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# Vegetation on tiled-based terrain
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### #1Makers_F Members - Reputation: 680
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Posted 07 April 2011 - 05:07 PM
Hi everyone,
in my game i already wrote the part that loads the terrain in many tiles, and now i have to wrote the part that puts the vegetation on it.
I need a procedural way to set the coordinates.
I thought of using
x = sin(T(x,y))* size_of_the_tile's_side/2
and
y = cos(K(x,y))*size_of_the_tile's_side/2
to calculate the position relative to the tile center(in this way i'm sure the coords can't fell out of the tile).
The problems i have are:
1) i can't use any random function (the vegetation must not change, every time you are on a tile the vegetation must be the same)
2) i need to have the T(x,y) and K(x,y) functions a bit vary, since i don't want the vegetation to be much repetitive(since sin & cos are periodic functions)
3) i need an "algorithm" to calculate how much vegetation add (i can't add always 50 trees, i need it to vary, and it should be dependent from the sector(so that the density is quite costant in macro-zones))
Long story short, i need to set how many vegetation to add and where..
Is there any docs, resources, papers to get informations from?
Thank you very much in advance
Ps: i said cos and sin since they are the simplest functions that always return [-1;+1], but i'm open to more complex functions
PPs: x and y are the integer index of the tile. Watching from above, the lower-left tile is (0,0) , the upper-right is the ,eg, (300,300)
PPPs: the game is 3D, but the z coord is not a problem, since i'll throw a ray from above and find the intersection with the terrain, and than i'll have the z coord of the hit point and the normal of that face(and then if the terrain is too steep i'll add a different type of vegetation, and i'll load different meshes in base of the height of the terrain)
### #2JTippetts Moderators - Reputation: 8159
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Posted 07 April 2011 - 08:56 PM
Hi everyone,
in my game i already wrote the part that loads the terrain in many tiles, and now i have to wrote the part that puts the vegetation on it.
I need a procedural way to set the coordinates.
I thought of using
x = sin(T(x,y))* size_of_the_tile's_side/2
and
y = cos(K(x,y))*size_of_the_tile's_side/2
to calculate the position relative to the tile center(in this way i'm sure the coords can't fell out of the tile).
The problems i have are:
1) i can't use any random function (the vegetation must not change, every time you are on a tile the vegetation must be the same)
2) i need to have the T(x,y) and K(x,y) functions a bit vary, since i don't want the vegetation to be much repetitive(since sin & cos are periodic functions)
3) i need an "algorithm" to calculate how much vegetation add (i can't add always 50 trees, i need it to vary, and it should be dependent from the sector(so that the density is quite costant in macro-zones))
Long story short, i need to set how many vegetation to add and where..
Is there any docs, resources, papers to get informations from?
Thank you very much in advance
Ps: i said cos and sin since they are the simplest functions that always return [-1;+1], but i'm open to more complex functions
PPs: x and y are the integer index of the tile. Watching from above, the lower-left tile is (0,0) , the upper-right is the ,eg, (300,300)
PPPs: the game is 3D, but the z coord is not a problem, since i'll throw a ray from above and find the intersection with the terrain, and than i'll have the z coord of the hit point and the normal of that face(and then if the terrain is too steep i'll add a different type of vegetation, and i'll load different meshes in base of the height of the terrain)
Perlin noise.
### #3Katie Members - Reputation: 1283
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Posted 08 April 2011 - 02:22 AM
You know, people who've been here long enough should get little buttons for these. One that just adds "perlin noise" to a thread. One which adds "OpenGL contexts are NOT threadsafe". One which adds "No, you should not try and write an MMO as your first game, how about you write tetris or breakout to get some practice in first?"
### #4GregMichael Members - Reputation: 147
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Posted 08 April 2011 - 02:29 AM
### #5FetDaniel Members - Reputation: 122
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Posted 08 April 2011 - 04:09 AM
Hi everyone,
in my game i already wrote the part that loads the terrain in many tiles, and now i have to wrote the part that puts the vegetation on it.
I need a procedural way to set the coordinates.
I thought of using
x = sin(T(x,y))* size_of_the_tile's_side/2
and
y = cos(K(x,y))*size_of_the_tile's_side/2
to calculate the position relative to the tile center(in this way i'm sure the coords can't fell out of the tile).
The problems i have are:
1) i can't use any random function (the vegetation must not change, every time you are on a tile the vegetation must be the same)
2) i need to have the T(x,y) and K(x,y) functions a bit vary, since i don't want the vegetation to be much repetitive(since sin & cos are periodic functions)
3) i need an "algorithm" to calculate how much vegetation add (i can't add always 50 trees, i need it to vary, and it should be dependent from the sector(so that the density is quite costant in macro-zones))
Long story short, i need to set how many vegetation to add and where..
Is there any docs, resources, papers to get informations from?
Thank you very much in advance
Ps: i said cos and sin since they are the simplest functions that always return [-1;+1], but i'm open to more complex functions
PPs: x and y are the integer index of the tile. Watching from above, the lower-left tile is (0,0) , the upper-right is the ,eg, (300,300)
PPPs: the game is 3D, but the z coord is not a problem, since i'll throw a ray from above and find the intersection with the terrain, and than i'll have the z coord of the hit point and the normal of that face(and then if the terrain is too steep i'll add a different type of vegetation, and i'll load different meshes in base of the height of the terrain)
Hi im really an amateur compared what to most people here, but I have a suggestion to you problem. Like a previous person replying said perlin noise is a good way to make deterministic procedural generation, that is a way of generating something that doesn't change when you look it up again.
