside a 2-D planar surface, and our objective function (number of H pairs) is a thermodynamic interpretation of how protein molecules behave.

However, solving this problem can help us incrementally solve lower-order abstractions of the protein folding problem, and who knows? Lead us to finally solve how proteins behave in a molecular level.

## Protein Folding as an RL Problem

We’ve seen RL being used successfully in games (Mnih, Silver, et al., 2013). Perhaps, formulating protein folding as a sequence of states, actions, and rewards like a game opens up the possibility of solving this via reinforcement learning. First, I will discuss what a typical RL framework looks like, then, we’ll start formulating the protein folding problem as an RL problem.

### A typical reinforcement learning problem

Most reinforcement learning problems are formulated as the following (Sutton and Barto, 1998):

• We have an agent ($\mathcal{A}$) that decides an action $a$ given an observation $o$ and reward $r$. Sometimes, the agent’s policy (how it acts given an observation and reward) is parameterized by $\theta$. It could be a neural network with weights $\theta$.
• This action goes into the environment ($\mathcal{E}$) that takes the agent’s action, determines the equivalent reward $r$, and updates its state $s$.
• The next state $s_{t+1}$ and reward $r_{t+1}$ is then transferred back to the agent for deciding the next action. Just a note: sometimes we have partially-observed cases where $s_{t+1} \neq o_{t+1}$. Imagine the fog-of-war in DoTA where you cannot see beyond your visibility range. Ours is fully-observed where $s_{t+1} = o_{t+1}$ (like chess, you can see the position of all pieces.)

The goal ($\mathcal{G}$) then is to maximize the expected reward for all timesteps. For a more thorough discussion of RL, please check Sutton’s book that I referenced below. For a more leisurely yet informative read, check out this great post from Thomas Simonini.

### Reinforcement Learning + Protein Folding

Now that we have a rough idea of how reinforcement learning works, we can then combine our knowledge of the protein folding game to create our framework:

• Our agent ($\mathcal{A}$) takes the current state of the lattice plus the reward, and depending on its policy, outputs an action $a \in \{L,D,U,R\}$ to place the next molecule.
• The environment ($\mathcal{E}$) takes this action and updates the lattice by placing the next molecule on the location decided upon by the agent. Afterwards, it computes the number of adjacent H-H pairs that are not consecutive inside the sequence. More formally:
• The agent takes this next state and reward (energy function) and again decides where to put the next molecule until all molecules have been placed. An episode ends when the whole sequence has been exhausted or when the agent was trapped.

For RL practitioners, it is obvious that the sign of the reward is a bit funky. Negative rewards often mean penalties. We wil still modify this reward function as you will see in the gym-lattice environment.

## The Gym-Lattice Environment

My project aims to provide an environment ($\mathcal{E}$) that simulates the protein folding problem for training RL agents. It follows a similar API with OpenAI-Gym, and is built from primitives found in the Gym library. This means that the common step(), reset(), and render() methods are available. You can find the Github link here and a good Reddit discussion of the project here.

• In gym-lattice, the state $s$ is represented as a 2D-matrix $S \in \{-1,0,+1\}^{2}$. The observation-space is defined as Box(high=1, low=-1, shape=(2*n+1,2*n+1), dtype=int)
• +1 represents hydrophobic (H) molecules
• -1 represents polar (P) molecules; and
• 0 represents unassigned spaces in the grid.
• Your agent can perform four possible actions: 0 (left), 1 (down), 2 (up), and 3 (right). The number choices may seem funky at first but just remember that it maps to the standard vim keybindings.
• An episode ends when all molecules are added to the lattice OR if the sequence of actions traps the polymer chain (no more valid moves because surrounding space is fully-occupied). Whenever a collision is detected, the agent should enter another action.

### Small note about the reward function

The reward function $r$ has been modified. For every timestep, it gives sparse rewards $r_{t}=0$. The energy function is only computed at the end of the episode (when all molecules are placed). Whenever the agent collides at a specific timestep, a collision penalty is computed. Overall, the reward at t $r_{t}$ is computed in the following manner:

# Reward at timestep t
reward_t = state_reward + collision_penalty + trap_penalty

• The state_reward is the number of adjacent H-H molecules in the final state. In protein folding, the state_reward is synonymous to computing the Gibbs free energy, i.e., thermodynamic assumption of a stable molecule. Its value is 0 in all timesteps and is only computed at the end of the episode.
• The collision_penalty at timestep t accounts for collision events whenever the agent chooses to put a molecule at an already-occupied space. Its default value is -2, but this can be adjusted by setting the collision_penalty at initialization.
• The trap_penalty is only computed whenever the agent has no more moves left and is unable to finish the task. The episode ends, thus computing the state_reward, but subtracts a deduction dependent on the length of the actual sequence.

### Basic Usage

It’s very simple to use gym-lattice. Once you have your agent ready, just call the step(action) function to input your action. Remember that at the beginning of each episode, you must reset your environment. Below is a basic skeleton of how to use this package:

from gym_lattice.envs import Lattice2DEnv
from gym import spaces
import numpy as np

np.random.seed(42)

seq = 'HHPHH' # Our input sequence
action_space = spaces.Discrete(4) # Choose among [0, 1, 2 ,3]
env = Lattice2DEnv(seq)

for i_episodes in range(5):
env.reset()
while True:
# Random agent samples from action space
action = action_space.sample()
obs, reward, done, info = env.step(action)
env.render()
if done:
print("Episode finished! Reward: {} | Collisions: {} | Actions: {}".format(reward, info['collisions'], info['actions']))
break

Of course, at each step, you can call render() to see what the lattice looks like in your console:

### Last Notes

I haven’t trained an agent yet to solve this problem, but one idea I have in mind is by using a Deep Q-Network with a convolutional layer to take-in the grid, and is connected to a Fully-Connected Network to output an action. I’ve been very busy with thesis lately so we’ll see what happens in the future.


text:
Задание#T5474

Прочитайте текст и заполните пропуски A–F частями предложений, обозначенными цифрами $1–7$. Одна из частей в списке $1–7$ лишняя.

The Man Who Loved the Sea

Jacques Cousteau was born in France in 1910. Although he was sickly as a child, he learned to swim at an early age and developed a love for the ocean. He joined the French navy in 1933, and it was there A________. Amazed at what he saw beneath the sea, he decided to build a device that would allow people to breathe underwater. In 1942, he finished the Aqua-Lung, a piece of early underwater breathing equipment B________.

After World War II, Cousteau began his life’s work onboard the research ship Calypso. He worked with divers and scientists to photograph and gather samples of underwater plants and animals. In doing so, he learned about many ocean creatures C________.

In 1960, he successfully worked to stop nuclear waste D________. He worked tirelessly E________ and won many awards for his efforts. His television show, The Undersea World of Jacques Cousteau, ran from 1968 to 1976. The series helped raise awareness of the creatures who inhabit the world’s oceans. Cousteau died in 1997 at the age of 87 and is still celebrated F________ of the twentieth century.
Показать полностью
1. from being dumped into the Mediterranean Sea
2. that would eventually lead to the SCUBA diving gear
3. as one of the most important explorers and environmentalists
4. even though he became interested in exploring the ocean
5. that he first used a pair of underwater goggles
6. to improve the ecological conditions of the world’s oceans
7. that had never been studied before
Запишите в поле для ответа последовательность цифр, соответствующих частям ABCDEF.
Показать разбор и ответ
Это задание составили эксперты «СтатГрада» для Яндекса
517 попыток решения17% решили верно

Задание 11. Чтение

Теория

Яндекс.Репетитор пришёл на смену сервису Яндекс.ЕГЭ, и мы активно собираем отзывы пользователей. Пожалуйста, пишите нам через форму обратной связи.


text:
# How can I get identifier style to apply to '%' (in a Perl listing)?

When using Perl variable names with sigils with listings, the $ and @ sigils somehow get coloured in identifierstyle, but the % sigil remains unstyled. Therefore, this code: \documentclass{article} \usepackage{listings,xcolor} \lstdefinestyle{perl}{ language=Perl, basicstyle=\ttfamily, keywordstyle=\bfseries\color{green!40!black}, commentstyle=\color{purple!40!black}, identifierstyle=\color{blue}, stringstyle=\color{orange}, } \lstset{style=perl} \begin{document} \begin{lstlisting} my ($a, $b,$c) = ('a'..'z');
my ($a,$b, @c) = ('a'..'z');
my ($a,$b, %c) = ('a'..'z');
\end{lstlisting}
\end{document}

gives this result:

Is there a way I could make listings understand that % should have the same style as $ or @? The manual is pretty clear about keywords and comments, but it didn't help me understand the difference between an identifier and an operator (?) that doesn't get styled. Looking at the Perl language definition in lstlang1.sty didn't help either since there is nothing there about either $ and @ or %.

-
Please make your code compilable, starting with \documentclass{...} and ending with \end{document}. That may seem tedious to you, but think of the extra work it represents for TeX.SX users willing to help you. Help them help you: remove that one hurdle between you and a solution to your problem. – Jubobs Nov 6 '13 at 14:00
@Jubobs: thank you, I have done as you suggest. – scozy Nov 6 '13 at 15:12

By default, identifiers cannot start by %. You can allow identifiers to start by % by specifying alsoletter={\%} in the definition of your custom perl style.

Look up the alsoletter key in subsection 4.18 of the listings manual:

All identifiers (keywords, directives, and such) consist of a letter followed by alpha-numeric characters (letters and digits). For example, if you write keywords={one-two,\#include}, the minus sign must become a digit and the sharp a letter since the keywords can’t be detected otherwise.

According to Table 2, % is (by default) treated, not as a "letter", but as "other". The Perl style (which is defined in lstdrvrs.dtx, a file that ships with listings.sty) doesn't change that.

Therefore, in order to allow identifiers to begin by %, you must specify alsoletter={\%}. Note that % must be escaped, here; see item 5 in subsection 4.1 for more details.

\documentclass{article}

\usepackage{listings,xcolor}

\lstdefinestyle{perl}
{
language=Perl,
basicstyle=\ttfamily,
keywordstyle=\bfseries\color{green!40!black},
identifierstyle=\color{blue},
stringstyle=\color{orange},
alsoletter={\%},
}

\lstset{style=perl}

\begin{document}
\begin{lstlisting}
my ($a,$b, $c) = ('a'..'z'); my ($a, $b, @c) = ('a'..'z'); my ($a, \$b, %c) = ('a'..'z');
\end{lstlisting}
\end{document}

-


text:
Suggested problems

Nov. 4, 2022, 9:30 a.m. by norxhealthcare

Biological Motivation

-------------- : https://norxhealthcare.com/product-category/buy-adderall-online/ ADHD is a medical condition that affects how well someone can focus, pay attention, and control impulsive behaviors. People with ADHD may have trouble paying attention to details or may be easily distracted. They may also act impulsively without thinking about what they are doing.

Most people with ADHD have problems with more than one of these areas. ADHD can make it hard for people to do well in school, at work, or in social situations. It can also lead to problems with relationships.

Problem

A string is simply an ordered collection of symbols selected from some alphabet and formed into a word; the length of a string is the number of symbols that it contains.

An example of an DNA string (whose alphabet contains the symbols A, C, G, and T) is ATGCTTCAGAAAGGTCTTACG.

Given: A DNA string $s$ of length at most 1000 nucleotides.

Return: Four integers corresponding to the number of times that the symbols A, C, G, and T occur in $s$.

Sample Dataset

AGCTTTTCATTCTGACTGCAACGGGCAATATGTCTCTGTGTGGATTAAAAAAAGAGTGTCTGATAGCAGC

Sample Output

20 12 17 21


text:
# representative matrix of a linear transformation

I am trying to solve this two questions:

1. given a linear transformation: $T:M_n(\mathbb{C}) \rightarrow M_n(\mathbb{C})$, $T(A)=A-2A^T$, what is the representative matrix on this transformation with the standart base.

2. Let $T: \mathbb{F}^2 \rightarrow \mathbb{F}^2$ a linear tranformation such that $T^2=0$, Prove that $T=0$, or there exists a basis of $M_2(\mathbb{F})$ in which the representative matrix is: $\begin{bmatrix}0 & 1 \\ 0 & 0\end{bmatrix}$.

Thank you.

For your second question assume that $T\ne0$ then there's $u\in\Bbb F^2$ such that $T(u)=v\ne0$. Prove that $\mathcal B=(v,u)$ is a basis of $\Bbb F^2$ and the matrix of $T$ in this basis has the desired form.


text:
# Quick! Escape the black hole!

It is the year 87,539,319 and solitary space-walking is now commonplace, many people travel into space by themselves, propelled by nothing but a jetpack on their backs, programming their course with a personal computer and keyboard as they go.

You are one such person; you were out on a lovely, peaceful spacewalk, when, all of a sudden, you were ensnared by the gravity of a black hole!

As you plummet towards this black hole, spiraling ever faster inwards, you realise your one chance of survival is to broadcast a distress message, and hope a nearby ship comes to rescue you.

So, you break out your keyboard, and begin typing away a program.

Your program can be in any language, and must print HELP! to stdout (your PC broadcasts all stdout far into the depths of space.)

However, as you are near a blackhole, your keyboard is slowly being ripped to shreds!

Assume you are using a QWERTY keyboard like the one below, and that the blackhole is to your left;

Remember, left and right shift are two different keys.

after every keypress, the left-most row of your keyboard (keys covered by left-most red line) is ripped off and flung into the black hole!

So, your first keypress could be any key on the keyboard, but from then onwards none of the leftmost Tab, Caps, Shift, Ctrl or  keys may be used, at all. (r-shift and r-ctrl can still be used)

After the next keypress, the keys 1, Q, A,Z and Alt are flung into the abyss, and may not be used thereafter. After that, you lose Space, X, S, W, 2 and so forth.

Obviously, you want to complete your program as quickly as possible, so that rescue-time is increased; therefore, this is code-golf, and the shortest program in key presses wins!

!HELP\.

a keylist could look like:

Shift!HELP release shift \.

length: 8

I'm worried this challenge might be too difficult, but I'd love to see the kinds of answers submitted!

• I'm downvoting this because it feels too constrained to have much creativity. – isaacg Apr 23 '15 at 17:44
• Can we assume that using the python shell without print qualifies as STDOUT? – user80551 Apr 23 '15 at 20:02
• What if my keyboard has a number pad? – mbomb007 Apr 23 '15 at 20:24
• This could be slightly better with arrow keys. – user80551 Apr 23 '15 at 20:27
• Is caps lock still effective if it's been pressed although the key has disappeared? – jscs Apr 23 '15 at 21:26

# CJam, 11 keystrokes

The code is

"HELP*")9-

and the keylist is

Shift"HELP*") release shift 9-

and here is a demonstration of how it looks:

and here is how the code works:

"HELP*"              "This puts the string HELP* on stack";
)             "This takes out the last character of the string and puts it
on the stack as a character";
9-           "This simply reduces 9 from the ASCII code of * character
present on the stack which makes it an !";
"CJam automatically prints everything that is on stack";

Try the code here

• Using the asterisk was pretty clever! I'd never thought of that. – theonlygusti Apr 23 '15 at 18:37
• Well, I was unable to do this in GolfScript. It's a little too long. Converting from an integer to ascii is inefficient. "HELP*")9-[]+''+. I can't type the last four. – mbomb007 Apr 23 '15 at 21:23
• I just knew CJam would have an answer... – Jerry Jeremiah Apr 23 '15 at 23:25
• So one of the most future-proof languages in the world is apparently CJam. – Fors Apr 24 '15 at 12:41
• Watch your finger when you hit the E, it looks like it might get taken into the abyss! – Canadian Luke Apr 24 '15 at 17:30

# rs, 10 keystrokes (assumes the user is using Nano)

Or equivalent editor where Shift doesn't select text.