Im not sure I understand, but are you using a lattice(2d array) and populating it using a sin/cos function, or are you placing the vegetation on different places inside the tile?
Personal experiences from using noise:
I've not implemented perlin noise as Ken Perlin done it, I took a Xor based pseudo random number generator (prng) and made it seedable with x, y coordinates and a single seed number. Thus I had deterministic noise that i could access one tile at a time. The noise is just a random number but can be used to with conditions to make statistical distribution of trees or terrain or whatever really. Its quite magic comparing to storing and manipulating a lattice. To make something more like Perlin Noise I made another function(method since I use Java) that used linear interpolation of different noise wavelength. This is really just adding an interpolation technique that is used when you access tiles in between high wavelength noise, and also adding different "octaves" that is of different wavelength and amplitude. So the number of octaves defines the number of executions of the noise function. The relation between the octaves was called persistance in a tuturial I read, but I've read conflicting uses of the word. My persistance in making a heigthmap is for example= Each octave -> amplitude / 2 and wavelength / 2. The result is high mountatins with smaller hills, and down to noised ground.
A response to your problem:
I've been thinking of using this to make vegetation also, And in this case I have thought about using a reversed persistance, that is higher amplitude on lower wavelengths. The result should be that trees are spaced apart like white noise on a tv when densely packed and over a bigger area small fluctuations of concentrations will be seen. And then it's up to you to decide how dense the forest or other flora should be.
I have no good solution on how to populate your area with trees. Im just thinking perverse thoughts about using cellular automata and some nifty rules. Like that a tile can only have so many neighbours before its tree dies, and that it needs some neighbors to come alive.
PS: Im using my heightmap to declare biome zones and then aplying varying vegetation depending on these. A climate zone is mostly a combination of height and latitude, since that would affect temperature and precipitation.
//FetDaniel
### #6Makers_F Members - Reputation: 680
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Posted 08 April 2011 - 04:30 AM
Ok, this can be the way to go. I googled it, and found lots of articles about the perlin noise, but quite nothing specific to my problem(the coordinates in which punt the vegetation inside the tile)
I saw your ( JTippetts) answer in this topic, but it's already too complex for what i need, i'm looking for a solution far more simple(for start from).
I've also seen the link to libnoise (although i'm using python, i can wrap the library to use it), and some functions, but i didn't get how to use them. Usually the program is used to generate planes or volumes of points, but i need only "few" (x,y) points, not a full map of points..
I give the (x,y) couple (integer), and it should return K couple of (x,y) coords(float), where K is variable. If you can post a simple example (pseudo-code is fine to), i'll be really grateful.
(the climate zones map thing is really interesting, but more advanced than i need for this project)
Sorry for the noobness
Edit(i haven't seen fatdaniel reply):
here what i'm doing.
I'm dynamically loading the terrain (from file, but maybe later i can make it procedural), and now i need to put on it the vegetation. So, each tile, i need a finite number(that is how many trees there will be) of (x,y) coords (that is where the trees will be)
The first problem is that i don't know how to find that finite number
Looking here, i think i need to set up the function so that for small variation of the input gives small variation of the output, but on a large variation of the input, the output can vary a lot. But i don't really know how to set the parameters(for the wavelength and the amplitude)[ i'm using this implementation]
After solving this problem, i think that just varying the number of summed octaves will give nice coords in with put my plants
### #7PropheticEdge Members - Reputation: 150
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Posted 08 April 2011 - 12:14 PM
I'm really starting to think you could look at a thread that contains "procedural graphics", reply with "Perlin Noise", and be right 90% of the time...
### #8Makers_F Members - Reputation: 680
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Posted 08 April 2011 - 02:13 PM
Using this code
w , h = 800, 800
image = Image.new("L", (w,h))
for i in range(0,w):
for l in range(0,h):
x = i+math.sin(i)
y = l+math.cos(l)
pix[i,l] = 255-round((pnoise(x,y,0)+1)*255/2)
image.save("noise.jpeg")
(in the link in my previous post there is the python module from which i use pnoise function. This script write in a greyscale image the output of pinoise for each coord)
I obtained the attached immage
But i expected something more like this
http://2.bp.blogspot.com/_jRVUemIYFxY/SzIyeaLoWuI/AAAAAAAAABw/abGefrTdffw/s1600-R/perlin_noise2.jpg
(with areas more divided, while in my image is quite random... )
### #9JTippetts Moderators - Reputation: 8159
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Posted 09 April 2011 - 08:15 AM
You're doing something weird to generate your noise image:
x=i+math.sin(i)
y=l+math.cos(l)
From what I can see, i and l get pretty large (800 and 600, respectively) which isn't really the best way to go about calling a Perlin noise function if you want to see detail. Consider a standard Perlin fBm fractal of 8 octaves, where each octave is *2 the frequency of the previous one. The first layer has a frequency of 1, meaning that the average "feature size" of the hills and valleys is 1 unit. Then a layer of details is added whose feature size is 1/2 unit (Frequency 2), and so on. So as you can see, the feature size is important, because when you sample an area sized 800x600 units, one per pixel, you are essentially sampling 1 hill per pixel, and the result is an image of the fractal in which the features are so small that the whole thing just appears as white noise, or close to white noise. Also, the value of sin(i) is going to be tiny in relation to i as i grows large, so you might as well not even bother with the +sin(i) and +cos(l) terms in this case, although they do serve the useful purpose of moving the i and l coordinates off of the integer boundaries of the units, since gradient Perlin noise sampled at integer boundaries evaluates to 0.