This isn't really a programming language, but if sed can be used on Code Golf, then rs can be used.

Right Shift ! Left E Left H Right L P Enter

HELP!

It just replaces the empty string with "HELP!", effectively printing it to the screen. Roughly equivalent to the sed script:

s/^/HELP!/

The cool part is that rs automatically puts ^/ in front of a replacement pattern where the delimiter (/) is not found. Handy for indenting code.

• You forget that Enter` is a stroke, too. 10 strokes. – vapcguy Apr 27 '15 at 20:26
• @vapcguy Right. Fixed. – kirbyfan64sos Apr 27 '15 at 20:31


text:
Is the Heisenberg-picture commutator $[x(t),p(t)]$ between position and momentum always equal to $i\hbar$?

Some misconceptions over here, For $$x=$$position and $$p=$$ momentum,

I know $$[x,p]=i\hbar$$ but does $$[x(t),p(t)]$$ still have the same relation where $$t$$ here represents time.

$$[\hat{x}(t),\hat{p}(t)] = [\hat{x}_0,\hat{p}_0] = i\hbar$$

This is easily proven as follows. We have the unitary time evolution operator given by $$\hat{T}(t)$$. Unitary means $$\hat{T}(t)\hat{T}^{\dagger}(t) = \hat{T}^{\dagger}(t)\hat{T}(t) = \hat{I}$$ where $$\hat{I}$$ is the identity operator.

Let $$A_0$$ and $$B_0$$ be arbitrary operators with $$[A_0,B_0]=C_0$$.

In the Heisenberg picture we have

\begin{align} \hat{A}(t) &= \hat{T}^{\dagger}(t)\hat{A}_0\hat{T}(t)\\ \hat{B}(t) &= \hat{T}^{\dagger}(t)\hat{B}_0\hat{T}(t)\\ \hat{C}(t) &= \hat{T}^{\dagger}(t)\hat{C}_0\hat{T}(t)\\ \end{align}

So

\begin{align} [\hat{A}(t),\hat{B}(t)] &= \hat{A}(t)\hat{B}(t) - \hat{B}(t)\hat{A}(t)\\ &= \hat{T}^{\dagger}(t)\hat{A}_0\hat{T}(t)\hat{T}^{\dagger}(t)\hat{B}_0\hat{T}(t) - \hat{T}^{\dagger}(t)\hat{B}_0\hat{T}(t)\hat{T}^{\dagger}(t)\hat{A}_0\hat{T}(t)\\ &= \hat{T}^{\dagger}(t)[\hat{A}_0,\hat{B}_0]\hat{T}(t) = \hat{T}^{\dagger}(t)C_0\hat{T}(t)\\ &=C(t) \end{align}

So we see that commutation relations are preserved by the transformation into the Heisenberg picture. Actually, we see that commutation relations are preserved by any unitary transformation which is implemented by conjugating the operators by a unitary operator.

Note that unequal time commutation relations may vary. For example, if we have a Harmonic oscillator Hamiltonian

$$\hat{H}_0 = \frac{1}{2}m\omega^2 \hat{x}^2 + \frac{1}{2m} \hat{p}^2$$

We can derive and solve the Heisenberg equations of motion. Upon doing this we will get the usual classical equations of motion but with hats.

\begin{align} \hat{x}(t) = \hat{x}_0 \cos(\omega t) + \hat{p}_0 \sin(\omega t)\\ \hat{p}(t) = \hat{p}_0 \cos(\omega t) - \hat{x}_0 \sin(\omega t) \end{align}

Consider $$\hat{x}(0) = \hat{x}_0$$ and $$\hat{x}(\frac{\pi}{2}\frac{1}{\omega}) = \hat{p}_0$$.

\begin{align} \left[\hat{x}(0),\hat{x}\left(\frac{\pi}{2}\frac{1}{\omega}\right)\right] = [\hat{x}_0,\hat{p}_0] = i\hbar \end{align}

So we see that the commutator of $$\hat{x}$$ with itself at different times can be non-zero.

As always $$\vec p = - i\hbar \vec \nabla$$ this is always true in Schrödinger quantum mechanics.

$$[x,p] =i \hbar$$

Inherently mean only for equal time. That's why these type of commutation relations sometimes ,for better care, also called as equal-time commutation relation. If we calculate at unequal time, this relation will not hold instead in that case $$x$$ and $$p$$ will commute.

Physically this means that you can not simulteneously know the position and momentum of a particle. More and more accurate knowledge of x means less and less knowledge of momentum or vice a versa. But if you want to know $$x$$ at one time and $$p$$ at other different time you can know at any degree of accuracy.

• "If we calculate at unequal time, this relation will not hold instead in that case x and p will commute." <--This is not true. They COULD commute but generally do NOT. – Jahan Claes Oct 2 '18 at 4:11
• @Jahan please check, I'm totally sure about it. or if you still believe what you commented above, please give the source. – Aman pawar Oct 2 '18 at 4:44
• So you are saying $[x(t),p(t')]=\delta_{t,t'}i\hbar$? – BioPhysicist Oct 3 '18 at 2:54
• Jahan's observation here is completely right. There is an explicit example in the other answer which you can use to check. – Emilio Pisanty Oct 3 '18 at 6:39


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# What is the image of (5,-1) under same translation?

###### Question:

What is the image of (5,-1) under same translation?

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## Jan ŠarochOn the nontrivial solvability of systems of~homogeneous linear equations over $\mathbb Z$ in ZFC

Comment.Math.Univ.Carolin. 61,2 (2020) 155-164.

Abstract:Motivated by the paper by H.\ Herrlich, E.\ Tachtsis (2017) we investigate in ZFC the following compactness question: for which uncountable cardinals~$\kappa$, an arbitrary nonempty system $S$ of homogeneous $\mathbb Z$-linear equations is nontrivially solvable in $\mathbb Z$ provided that each of its subsystems of cardinality less than $\kappa$ is nontrivially solvable in $\mathbb Z$?