What you need to try is to map a smaller region of noise into your 800x600 buffer. The easiest way to do this is to turn down your frequency. Decide how many hills or features you want in your image, and set the frequency to NumFeatures/ImageWidth. So if you want around 4 "hills" or features per image, you'd set the frequency to 1/200, meaning that you'd get a feature on average every 200 units or pixels.
libnoise is actually pretty simple to use. You have 3 basic types of function: generators (that generate noise), combiners (that add, multiply, etc... noise functions together) and transforms (that modify the input coords to a noise function in some way). Simple building blocks that can produce complex results when they are chained together.
Now, once you have your Perlin noise working to your liking, then consider you have a Perlin noise fractal that covers the map, assigning a value of -1 to 1 to each tile of the map. You can look at that as a density map for vegetation. For example, say a value between -1 and 0 is fully clear of vegetation, and a value between 0 and 1 has some amount of vegetation. You can first take the output of your fractal and clamp it to the range [0,1] so that anything below 0 is considered to be 0. Now say that you want to have up to 6 trees per tile. Just multiply the clamped result by 6 and truncate it to an integer. Areas where the clamped function evaluates to 0 will have no trees, while other areas will have a number of trees dependent upon the "height" of the fractal at their location. You can further modify this by adding small amplitude white noise to each tile location that is non-0, to slightly tweak the number of trees per tile.
### #10Makers_F Members - Reputation: 680
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Posted 09 April 2011 - 11:24 AM
Got it!
Unfortunately, the script i use is really simple (i can't set the frequency and octaves number as input), i'll try using libnoise(maybe swig can do the magic) with python.
Btw now i understood how to generate the vegetation map.
The last question i have is:
once i know how many trees add in a tile, how can i calculate their coordinates(x,y)? I think a method could be iterate for each coord in the tile calling the perlin noise, and if the value is greater the, let's say, 0,5, put there a tree. But this is computationally heavy, i prefer to have a simpler method.. Do you have any idea?
(last time i bother you )
Ps: yes, the sin and cos where to change the values from integer
### #11JTippetts Moderators - Reputation: 8159
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Posted 09 April 2011 - 12:40 PM
Got it!
Unfortunately, the script i use is really simple (i can't set the frequency and octaves number as input), i'll try using libnoise(maybe swig can do the magic) with python.
Btw now i understood how to generate the vegetation map.
The last question i have is:
once i know how many trees add in a tile, how can i calculate their coordinates(x,y)? I think a method could be iterate for each coord in the tile calling the perlin noise, and if the value is greater the, let's say, 0,5, put there a tree. But this is computationally heavy, i prefer to have a simpler method.. Do you have any idea?
(last time i bother you )
Ps: yes, the sin and cos where to change the values from integer
Well, the easy way to implement changing frequency is just to multiply your x and y coordinates by frequency before calling pnoise.
As far as determining the coordinates of a tree within a tile, this might not be as simple as calling a noise function, if you have to take into account keeping trees from overlapping each other. This becomes a physical modeling problem, and for this type of situation I like to use a hash of the tile coordinates to generate sequences of pseudo-random numbers that are deterministic per-tile. A simple example might be to use a FNV-1 hash + a basic seedable random number generator:
// FNV-1a hash
unsigned int fnv_hash(void *data, size_t size, unsigned int hash=2166136261)
{
for(unsigned char *p=(unsigned char *)data; p<(unsigned char *)data+size; ++p)
{
hash ^= *p;
hash *= 16777619;
}
return hash;
}
unsigned int hashTileCoords(unsigned int tx, unsigned int ty)
{
unsigned int tc[2]={tx,ty};
return fnv_hash((void *)tc, sizeof(unsigned int)*2);
}
Once you have hashed your tile coords to an unsigned int, use that unsigned int to seed a random number generator (for example, call srand() with the hash, then generate random numbers via rand()). This generates a sequence of random numbers that will always be the same sequence for a given tile coordinate, suitable for a streaming-type setup where you can't just globally seed a random generator and hope for sane results.
With this in hand, you can do something to scatter trees at randomized locations within a tile. You can iterate some number of times, generating randomized locations within the tile and checking for overlap with already-generated positions, until you have enough positions or the procedure fails because it can't find a suitable spot. Or you could place locations at evenly-spaced starting points, then use a series of random numbers, scaled to the range [-1,1] then multiplied by some kind of "wobble factor", to perturb the locations randomly from their starting location.
### #12Makers_F Members - Reputation: 680
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Posted 10 April 2011 - 09:53 AM
Ok, since swig has a bit of problems with c++, i followed another way.
I created a dll using a C implementation of perlin noise (python can load c written dll without any problems. With c++ it has some problems because of the name of the functions, but if them can be exported with extern C there wouldn't be any problem to load libnoise dll, but i haven't tryed)
Here the .c file
/* Coherent noise function over 1, 2 or 3 dimensions */
/* (copyright Ken Perlin) */
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "perlin.h"
#define random rand
static int p[B + B + 2];
static double g3[B + B + 2][3];
static double g2[B + B + 2][2];
static double g1[B + B + 2];
static int start = 1;
double noise1(double arg)
{
int bx0, bx1;
double rx0, rx1, sx, t, u, v, vec[1];
vec[0] = arg;
if (start) {
start = 0;
init();
}
setup(0,bx0,bx1,rx0,rx1);
sx = s_curve(rx0);
u = rx0 * g1[ p[ bx0 ] ];
v = rx1 * g1[ p[ bx1 ] ];
return(lerp(sx, u, v));
}
double noise2(double vec[2])
{
int bx0, bx1, by0, by1, b00, b10, b01, b11;
double rx0, rx1, ry0, ry1, *q, sx, sy, a, b, t, u, v;
int i, j;
if (start) {
start = 0;
init();
}
setup(0, bx0,bx1, rx0,rx1);
setup(1, by0,by1, ry0,ry1);
i = p[ bx0 ];
j = p[ bx1 ];
b00 = p[ i + by0 ];
b10 = p[ j + by0 ];
b01 = p[ i + by1 ];
b11 = p[ j + by1 ];
sx = s_curve(rx0);
sy = s_curve(ry0);
q = g2[ b00 ] ; u = at2(rx0,ry0);
q = g2[ b10 ] ; v = at2(rx1,ry0);
a = lerp(sx, u, v);
q = g2[ b01 ] ; u = at2(rx0,ry1);
q = g2[ b11 ] ; v = at2(rx1,ry1);
b = lerp(sx, u, v);
return lerp(sy, a, b);
}
double noise3(double vec[3])
{
int bx0, bx1, by0, by1, bz0, bz1, b00, b10, b01, b11;
double rx0, rx1, ry0, ry1, rz0, rz1, *q, sy, sz, a, b, c, d, t, u, v;
int i, j;
if (start) {
start = 0;
init();
}
setup(0, bx0,bx1, rx0,rx1);
setup(1, by0,by1, ry0,ry1);
setup(2, bz0,bz1, rz0,rz1);
i = p[ bx0 ];
j = p[ bx1 ];
b00 = p[ i + by0 ];
b10 = p[ j + by0 ];
b01 = p[ i + by1 ];
b11 = p[ j + by1 ];
t = s_curve(rx0);
sy = s_curve(ry0);
sz = s_curve(rz0);
q = g3[ b00 + bz0 ] ; u = at3(rx0,ry0,rz0);
q = g3[ b10 + bz0 ] ; v = at3(rx1,ry0,rz0);
a = lerp(t, u, v);
q = g3[ b01 + bz0 ] ; u = at3(rx0,ry1,rz0);
q = g3[ b11 + bz0 ] ; v = at3(rx1,ry1,rz0);
b = lerp(t, u, v);
c = lerp(sy, a, b);
q = g3[ b00 + bz1 ] ; u = at3(rx0,ry0,rz1);
q = g3[ b10 + bz1 ] ; v = at3(rx1,ry0,rz1);
a = lerp(t, u, v);
q = g3[ b01 + bz1 ] ; u = at3(rx0,ry1,rz1);
q = g3[ b11 + bz1 ] ; v = at3(rx1,ry1,rz1);
b = lerp(t, u, v);
d = lerp(sy, a, b);
return lerp(sz, c, d);
}
void normalize2(double v[2])
{
double s;
s = sqrt(v[0] * v[0] + v[1] * v[1]);
v[0] = v[0] / s;
v[1] = v[1] / s;
}
void normalize3(double v[3])
{
double s;
s = sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
v[0] = v[0] / s;
v[1] = v[1] / s;
v[2] = v[2] / s;
}
void init(void)
{
int i, j, k;
for (i = 0 ; i < B ; i++) {
p[i] = i;
g1[i] = (double)((random() % (B + B)) - B) / B;
for (j = 0 ; j < 2 ; j++)
g2[i][j] = (double)((random() % (B + B)) - B) / B;
normalize2(g2[i]);
for (j = 0 ; j < 3 ; j++)
g3[i][j] = (double)((random() % (B + B)) - B) / B;
normalize3(g3[i]);
}
while (--i) {
k = p[i];
p[i] = p[j = random() % B];
p[j] = k;
}
for (i = 0 ; i < B + 2 ; i++) {
p[B + i] = p[i];
g1[B + i] = g1[i];
for (j = 0 ; j < 2 ; j++)
g2[B + i][j] = g2[i][j];
for (j = 0 ; j < 3 ; j++)
g3[B + i][j] = g3[i][j];
}
}
/* --- My harmonic summing functions - PDB --------------------------*/
/*
In what follows "alpha" is the weight when the sum is formed.
Typically it is 2, As this approaches 1 the function is noisier.
"beta" is the harmonic scaling/spacing, typically 2.
*/
double PerlinNoise1D(double x,double alpha,double beta,int n)
{
int i;
double val,sum = 0;
double p,scale = 1;
p = x;
for (i=0;i<n;i++) {
val = noise1(p);
sum += val / scale;
scale *= alpha;
p *= beta;
}
return(sum);
}
double PerlinNoise2D(double x,double y,double alpha,double beta,int n)
{
int i;
double val,sum = 0;
double p[2],scale = 1;
p[0] = x;
p[1] = y;
for (i=0;i<n;i++) {
val = noise2(p);
sum += val / scale;
scale *= alpha;
p[0] *= beta;
p[1] *= beta;
}
return(sum);
}
double PerlinNoise3D(double x,double y,double z,double alpha,double beta,int n)
{
int i;
double val,sum = 0;
double p[3],scale = 1;
p[0] = x;
p[1] = y;
p[2] = z;
for (i=0;i<n;i++) {
val = noise3(p);
sum += val / scale;
scale *= alpha;
p[0] *= beta;
p[1] *= beta;
p[2] *= beta;
}
return(sum);
}
Here the .h file
#define B 0x100
#define BM 0xff
#define N 0x1000
#define NP 12 /* 2^N */
#define NM 0xfff
#define s_curve(t) ( t * t * (3. - 2. * t) )
#define lerp(t, a, b) ( a + t * (b - a) )
#define setup(i,b0,b1,r0,r1)\
t = vec[i] + N;\
b0 = ((int)t) & BM;\
b1 = (b0+1) & BM;\
r0 = t - (int)t;\
r1 = r0 - 1.;
#define at2(rx,ry) ( rx * q[0] + ry * q[1] )
#define at3(rx,ry,rz) ( rx * q[0] + ry * q[1] + rz * q[2] )
#ifdef BUILDING_NOW_DLL
#define DLL_DECLSPEC __declspec(dllexport)
#else
#define DLL_DECLSPEC __declspec(dllimport)
#endif
void init(void);
double noise1(double);
double noise2(double *);
double noise3(double *);
void normalize3(double *);
void normalize2(double *);
double DLL_DECLSPEC PerlinNoise1D(double,double,double,int);
double DLL_DECLSPEC PerlinNoise2D(double,double,double,double,int);
double DLL_DECLSPEC PerlinNoise3D(double,double,double,double,double,int);
Here the python module that "wrap" the library
import ctypes
class Perlin_Noise():
#using the implementation described here
# http://paulbourke.net/texture_colour/perlin/
def __init__(self, path_to_library , weight = 2.0, spacing = 2.0, zoom = 10, octaves = 5.0):
#Typically it is 2, As this approaches 1 the function is noisier.