Keywords: homogeneous $\mathbb Z$-linear equation; $\kappa$-free group; $\mathcal L_{\omega_1\omega}$-compact cardinal

DOI: DOI 10.14712/1213-7243.2020.017
AMS Subject Classification: 08A45 13C10 20K30 03E35 03E55

PDF


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The key observation to make is that the magnitude of the cross-product of two 3D vectors is equal to the area of the parallelogram spanned by them, since where is the angle between the two vectors v and w. Use the language of calculus to discuss motion. 3D Graphing Calculator. (Example: f 1 (t,s)=5 and f 2 (t,s)=3/sin t) Up to 3 functions can be graphed simultaneously To remove a function from the graph, click (to its "off" state) the check box next to the associated text input field and click the "Graph" button to refresh. Nx matrix is a 2D array that specifies the length of the x vector in relation to the z-plane. Angle Between Two 3D Vectors Below are given the definition of the dot product (1), the dot product in terms of the components (2) and the angle between the vectors (3) which will be used below to solve questions related to finding angles between two vectors. com To create your new password, just click the link in the email we sent you. 3D Grapher - David Lippman. The 3D vectors are using the x-y-z axes. - [Voiceover] So in the last video, I talked about vector fields in the context of two dimensions, and here, I'd like to do the same but for three-dimensions. Given vector v_1 = (8, -4), calculate the the magnitude. Matlab remem b ers that the v ector x is already de ned. The 3D grapher can graph 3D functions, parametric curves (spacecurves), parametric surfaces, implicitly defined surfaces, implicit spherical surfaces, implicit cylindrical surfaces, 3D vector fields. Academo features an easy to use 3D graphing calculator software tool. Use the middle mouse key to redisplay. y vector is a 1D array that specifies the y-coordinates that graph the plot. Matlab remem b ers that the v ector x is already de ned. com is a leading digital marketplace for high quality and ready-to-use logo templates at an affordable price. This is a special case of the point-direction form (x - x1)/a = (y - y1)/b = (z - z1)/c This equation is best described in terms of vectors. Ask Question Asked 8 years, data and histograms in 3D, and saving outputs in vector-graphics formats. Plotting Points And Vectors In 3d With Geogebra. Click below to download the free player from the Macromedia site. If you like to plot one or two functions then leave the rest of the function boxes empty. Object whose content is copied to the added elements in case that n is greater than the current container size. You can check out item reviews left by other users, and use collections to. The tool just worked how people expected it to work. When plotting in 3D we need evenly spaced x- and y-values, spaced on a grid where each function value z is taken of a point (x, y) on the grid. This calculator performs all vector operations. Use plot3d to graph a function of the form f(x,y) = z: sage: x, y = var('x,y') sage: plot3d(x^2. Free 3d Plotter Online vector download in AI, SVG, EPS and CDR. For more information about specifying colors, see SAS/GRAPH Colors and Images in the SAS/GRAPH: Reference, Second Edition. svg) Click to share this graph on your favourite social network:. ii-doc/changelog. Enter your x and y ranges in the range boxes. Here’s the program: Graph 3D v4. A vector graph is a multidimensional graph used in industries such as meteorology, aviation, and construction that illustrates flow patterns (e. Plots are displayed in 2D or 3D. Download Business 3D graph vector material 01 in EPS format. The equation of the plane can be rewritten with the unit vector and the point on the plane in order to show the distance D is the constant term of the equation;. Vector chart with 3d rectangles in different colors. The hodograph is surprising: it's just a circle, but the center of the circle is not v =0. Wolfram Demonstrations Project 12,000+ Open Interactive Demonstrations. Viewing options of the 3D graphing calculator software tool are pretty basic, but sufficient – The plot can be. They are mostly standard functions written as you might expect. Geodesics on the Earth. Vector image at 300% Download 10 FREE images now with a risk-free trial. (Example: f 1 (t,s)=5 and f 2 (t,s)=3/sin t) Up to 3 functions can be graphed simultaneously To remove a function from the graph, click (to its "off" state) the check box next to the associated text input field and click the "Graph" button to refresh. Polar: Rose example. Like I would like to have arctan(a) I've looked at the Wolfram Alpha documentation and haven't been able to find a way to do this. It is a well known DOS based graphing software and a bit complex to use. To the left zooms in. com To create your new password, just click the link in the email we sent you. VectorPlot3D omits any vectors for which the v i etc. This tutorial will show you how to install and use three applications to add 3D graphing, symbolic differentiation, simplifying equations, and pretty-print to your TI-83+ or TI-84+. Vector Field 3d Geogebra. Look below to see them all. Plot Three-Dimensional Vector Function. 8 or greater DESCRIPTION: The draw_surface proc generates sample points on a parametric surface defined by three two-variable functions 'f', 'g', and 'h'. Dia is a cross platform diagramming utility which can export eps images, or generate tex drawn using the tikz package. The Graphical Web 2016 will be held in Exeter, United Kingdom, USA, on 1-4 November 2016, and. Download Flash Player. The equation of the plane can be rewritten with the unit vector and the point on the plane in order to show the distance D is the constant term of the equation;. 5D and 3D function graphs. You clicked a link that corresponds to this MATLAB command:. 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The TI-89 series of calculators is packed with features that, unfortunately, are lacking in the TI-83+ and TI-84+. Hi! I would like to graph the following: (x,y,z) = (1,2,3) + t(3,2,1) (1,2,3) = position vector (3,2,1) = direction vector. 1 Color 3D Grapher - Cemetech This program was originally designed for the TI-84 Plus C Silver Edition, but will work on the TI-84 Plus CE as well. Introduce the x, y and z values of the equations and the parameter in t. Contacting the author of this tutorial. The length of a vector represented by a three-component matrix is:. These points will be highlighted and the corresponding observations in every other graph window will also turn red. Scalar Product of Vectors. Calculus Grapher Project: A link to a math student's java calculus calculator. Explore vectors in 1D or 2D, and discover how vectors add together. However, this area is also equal to the magnitude of the base times the height of the parallelogram,. Chaco is easy to embed in python GUI applications (wxWindows, Qt) and provides nice abstractions for overlays and tools (select. Points in the direction of greatest increase of a function ( intuition on why) Is zero at a local maximum or local minimum (because there is no single direction of increase) The term "gradient" is typically used for. INPUT: functions - a list of three functions, representing the x-, y-, and z-coordinates of a vector. The source code is copyrighted but freely distributed (i. , you don't have to pay for it). Master the key principles of statistics with GraphPad's hugely popular educational guides and resources. •calculate the length of a position vector, and the angle between a position vector and a coordinate axis; •write down a unit vector in the same direction as a given position vector; •express a vector between two points in terms of the coordinate unit vectors. The demo above allows you to enter up to three vectors in the form (x,y,z). Scalable Vector Graphics (. It lets you plot 2D as well as 3D graphs through expressions, equations, and functions. Graph maker to create 2D, 2. Common vector image file extensions include. Help Link to this graph. We see that a necessary and su¢ cient condition for the point Pto be on the line Lis that! P 0Pbe parallel to!v. Because some functions used in VectorColorFunction are common, the Wolfram Language allows you to call them as variables. As time goes on, more and more Illustrator techniques are introduced by talented designers and artists in the industry who achieve some of the best results on the Web. If you like what I'm doing, support me on Patreon! The documents generated here are considered to be in the Public Domain. Vector Math for 3D Computer Graphics Fourth Revision, July 2009 This is a tutorial on vector algebra and matrix algebra from the viewpoint of computer graphics. These are represented by integers ranging from 1 to 5, where 1 is the variable, 2 is the variable, 3 is the first field component, 4 is the second field component, and 5 is the vector magnitude. 