self._sum_weight = weight
#It is the harmonic scaling/spacing, typically 2
self._harmonic_spacing = spacing
#The zoom of the generate texture
self._zoom = zoom
#The number of octaves(note: high values can bringh to overflow[caused by python])
self._octaves = octaves
self._libc.PerlinNoise1D.restype = ctypes.c_double
self._libc.PerlinNoise2D.restype = ctypes.c_double
self._libc.PerlinNoise3D.restype = ctypes.c_double
self._last1D = None
self._last2D = None
self._last3d = None
def setSumWeight(self, weight):
self._sum_weight = weight
def setHarmonicSpacing(self, spacing):
self._harmonic_spacing = spacing
def setZoom(self, zoom):
self._zoom = zoom
def setOctaves(self, octaves):
self._octaves = octaves
def getLast1D(self):
if hasattr(self, "_last1D"):
return self._last1D
else:
return None
def getLast2D(self):
if hasattr(self, "_last2D"):
return self._last2D
else:
return None
def getLast3D(self):
if hasattr(self, "_last3D"):
return self._last3D
else:
return None
def noise1D(self, x):
self._last1D = self._libc.PerlinNoise1D(
ctypes.c_double(x / self._zoom),
ctypes.c_double(self._sum_weight),
ctypes.c_double(self._harmonic_spacing),
ctypes.c_int(self._octaves)
)
return self._last1D
def noise2D(self, x , y):
self._last2D = self._libc.PerlinNoise2D(
ctypes.c_double(x / self._zoom),
ctypes.c_double(y / self._zoom),
ctypes.c_double(self._sum_weight),
ctypes.c_double(self._harmonic_spacing),
ctypes.c_int(self._octaves)
)
return self._last2D
def noise3D(self, x , y, z):
self._last3D = self._libc.PerlinNoise3D(
ctypes.c_double(x / self._zoom),
ctypes.c_double(y / self._zoom),
ctypes.c_double(z / self._zoom),
ctypes.c_double(self._sum_weight),
ctypes.c_double(self._harmonic_spacing),
ctypes.c_int(self._octaves)
)
return self._last3D
Here a script to try if the module works
import perlin_noise
import math
from PIL import Image
w , h = 1000, 1000
new_noise = perlin_noise.Perlin_Noise("perlin.dll", 1, 3, 10, 0)
new_noise.setSumWeight(2)
new_noise.setHarmonicSpacing(200)
new_noise.setZoom(5)
new_noise.setOctaves(1)
image = Image.new("L", (w,h))
for i in range(0,w):
for l in range(0,h):
x = i+math.sin(i)
y = l+math.cos(l)
pix[i,l] = ( (new_noise.noise2D(x,y) + 1) / 2 ) * 255
image.save("noise.jpeg")
new_noise.noise1D(new_noise.getLast2D())
new_noise.noise3D(new_noise.getLast1D(), new_noise.getLast2D(), x+y)
new_noise.getLast3D()
Here part of the code in used to generate the coords of the trees:
sector = square["mysector"]
vegetation = Perlin_Noise(g.expandPath("//") + "Perlin" + os.path.sep + "perlin.dll",2, 1000, 10, 1)
# tree_number = (max_trees_per_square_meter) * size_of_the_tile || in this case max 1 tree per 3 square meter
tree_number = int( abs( vegetation.noise2D( sector[0], sector[1] ) / 3 ) * 16 * 16)
rand = random.Random()
rand.seed(hash(tuple(sector)))
for k in range(0, tree_number):
x = (rand.random() -0.5 ) * bge.size
y = (rand.random() - 0.5) * bge.size
#make it relative to the center of the tile
x = square.worldPosition[0] + x
y = square.worldPosition[1] + y
I added all this code so that if someone will have the same problem can find here a good way to start from. I managed to create the system for loading the trees, now it will just need polishing and a bit of improvement. I'm sorry i dind't managed to use the libnoise library, it seams well coded and feature complete, if someone have any hints about how to export its functions as C functions let me know
Thanks very much to who made this possible helping me, now i'm a little less noob
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.