4,000+ Vectors, Stock Photos & PSD files. A vector graph is a multidimensional graph used in industries such as meteorology, aviation, and construction that illustrates flow patterns (e. Some people deem PLplot is a replacement of the traditional gnuplot in Octave. Click below to download the free player from the Macromedia site. Wolfram|Alpha can now plot vectors with this arrow representation in 2D and 3D and return many other properties of the vector. Download this free picture about Laptop 3D Line Graph from Pixabay's vast library of public domain images and videos. Dia is a cross platform diagramming utility which can export eps images, or generate tex drawn using the tikz package. It can run natively under Windows, Linux or Mac OS X (with X11). In "amazon" are sold the two books on GDI+: Symmonds N. Trusted by 20M+ businesses, our online logo maker makes it easy to find the best logo for your business. The calculator will find the angle (in radians and degrees) between the two vectors, and will show the work. Vector drawing is a complicated and yet interesting way to draw graphics. Connect with Neo4j in a City Near You. If a graph uses more than one graph type, you may want one set of data along the right axis and the other set of data along the left axis. If stepis not a multiple of the difference upper-lower, the last element of X, X(end), will be less than upper. Help Link to this graph. Graphing Vector Calculator - Paul Flavin An interactive Java applet which, given two vectors, will add or subtract. Radial Bar Chart Illustrator. Find answers to I am making a graph for 3d vector help from the expert community at Experts Exchange. The vector $\vc{a}$ is drawn as a green arrow with tail fixed at the origin. Use the language of calculus to discuss motion. 1) Using templates. Recommended for you. Matlab remem b ers that the v ector x is already de ned. The vector OP has initial point at the origin O (0, 0, 0) and terminal point at P (2, 4, 5). This article is about GeoGebra command. Colors are global, so they can be modified easily. Graphs in 3D Entering equations and viewing surfaces Some View Menu Options. com and is distributed under our Standard License Find 96451 more Stock Profit Graph with Map and 3D Figures Premium Vectors for as low as 0,21 € per download at Shutterstock. In ArcMap, click the layer drop-down arrow on the 3D Analyst toolbar and click the surface that you want to profile. Vector Magnitude Calculator to find the resulting magnitude of 2D and 3D vectors. April 20-22, 2020 | New York. Go to a Mac that’s not too old and find Grapher under the Applications -> Utilities Folder. x vector is a 1D array that specifies the x-coordinates that graph the plot. Download 12,919 3d graph free vectors. •calculate the length of a position vector, and the angle between a position vector and a coordinate axis; •write down a unit vector in the same direction as a given position vector; •express a vector between two points in terms of the coordinate unit vectors. Vector Field 3d Geogebra. Vector Equation Of A Plane 3d Geogebra. The magnitude or length of a 2D or 3D vector is denoted by |A|. You can define vectors as (X, Y, Z) for example (-1, 3, 5) assuming that the vector begins at point (0, 0, 0). Download 12,919 3d graph free vectors. On the other hand, the components are modified when the coordinate axes are rotated. For a much more sophisticated phase plane plotter, see the MATLAB plotter written by John C. For example, the structure of the vector field $\dlvf = (-y, xy,z)$ is harder to see from the graph. Since im not that sure about my 3D case when i look onto the attached picture it seems for the line given by x=0,y=0,z there are no "red vectors" for example which point into the center. The Euclidean plane has two perpendicular coordinate axes: the x-axis and the y-axis. Entering Asymptote code directly into the LaTeX source file, at the point where it is needed, keeps figures organized and avoids the need to invent new file names for each figure. TeraPlot scientific plotting software gives you everything you need for publication quality graph plotting in science and engineering. Permanent link to this graph page. Change the Scale to provide a better visualisation of the vector field. Graph Points in 3D Using 3D Calc Plotter Graph 3D Vectors Using 3D Calc Plotter Graph Tangent Planes to Surfaces Using 3D Calc Plotter Graph a Function of Two Variable Using 3D Calc Plotter Graph a Contour Plots (Level Curves) Using 3D Calc Plotter. 3D Vector Plotter. INPUT: functions - a list of three functions, representing the x-, y-, and z-coordinates of a vector; xrange, yrange, and zrange - three tuples of the form (var, start, stop), giving the variables and. SigmaPlot Graphing Features. 4,000+ Vectors, Stock Photos & PSD files. There are a two different ways to calculate the resultant vector. Vector EPS 10 - PD0REM from Alamy's library of millions of high resolution stock photos, illustrations and vectors. 6: The tangent, normal, and binormal vectors define an orthogonal coordinate system along a space curve In Sects. To see an interactive demonstration showing several ways to visualize x- and y-components of a vector see the Components of a Vector page. use the scene graph of the Virtual Rendering System (VRS) [3]. md /usr/share/doc/libdeal. This VI can be found by right clicking on the front panel then following the tabs, Classic->Graph->ActiveX 3d Curve Graph. Calculus Grapher Project: A link to a math student's java calculus calculator. js and stack. Download 13,070 3d graph free vectors. Enter values into Magnitude and Angle or X and Y. Create Accountor + New Blank Graph. Shorthand for writing Vector2 (0, 0). In this page you can find 39+ 3d Vector Grapher images for free download. High-quality graphic assets are guaranteed on GraphicRiver. Here’s the program: Graph 3D v4. This paper is used by many people for creating perspective drawings of buildings, product boxes and more. Graph Space Curves Given As A Vector Function Using 3d Calc Plotter. I am new to raster data. A stream particle animation is useful for visualizing the flow direction and speed of a vector field. Turing Award for their respective fundamental contributions to 3D computer graphics and the revolutionary impact of these techniques on […]. Download Coreldraw Vector (. Vector image "Vector 3d bar graph" can be used for personal and commercial purposes according to the conditions of the purchased Royalty-free license. Quick Graph is a calculator app that's dedicated to graphing. Least Squares Regression Line. Its graph, however, is the set of points $(t,3\cos t, 2\sin t)$, which forms a spiral. graph,material Vector Business and more resources at freedesignfile. Online Graphing Calculator: Provides a simple online graphing calculator. It is a scalar and must be non-negative. Ask Question Asked 8 years, data and histograms in 3D, and saving outputs in vector-graphics formats. Apr 24, 2020 - Skill level: Easy Requires 2 colors. - [Voiceover] So in the last video, I talked about vector fields in the context of two dimensions, and here, I'd like to do the same but for three-dimensions. Any vector whose length 1 is called a unit vector; unit vectors will usually be denoted by e. They can be used, shared, and republished without need of permission. Calc 3D is a free program for calculating 3-dimensional vectors, matrices and complex numbers with Windows 95/98/NT. plot_field3d. Siemens Digital Industries Software. (Pat) Hanrahan had jointly received the 2019 ACM A. Chaco is easy to embed in python GUI applications (wxWindows, Qt) and provides nice abstractions for overlays and tools (select. The focus of this study is the classical task of building pattern classification, which remains limited by the use of design rules and manually extracted features for specific patterns. In multivariable calculus, we will need to get accustomed to working in three dimensional space, or R 3. VectorPlot3D by default shows vectors from the vector field at a specified grid of 3D positions. On the graph, u is the unit vector (in black) pointing in the same direction as vector OA, and i, j, and k (the unit vectors in the x-, y- and z- directions respectively) are marked in green. In two dimensions, Sage can draw circles, lines, and polygons; plots of functions in rectangular coordinates; and also polar plots, contour plots and vector field plots. plot_field3d. Processing • ) - - - - - - - - - - - -. iTune Icon Replicating the iTune icon by using various blend techniques. Grapher offers high-quality graphing tools so you can get the most out of your data. Conic Sections: Parabola and Focus example. Sample Learning Goals. After our first implementation of vector networks, we did a series of user studies to refine the concept. The number of mesh in the X- and Y-directions can be specified by set dgrid3d x-mesh, y-mash. 322 free vectors graphics. pdf files and print your own isometric graph paper - also known as "3D drawing paper. Since vector graphics store image data as paths, they can be enlarged without losing quality, which makes them a good choice for logos and other types of drawings. Added Nov 22, 2014 by sam. 2: Quiver (vector) plot superimposed. This means that any 3D vector a from (0,0,0) to (x, y, z) can be written as a linear combination of i, j, and k like so: a = xi + yj + zk To get used to visualizing 3D vectors try testing out this applet. Physics 215 - Experiment 2 Vector Addition 3 with force 3 (then force 2 and then force 1) The resultant is drawn from the origin to the tip of the last force drawn. png) Scalable Vector Graphics (. ii-doc/changelog. Scalable Vector Graphics (. To zoom, use the zoom slider. - [Voiceover] So in the last video, I talked about vector fields in the context of two dimensions, and here, I'd like to do the same but for three-dimensions. 