PARTNERS | 2014-07-25 18:39:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4391312003135681, "perplexity": 3239.3914063933403}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997894689.94/warc/CC-MAIN-20140722025814-00198-ip-10-33-131-23.ec2.internal.warc.gz"} |
http://openstudy.com/updates/55f86d3be4b0a91f39320b4c | ## anonymous one year ago Use mathematical induction to prove that the statement is true for every positive integer n. 2 is a factor of n2 - n + 2 I really need help on this one
1. anonymous
@Loser66
2. mathmate
Have you done mathematical induction before, like -Base case -hypothesis for case n -proof for case n+1
3. anonymous
i has not mate
4. anonymous
5. anonymous
are you there my fellow good sir
6. mathmate
Yes, I was looking for a good reference for you. The following link shows us how to do mathematical inductions, with examples. Example 4 is particularly similar to your problem. http://www.analyzemath.com/math_induction/mathematical_induction.html
7. anonymous
ok thnx mate i will chat you up if i have any problems
8. mathmate
Good, way to go! :)
9. anonymous
ok cheerio
10. anonymous
Statement P (n) is defined by n 3 + 2 n is divisible by 3 STEP 1: We first show that p (1) is true. Let n = 1 and calculate n 3 + 2n 1 3 + 2(1) = 3 3 is divisible by 3 hence p (1) is true. STEP 2: We now assume that p (k) is true k 3 + 2 k is divisible by 3 is equivalent to k 3 + 2 k = 3 M , where M is a positive integer. We now consider the algebraic expression (k + 1) 3 + 2 (k + 1); expand it and group like terms (k + 1) 3 + 2 (k + 1) = k 3 + 3 k 2 + 5 k + 3 = [ k 3 + 2 k] + [3 k 2 + 3 k + 3] = 3 M + 3 [ k 2 + k + 1 ] = 3 [ M + k 2 + k + 1 ] Hence (k + 1) 3 + 2 (k + 1) is also divisible by 3 and therefore statement P(k + 1) is true.
11. anonymous
ok so mate i need more explanation on this it so short worded and down righ confusing
12. anonymous
@mathmate could you help me for a sec mate
13. mathmate
The first step is to establish that the statement you want to prove is true for some n. So P(1)=n^3+2n=1^3+2(1)=3 is divisible by three. In principle, if we have time to show this for all integers, we're done, but we cannot, because n goes to infinity So the next best thing is to show that, if 3|P(n), then 3|P(n+1). 3|x reads 3 divides x. Why ? Because if the hypothesis 3|P(n) is true, then 3|P(n+1) is true, then 3|P(n+2) is true, and so on. Once we have achieved that, we go back to say that 3|P(1), therefore 3|P(2), 3|P(3)... without having to do ALL of the integers.
14. anonymous
ok mate so i get that so how di i do part two of my fiding my answer mate
15. anonymous
you there mate
16. anonymous
@Ashleyisakitty
17. anonymous
@sky425
18. anonymous
@leon549
19. anonymous
@MrNood
20. anonymous
anybody of service here mate
21. anonymous
@helpppppppppp
22. anonymous
f n is even, then n = 2m for some integer m. then substitute n^2 - n + 2 = (2m)^2 - (2m) + 2 =4m^2 - 2m + 2 = 2 ( 2m^2 - m + 1) . and this is a factor of 2 by definition, since it is 2 times some integer , if n is odd , then n = 2r+1 for some integer r n^2 - n + 2 = (2r + 1) ^2 - (2r + 1) + 2 = 4r^2 + 4r + 1 - 2r -1 + 2 by foiling and distributing = 4r^2 + 2r + 2 = 2 ( 2r^2 + r + 1) . and this is a factor of 2 again. we are done :) ok i tried my best and this is what i got is it true
23. mathmate
This is a correct direct proof using "proof by cases". The question asks for proof by mathematical induction, which involves the three steps: 1. Proof a base case (say, n=1). 2. Inductive hypothesis: assume statement is true for case n=k. 3. Inductive proof and conclusion: prove that statement is true for case n=k+1. Done. The steps are extremely similar to example 4 that you have studied. Just have to replace the statement with yours. 1. base case : 2 is a factor of f(n)=n2 - n + 2 when n=1. Well, n^2-n+2 = f(1)= 1^2-1+2 = 2, so 2 is a factor of 2, hence statement is true for n=1 (base case). 2. Inductive hypothesis: Assume that (or IF) statement is true for case n=k: 2 is a factor of n2 - n + 2 for n=k, therefore 2 is a factor of f(k)= k^2-k+2, or f(k)=2m, where m$$\in$$Z 3. Work on case n=k+1 f(k+1)=(k+1)^2-(k+1)+2 = k^2+2k+1-k-1+2 =(k^2-k+2) +2k =(2m)+2k =2(m+1), hence 2 is a factor of f(k+1), given that 2 is a factor of f(k). we have just shown that 2 is a factor of f(k+1), which completes the proof by mathematical induction that 2 is a factor of f(n) for all n$$\in$$Z+. | 2017-01-21 11:04:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7093021273612976, "perplexity": 604.1244943541894}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560281069.89/warc/CC-MAIN-20170116095121-00548-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://www.yaclass.in/p/science-state-board/class-6/matter-around-us-5650/re-993644a8-de4a-4f4f-a82d-1e99bd93fd43 | ### Theory:
What is matter?
Matter is all around us. In other hand, it can be defined as anything that has mass and occupies space. The air you are breathing is also a matter. See some examples given below:
Matter consists of atoms. Atom is the smallest particle that we cannot see through nacked eyes, even on the standard microscopes. Science introduced a technology to identify the structure of atoms: SEM (Scanning Electron Microscope) and TEM (Tunneling Electron microscope) that uses electricity to map atoms.
An atom consists of particles of neutron (N), electron (E) and protons (P) in which neutrons and protons are present in the nucleus of the atom and electrons are present outside of the nucleus.
The matter is made up of tiny particles. For example, water is made up of small water particles that one drop of water has ${10}^{21}$ water particles, and a single dot made by pen has more than $$2$$ Lacs of particles.