9 Graphically show the result of multiplying a vector by a negative scalar. The vector we will use in the following discussion is a force vector. In the example, we represent the pipeline by a vector-data scene graph that consists of a 2D line, attributed by a red color, and two 2D points, attributed by a blue color. So, we've gathered together some **3D tutorials** to give you an. it has simple plotting functions and nice 3D graphing as well. Download 13,070 3d graph free vectors. A vector-valued function $\dlvf:\R^2 \rightarrow \R^2$ can be visualized as a vector field. Graphing Lines In 3d With Geogebra. Create printable equations for school tests and reports with this program. Graphing Calculator 3D is a powerful software for visualizing math equations and scatter points. Enter a mathematical expression using the variables x and y. Logo Maker is the #1 logo design company worldwide. A vector graph is a multidimensional graph used in industries such as meteorology, aviation, and construction that illustrates flow patterns (e. Plots Vector Surface Plots Scalar 3D Line Plots Vector 3D Line Plots Scalar 2D Line Plots Scalar Point. , you don't have to pay for it). If you’re unfamiliar with the process of creating graphs in Adobe Illustrator. Plotting Points and Planes4. Download 12,919 3d graph free vectors. Join 100 million happy users! Sign Up free of charge:. Advanced Scientific Library. org for more infoget. The vector plots themselves are based on the vanilla ActiveX 3d Curve Graph. Creates a vector from Start Point to End Point. 3D Vector Plotter. js ships with over 40 chart types, including 3D charts, statistical graphs, and SVG maps. When we talk about combining rotation matrices, be sure you do not include the last column of the transform matrix which includes the translation information. A vertical guideline has been added to assist with these drawings. Just copy and paste the below code to your webpage where you want to display this calculator. Draw a graph of any function and see graphs of its derivative and integral. The velocity vector is, of course, changing as the position vector is changing. The gradient is a fancy word for derivative, or the rate of change of a function. The Official Website of RINEARN Graph 3D. The source code is copyrighted but freely distributed (i. Experiment with vector equations and compare vector sums and differences. Chaco is easy to embed in python GUI applications (wxWindows, Qt) and provides nice abstractions for overlays and tools (select. Window: Set the viewing window yourself, or have it adjust to the solution curves. The data elements must be of the same basic type. BUSINESS 3D GRAPH. Plotting Phase Space Trajectories of Differential Equations Plotting the direction field of a vector fields in 2D Generating Phase Space Trajectories for Second Order Differential Equations. This VI can be found by right clicking on the front panel then following the tabs, Classic->Graph->ActiveX 3d Curve Graph. Download Business 3D graph vector material 01 in EPS format. Example The parametric equations x = t , y = t2 ; t [-1,2] are an example of how to parameterize part of the graph of the function y = x2. Download 13,070 3d graph free vectors. To use the application, you need Flash Player 6 or higher. Vector 3D graph showing an increase and projected growth. Vector and Streamline Plots. Simple online geometry shapes graphing calculator that allows you to draw/graph a triangle given the required values. Explain what the effect of a discontinuity in a. This VI accepts three 1-dimensional arrays. In general, the behavior of a three-dimensional vector field isn't so easy to see from the graph. Change the Scale to provide a better visualisation of the vector field. Implicit Equations Vector Fields ©2010 Kevin Mehall. The package onion for visualizing quaternions and octonions is well suited to display 3D graphics based on derived meshes. These are represented by integers ranging from 1 to 5, where 1 is the variable, 2 is the variable, 3 is the first field component, 4 is the second field component, and 5 is the vector magnitude. You can add, subtract, find length, find dot and cross product, check if vectors are dependant. The other source of vector is the reaction between the zirconium and water. Fine-tune the result by setting the range for the variables. At its core is the ability to create 2D and 3D plots based on tabular data and/or mathematical expressions. The Organic Chemistry Tutor 383,412 views 10:28. If layout is a function, this function will be called with the graph as the single parameter to determine the actual coordinates. 1 - 75 of 789,706 images. If not specified, the default constructor is used instead. Introduce the x, y and z values of the equations and the parameter in t. Download high-quality 3d pie chart graph, 3d graph. 7 LaTeX usage. The direction of the arrow matches the direction of the vector, while the length represents the magnitude of the vector. This paper is used by many people for creating perspective drawings of buildings, product boxes and more. 2D & 3D TeX-Aware Vector Graphics Language Asymptote is a powerful descriptive vector graphics language for technical drawing, inspired by MetaPost but with an improved C++-like syntax. Window Settings. For every operation, calculator will generate a detailed explanation. So a three-dimensional vector field is given by a function, a certain multi-variable function that has a three-dimensional input given with coordinates x, y and z, and then a three. Click here to download this graph. They are mostly standard functions written as you might expect. results-effort graph drawn by 3d man over white Stock Vector Art & Illustration, Vector Image: 128146589 - Alamy. Scalable Vector Graphics (. There are a two different ways to calculate the resultant vector. Graphs in 3D Entering equations and viewing surfaces Some View Menu Options. VectorPlot3D displays a vector field by drawing arrows. You can plot six equations at the same in both 2D and 3D modes, though if you spend $2 and get the advanced feature set, that limit goes bye-bye. Because some functions used in VectorColorFunction are common, the Wolfram Language allows you to call them as variables. 3D vectors. Editing Points and Planes5. Graph Points in 3D Using 3D Calc Plotter Graph 3D Vectors Using 3D Calc Plotter Graph Tangent Planes to Surfaces Using 3D Calc Plotter Graph a Function of Two Variable Using 3D Calc Plotter Graph a Contour Plots (Level Curves) Using 3D Calc Plotter. The first vector can be a little longer: ( -15 x +15 ) and ( -15. The length of a vector represented by a three-component matrix is:. Click here to download this graph. 3 Define a vector in a sentence. Once you get comfortable with the 2D graphing, you might be interested in learning how to plot three-dimensional charts. Find Vector Illustration 3d Graph stock images in HD and millions of other royalty-free stock photos, illustrations and vectors in the Shutterstock collection. 97, and represent the same vector), it follows that the components of a general vector are not affected by a simple shift in the origin of a Cartesian coordinate system. 3D Grapher last updated: Jan 8, 2006. 3D vector graphing Anyone able to suggest a computer program that is optimal for graphing in the third dimension? There's heaps and I've got to model a redbull air race with vector parametrics for a school project. This VI accepts three 1-dimensional arrays. Introduction to the Desmos Graphing. DIRECTION must be entered in degrees, increasing 'counterclockwise'. Depending on the dimension of coordinate axis, vectline can plot both 3D and 2D vector field line. There are several techniques we use to sketch a curve generated by a pair of parametric equations. y = x (b = 0) y = (m = 0). js and stack. For more information about specifying colors, see SAS/GRAPH Colors and Images in the SAS/GRAPH: Reference, Second Edition. Axis Graphing 5mm. Download Coreldraw Vector (. To compare two 3D graphs, you should rotate them all into the same position. Scalable Vector Graphics (SVG) SVG, a vector graphics format designed at W3C, written in XML and stylable with CSS, is starting to become a popular choice for including graphics in XML documents. A vector-valued function$\dlvf:\R^2 \rightarrow \R^2\$ can be visualized as a vector field. 9 Graphically show the result of multiplying a vector by a negative scalar. Scalable Vector Graphics (. Vectors Physics, Basic Introduction, Head to Tail Graphical Method of Vector Addition & Subtraction - Duration: 10:28. Would really like to be able to use variables to define t. Applets' Home Kaskosz Home Math Home. Now able to manage complete 3D scenes with a fully positional camera, scene graph, lighting and rendering. Beyond simple math and grouping (like " (x+2) (x-4)"), there are some functions you can use as well.
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text:
3: Ethics in Public Speaking

Learning Objectives

After reading this chapter, the student will be able to:

• Understand the legal, cultural, philosophical, and social origins of ethics in public speaking;
• Explain the difference between plagiarism and correct appropriation of source materials;
• Understand the value of ethics in building a solid reputation as a speaker;
• Correctly use source material in a presentation

• 3.1: Sources of Ethical Stances on Communication and Public Speaking
Public speaking, or “rhetoric” as it was originally called, has long been considered a method in Western culture of building community, facilitating self-government, sharing important ideas, and creating policies. In fact, these are the reasons the ancient Athenian Greeks emphasized that all citizens should be educated in rhetoric: so that they could take part in civil society. Aristotle said that if a man was expected to defend himself physically and his ideas rhetorically.
• 3.2: Credibility and Ethics
Modern scholars of communication and persuasion speak more about “credibility” as an attitude the audience has toward the speaker, based on both reality and perception, rather than an innate trait of the speaker. Audience members trust the speaker to varying degrees, based on the evidence and knowledge they have about the speaker and how that lines up with certain factors.
• 3.3: Plagiarism
Although there are many ways that you could undermine your ethical stance before an audience, the one that stands out and is committed most commonly in academic contexts is plagiarism. A dictionary definition of plagiarism would be “the act of using another person’s words or ideas without giving credit to that person” (Merriam-Webster, 2015).

3: Ethics in Public Speaking is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Kris Barton & Barbara G. Tucker.


text:
# Thinking construction and skill realization of recursion

2021-02-05 18:05:36

The article begins with the official account of WeChat ： Geometric thinking

Recursion is a method of solving complex problems by repeated operations .

### 1. One dimensional recursion

#### 1.1 Problem description

There is one $$n$$ The stairs on the first floor , You can only climb up at a time 1 Layer or 2 layer , Ask after climbing $$n$$ How many different ways are there ？

#### 1.2 analysis

set up $$f(n)$$ Express $$n$$ There are totally different ways of building .
Let's say it's in the second $$i$$ layer , Because you can only climb every time 1 Layer or 2 layer , So by the end of $$i$$ Layer only 2 Ways of planting .

• From $$i-1$$ Climb up the floor .
• From $$i-2$$ Climb up the floor .

So the recurrence formula is $$f(n)=f(n-1)+f(n-2)$$. front 2 The sum of terms is equal to 3 term , It's actually the Fibonacci sequence ,
$$1, 1, 2, 3, 5, 8, 13, 21 \cdots \cdots$$

#### 1.3 Code implementation

f[0] = 1; f[1] = 1;
for (int i = 2; i < n; i++){
f[i] = f[i - 1] + f[i - 2]
}
cout << f[n - 1] << endl;

#### 1.4 Space optimization

The recursion of each step is only related to the previous 2 It's about , So just before recording 2 The number of steps , Using the scrolling array , Instead of driving $$o(n)$$ Space .
Manual assignment

int f[3];
f[0] = 1;
f[1] = 1;
for (int i = 2; i < 10; ++i) {
f[2] = f[1] + f[0];
f[0] = f[1];
f[1] = f[2];
cout << f[2] << endl;
}

Take the mold and roll

int f[3];
f[0] = 1;
f[1] = 1;
for (int i = 2; i < 10; ++i) {
f[i % 3] = f[(i - 1) % 3] + f[(i - 2) % 3];
cout << f[i % 3] << endl;
}

If it's only related to the previous state , such as $$f[n]=f[n-1]+1$$, It can be used 0,1 rolling , This is more commonly used in dynamic programming .

int f[2], t = 0;
f[0] = 1;
for (int i = 2; i < 10; ++i) {
t = 1 - t;
f[t] = f[1 - t] + 1;
cout << f[t] << endl;
}

The biggest difference between recursive and dynamic programming ： Each step of recursion is the sum of all the schemes , And dynamic programming in every step of recursion , Need to use max,min To choose an optimal strategy . In fact, the essence is to deduce large-scale results through repeated small-scale model problems .

#### 1.5 Time optimization

The recurrence formula of Fibonacci sequence is very simple , But when the data is big , It's less efficient , Because recursion is $$O(n)$$ Complexity .
Through matrix formula transformation, addition can be changed into multiplication
Let's put the recurrence formula into the matrix as follows ：
$$\begin {bmatrix}1&1\\1&0\end {bmatrix} \times \begin{pmatrix}f(n-1) \\ f(n-2)\end{pmatrix} =\begin{pmatrix}f(n-1)+f(n-2) \\ f(n-1)\end{pmatrix} =\begin{pmatrix}f(n) \\ f(n-1)\end{pmatrix}$$
hypothesis ：
$$A=\begin {bmatrix}1&1\\1&0\end {bmatrix}$$
be :
$$A^n \times \begin{pmatrix}f(1) \\ f(0)\end{pmatrix} = \begin{pmatrix}f(n+1) \\ f(n)\end{pmatrix}$$
$$A^n$$ It can be solved quickly by matrix power multiplication , The time complexity is $$log_2N$$, And then we can get the sequence value by bringing in the above formula .
See another article for details Recursive optimization - Matrix power multiplication

### 2. Multidimensional recursion

#### 2.1 Problem description

Starting from the origin , It's going east at a time , To the north , Go west , And you can't go where you've been , Ask to leave $$n$$ How many different ways are there ？

#### 2.2 analysis

Let's assume that we have reached the third stage $$i$$ Step , Because you can't walk where you've been , The way that this step can go is only related to the previous step . Because one step at a time , Make sure you don't go back , Just make sure you don't go where you've been .
Every time 3 A choice , To the East , To the north , To the West .

• The first $$i-1$$ Step East , So the first $$i$$ We can only go north 、 To the east .
• The first $$i-1$$ Step West , So the first $$i$$ We can only go north 、 To the West .
• The first $$i-1$$ Step North , So the first $$i$$ Step North 、 To the east , To the West .

One dimensional $$f[n]$$ Only one total can be recorded , Instead of recording the State , So one more dimension is needed to record the state of the last step .
set up $$f[n][0],f[n][1],f[n][2]$$ respectively ： The first $$n$$ Step East 、 To the West 、 There are different ways to go north .
Then there is the following recurrence relation ：

• $$f[n][0] = f[n - 1][0] + f[n - 1][2];$$
• $$f[n][1] = f[n - 1][1] + f[n - 1][2];$$
• $$f[n][2] = f[n - 1][0] + f[n - 1][1] + f[n - 1][2];$$

#### 2.3 Code implementation

int f[100][3] = {0};
f[0][0] = 1;
f[0][1] = 1;
f[0][2] = 1;

for (int i = 1; i < n; ++i) {
f[i][0] = f[i - 1][0] + f[i - 1][2];
f[i][1] = f[i - 1][1] + f[i - 1][2];
f[i][2] = f[i - 1][0] + f[i - 1][1] + f[i - 1][2];
}
cout << f[n - 1][0] + f[n - 1][1] + f[n - 1][2] << endl;

#### 2.4 Further optimization

Set the first $$n$$ The total number of steps is $$s[n], s[n]=f[n][0]+f[n][1]+f[n][2]$$.
$$s[n]=2\times f[n-1][0]+2\times f[n-1][1]+3\times f[n-1][2]$$.
$$s[n]=2\times s[n-1]+f[n-1][2]$$.
and $$f[n-1][2]=f[n-2][0]+f[n-2][1]+f[n-2][2]=s[n-2]$$.
have to $$s[n]=2\times s[n-1]+s[n-2]$$.
So the formula is distorted , It can also be done recursively in one dimension , But this relationship cannot be constructed directly through modeling .