Characteristic of the particles of matter:
• The sizes of particles are very small.
• They attract each other (the attractive force is different for a different form of matter).
• Particles move constantly.
• They have space between them; however, the spacing may vary for a different form of matter.
Physical states of matter:
Based on the characteristic of particles in matter, it can be classified into three states.
1. Solids
2. Liquids
3. Gases
Particles in solids:
Particles in the solids are tightly packed with no space between them. Hence, it has a definite shape and volume. Examples: Stone, granite and limestone.
Particles in liquids:
Particles in the liquids are arranged randomly with some space between them. Hence, it has a definite volume but not shape.
Example: Water
Particles in gases:
Particles in the gases are arranged far away. Hence, it has no definite shape and volume. It can move fast and colloid one another.
Example: Air
Diffusion:
Diffusion is the tendency of particles to spread out in order to occupy the available space.
In other words, diffusion is the movement of particles from a higher concentration to a lower concentration.
Diffusion occurs in liquids and gases since they can move easily. | 2021-08-05 07:49:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.535917341709137, "perplexity": 1097.7408214973432}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046155458.35/warc/CC-MAIN-20210805063730-20210805093730-00246.warc.gz"} |
https://www.groundai.com/project/quantum-state-transmission-in-a-superconducting-charge-qubit-atom-hybrid/ | Quantum State Transmission in a Superconducting Charge Qubit-Atom Hybrid
# Quantum State Transmission in a Superconducting Charge Qubit-Atom Hybrid
1
Hybrids consisting of macroscopic superconducting circuits and microscopic components, such as atoms and spins, have the potential of transmitting an arbitrary state between different quantum species, leading to the prospective of high-speed operation and long-time storage of quantum information. Here we propose a novel hybrid structure, where a neutral-atom qubit directly interfaces with a superconducting charge qubit, to implement the qubit-state transmission. The highly-excited Rydberg atom located inside the gate capacitor strongly affects the behavior of Cooper pairs in the box while the atom in the ground state hardly interferes with the superconducting device. In addition, the DC Stark shift of the atomic states significantly depends on the charge-qubit states. By means of the standard spectroscopic techniques and sweeping the gate voltage bias, we show how to transfer an arbitrary quantum state from the superconducting device to the atom and vice versa.
A quantum computer makes direct use of qubits to encode information and perform operations on data according to the laws of quantum mechanics Book:Nielsen2000 (). Due to the properties of superposition and entanglement of quantum states, such a computing device is expected to operate exponentially faster than a classical computer for certain problems. Recently, some basic quantum logic gates have been executed on various quantum systems composed of a small number of qubits, for instances, trapped ions Nature:Kielpinski2002 (), neutral atoms PRL:Brennen1999 (), photons RMP:Kok2007 (), NMR Nature:Vandersypen2011 (), and superconducting (SC) circuits RMP:Makhlin2001 (). However, the development of an actual quantum computer is still in its infancy since no quantum system practically fulfills all DiVincenzo criteria PRA:Loss1998 () for the physical implementation of quantum computation.
Hybridizing different quantum systems could inherit the advantages of each component and compensate the weaknesses with each other PRL:Tian2004 (); PRL:Rabl2006 (); RMP:Xiang2013 (). A promising structure is to combine the SC circuits with neutral atoms. Macroscopic solid-state devices including submicrometer-sized Josephson junctions (JJ) possess the advantages of rapid information processing ( ns), flexibility, and scalability. However, due to the strong coupling to the local electromagnetic environment, the relaxation and dephasing times of the SC circuits, which are of the order of Science:Mooij2003 (); PRL:Nakamura2002 (); PRB:Duty2004 (); PRA:Koch2007 (); PRB:Rigetti2012 (), are significantly limited by the fluctuations in background charge, flux, and critical current Science:Vion2002 () and even the readout back-action PRB:Schreier2008 (). In contrast, the microscopic atomic systems are characterized by precise quantum-state control and long coherence time (), though they own a relatively long gate operation time because of the weak coupling to external fields PRL:Monroe1995 (); Nat:Monroe2002 (); PRL:Isenhower2010 (); RMP:Saffman2010 () and have limited scalability. Transmitting information between these two distinct quantum realizations could lead to the rapid processing and long-term storage of quantum states, where the SC circuits serve as the fast processor while the atoms play the role of memory AnnuRevCondensMatterPhys:Daniilidis2013 (); PNAS:Kurizkia2015 (); PRA:Petrosyan2009 ().
The SC circuits and atoms can be indirectly coupled by integrating both of them on a microwave SC cavity, such as a LC resonator or a coplanar waveguide (CPW) resonator, which acts as a data bus to transfer the quantum information between the atomic memory and the SC processor PRL:Maitre1997 (); RMP:Raimond2001 (); Nature:Wallraff2004 (); Nature:Majer2007 (). However, the large detunings of the off-resonance SC qubit-resonator and atom-resonator interactions significantly weaken the virtual-photon-mediated SC qubit-atom coupling. Moreover, the fluctuation of intraresonator photon number increases the dephasing rate of qubits PRB:Rigetti2012 ().
The atoms can also directly talk to the SC devices via interacting with the local electromagnetic field. The current relevant research mainly focuses on the information transmission between neutral atoms and flux qubits, where the low-lying atomic states couple to the microwave-frequency alternating magnetic field from SC loops RevMexFis:Hoffman2011 (); PRA:Patton2013 (). Although replacing a single atom by an ensemble of atoms can enhance the magnetic intersubsystem coupling by a factor of , the atomic number fluctuation and the interparticle interaction challenge the experimental implementation. These issues may be solved by employing the electric dipole interface between the highly-excited Rydberg atomic states and local electric field from SC devices PRA:Yu2016 ().