### 3. Graph recursion

#### 3.1 Problem description

In a $$n\times m$$ In a two-dimensional map of , A person goes from the upper left corner to the lower right corner , You can only go right or down at a time , How many different ways to get to the end ？

#### 3.2 analysis

Suppose you're already in a position , Because you can only go right or down , The last step can only come from the top or from the left .
set up $$f[i][j]$$ It means to go to the coordinates $$(i,j)$$ The total number of programs .
be $$f[i][j]=f[i-1][j]+f[i][j-1]$$.

#### 3.3 Code implementation

int f[10][10] = {0};
f[0][0] = 1;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
if (i - 1 >= 0) {
f[i][j] += f[i - 1][j];
}
if (j - 1 >= 0) {
f[i][j] += f[i][j - 1];
}
}
}

#### 3.4 Further reflection

To get to the end , Be sure to go down $$n-1$$ Step , turn right $$m-1$$ Step .
Put each step together to see , In fact, the problem is equivalent to $$n+m-2$$ Choose in the step $$n-1$$ Step down , Or choose $$m-1$$ Step right , Through permutation and combination formula $$C_{n+m-2}^{n-1}$$ You can get the results directly .

### 4. State compression recursion

#### 4.1 Problem description

In a $$n\times n$$ Put pieces on your chessboard , There are some places that can't be placed . It is required to place the pieces at will 2 A piece can't be in the same 1 Line or same as 1 Column , Question placement $$k$$ How many different ways are there for a chess piece ？

#### 4.2 analysis

For each 1 A place , There will only be 2 In this case , Is to put or not to put . In the case of small data scale, you can use DFS( Depth-first search ) Just enumerate all the cases .

Is there a better way ？
This is ultimately the total number of required solutions , It's not necessary to consider whether you need to choose the best in each step , So it's consistent with the recursive model , The next step is to find out the recurrence relationship .

Let's first analyze some implied laws , Make things clearer ：

• Every time 1 OK or every 1 Columns can only be placed 1 A chess piece , So enumerate the placement methods on each line .
• In trying the second $$i$$ Line time , Every position $$(i,j)$$ Can you place it , It's not just about keeping up with the industry , It's about all the previous lines . This means that you need to record the method you placed before , That is the state .

How to record the status of the scheme placed before , This requires state compression .
State compression ： The essence is to record the corresponding position in binary system 2 States ,0 I won't let go ,1 It means to put .

about $$n$$ A place , You can use it $$2^n$$ A decimal number to represent all the placement schemes .

Go back to the question above , In trying the second $$i$$ Line time , Can you place it with the previous $$i-1$$ It's all about business , It means that you need to record the status of all previous rows placed .
But look below 2 In this case , chart 1 Sum graph 2 For trying to place 3 Line time , It's actually equivalent , front 2 Columns cannot be placed . That is to say 2 The number of schemes can be combined directly , Because each 1 There can only be one column , So the placed scheme states can also be directly merged into one line .

use $$f[i][j]$$ Before presentation $$i$$ That's ok , The placement scheme is $$j$$ The total number of programs .
The first 0 The process is as follows ：

The first 1 The process is as follows ：

So we can deduce $$n$$ That's ok ,$$2^n$$ The total number of placement schemes ,$$f[n][2^n]$$. Because it can only be placed $$k$$ A chess piece , So in $$2^n$$ It's just that $$k$$ A chess plan , That is, the corresponding state $$j$$ When converted to binary , Yes $$k$$ individual 1.

#### 4.3 Tips ： How to find the corresponding binary inclusion of decimal number quickly 1 How many are there ?

Target number $$n$$, adopt $$n \& (n-1)$$ operation , How many are included 1 Just how many times the operation is performed , You can quickly find out 1 The number of .

#### 4.4 Code implementation

Calculation $$n$$ Contained in the 1 The number of

int countOne(int n) {
int total = 0;
while (n > 0) {
total++;
n &= n - 1;
}
return total;
}

Variable definition and initialization

int i, n, k, line[8], f[2][256], num[256];

for (i = 0; i < 256; ++i) num[i] = countOne(i);

memset(f, 0, 2 * 256 * 4);
f[0][0] = 1;
int j, c, now = 0;

//  The chessboard reads
for (i = 0; i < n; ++i) {
int t = 0;
for (int j = 0; j < n; ++j) {
t <<= 1;
cin >> ch;
if (ch == '.') t += 1;
}
line[i] = t;
}

Core recursion

for (i = 0; i < n; ++i) {
now = 1 - now;
for (j = 0; j < 256; ++j)
if (num[j] <= k) {
// The first i You can't let go of the pieces
f[now][j] += f[1 - now][j];
// The first i All right, put the pieces
for (c = 0; c < n; ++c) {
if ((j & 1 << c) == 0 && (line[i] & 1 << c) == 0) {
f[now][j | 1 << c] += f[1 - now][j];
}
}
}
}

//  Enumerate all the objects that contain k The number of chess pieces
int ans = 0;
for (i = 0; i < 256; ++i) {
if (num[i] == k) {
ans += f[now][i];
}
}
cout << ans << endl;

### 5. summary

The most important idea of recursion , It's through every little step , Find out the relationship with the next step . The key is to think about the nature of the problem , Model the problem . Commonly used $$f[i][j][k]$$ And so on , One more dimension can record one-dimensional state information , Think about how many factors in the previous step will affect the current step , Generally, these are the information that must be recorded .

Scan the bottom two dimensional code to pay attention to the official account , Get updated information at the first time ！

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 Title: Exomolhd: Photodissociation Of Diatomic Molecules Author(s): Pezzella, Marco Contributor(s): Tennyson, Jonathan; Yurchenko, Sergei N. Subject(s): Photodissociation and photochemistry Abstract: \begin{wrapfigure}{r}{0pt} \includegraphics[scale=0.25,trim=0 0 0 2cm]{abstract.eps} \end{wrapfigure} The destruction of molecules by photodissociation influences the composition and dynamics of exoplanets, particularly in the presence of a UV-rich stellar environments, where molecules are hot. Current photodissociation calculations generally assume $T= 0$ K, appropriate for the cold interstellar medium but inadequate for hot (exo)planets and stars. We compute temperature-dependent photodissociation cross sections for molecules found in these atmospheres. The cross sections are calculated by solving the nuclear-motion Schrödinger equation as part of the ExoMol project using codes Duo and Exocross\footnote{Yurchenko \textit{et al} Comput Phys Commun 2016 \textbf{202} 262–275;Yurchenko \textit{et al} A\&A 2018 \textbf{614} A131 }, and averaging results obtained as discrete spectra. We benchmark our results for three systems. The general validity of the methodology is tested considering the A$^1\Pi \leftarrow$ X$^1\Sigma^+$ transition of HCl at low $T$. Our cross sections and rates agree with published results\footnote{Dishoeck \textit{et al} J. Chem. Phys. 1982 \textbf{77} 3693} (2.31*10$^{-10}$ s$^{-1}$ versus 2.10*10$^{-10}$ s$^{-1}$ respectively ). We also reproduce calculated photodissociation cross section of BeH$^+$ at T=1800 K.\footnote{Yang \textit{et al} J Quant Spectrosc Radiat Transf 2020 \textbf{254} 107203} We performed the simulations considering the three excited states, A$^1\Sigma^+$, B$^1\Pi$ and C$^1\Sigma^+$, see figure. The photodissociation spectrum of NaCl varies consistently with $T$: at $T=100$ K, there two peaks at 240 nm and 260 nm; while at $T=1500$ K the peaks merge. Issue Date: 2021-06-25 Publisher: International Symposium on Molecular Spectroscopy Genre: Conference Paper / Presentation Type: Text Language: English URI: http://hdl.handle.net/2142/111244 Date Available in IDEALS: 2021-09-24