Here, we propose a hybrid scheme, where a charge qubit is electrically coupled to an atomic qubit comprised of the ground and Rydberg states. The neutral atom placed inside the gate capacitor acts as the dielectric medium and affects the gate capacitance, resulting in the modulated charge-qubit energy bands. In addition, the local quasi-static electric field strongly depends on the charge-qubit state, leading to different DC Stark shifts of atomic-qubit states. We show that an arbitrary quantum state can be transmitted between these two distinct qubits. The two-qubit controlled-NOT (CNOT) logic gate and single-qubit Hadamard transform, which are necessary to entangle two qubits with different species and induce a -rotation of the control qubit, respectively, in the state-transmission protocol, can be implemented by means of standard spectroscopic techniques and sweeping the gate charge bias. Our state-transmission protocol also provides a potential for transferring the quantum state between or remotely entangling two distant noninteracting SC qubits via the flying-qubit-linked atoms.
RESULTS
Charge qubit-atom Hybrid. We consider a simple SC charge qubit PRL:Nakamura1997 (); PhysScripta:Bouchiat1998 (); Nature:Nakamura1999 (), where a single Cooper pair box (CPB) is connected to a SC reservoir via a JJ with a low self-capacitance (see Fig. 1a). The Cooper pairs can tunnel into or out of the box at a rate of (the magnetic flux quantum and the critical current of JJ). The CPB is biased by a voltage source via a parallel-plate capacitor with the plate area and the interplate separation . The Hamiltonian describing the dynamics of excess Cooper pairs in the box is written as
Hc=EC(N−Ng)2−EJ2(eiδ+e−iδ), (1)
where gives the Coulomb charging energy, is the offset charge, and is the phase drop across the JJ. The operator counts the number of excess Cooper pairs in the box, . Around the charge-degenerate spot (), two lowest charge states and are well separated from others and implement the charge qubit. We have omitted the work done by the gate voltage, whose effect on the system can be neglected.
A Rb atom placed inside the gate capacitor interacts with the internal electric field and plays a role of dielectric medium. The direction of is chosen as the the quantization axis. Two hyperfine ground states and with an energy spacing of 6.8 GHz are applied to form an atomic qubit (see Fig. 1b), where is the total angular momentum quantum number and gives the corresponding projection along the -axis. The qubit-state flipping of the atom is achieved by the resonant Raman transition via the intermediate state. A highly-excited Rydberg state is employed as an auxiliary state to enhance the charge qubit-atom interaction. In comparison with and , the hyperfine splitting of , which is of the order of several MHz PRA:Tauschinsky2013 (), can be neglected. Here denotes the principle quantum number of Rydberg atom. A resonant -laser pulse at 297 nm transfers the atomic component in or completely to .
The Cooper-pair tunneling through the JJ varies the internal electric field with a frequency typically of the order of (the reduced Planck’s constant ). The energy spacings of any electric-dipole transitions associated with are much larger than . Thus, can be treated as quasi-static. In the weak-field limit, the capacitance with the atom in is expressed as , where gives the empty gate capacitance (without the atom), is the vacuum permittivity, denotes the static polarizability of the atom in , and is the volume of homogeneous atomic distribution over the gate capacitor.
According to , the Coulomb energy , the offset charge , and the internal electric field are rewritten as , , and JLowTempPhys:Pekola2012 (), respectively, where the empty charging energy , the empty gate charge bias , , and the field amplitude . The ratio measures the relative variation of the total box capacitance caused by the single atom. A large reduces but enhances . Combining the energy associated with the atom, the system Hamiltonian is given by
H=∑u=a,b,r(H(u)c+ℏωu+ΔEu)Pu, (2)
where denotes the SC-circuit Hamiltonian with the atom in , is the intrinsic atomic energy of , indicates the DC Stark shift of induced by the electric field , and is the atomic projection operator. We restrict ourselves within the Hilbert space spanned by and obtain a hybrid system consisting of a charge qubit ( and ) and an atomic qubit ( and ). The auxiliary Rydberg state enables the strong interface between SC circuit and atom. Diagonalizing gives us the eigenvalues and eigenstates of the hybrid system,
Hψ(u)k=E(u)kψ(u)k, (3)
with denoting the different energy bands for a given .
For the zero gate voltage , we have and the hybrid-system eigenenergies are analytically derived as
E(u=a,b,r)k=0,1 = ℏωu+12(E(u)C+ΔEu)−(−1)k12√(E(u)C+ΔEu)2+E2J, (4)
and the corresponding eigenstates are given by
ψ(u=a,b,r)k=0,1=EJ|u,0⟩+(E(u)k−ℏωu)|u,1⟩√E2J+(E(u)k−ℏωu)2. (5)
In the limit of , we are left with , , , and . For the atom in the hyperfine ground states , whose static polarizabilities Hz/(V/cm) Book:Miller2000 () are extremely small, we obtain , , , and , meaning the atom hardly affects the SC circuit. Thus, the energy difference between and approximates to the intrinsic energy spacing , i.e., , while the energy separation between and is shifted away from , i.e., . Similarly, we have and .
Distinguishing the system energy spectrum with the atom in from that associated with , a large is necessary to induce the apparent variations of and compared with the small Josephson energy and the ratio , respectively, as well as a strong DC Stark shift . Thus, the SC circuit should be carefully designed and the Rydberg state needs to be chosen accordingly. As a specification, we list the structure of CPB in Table 1.
When a Rydberg atom is brought into the vicinity of SC circuit, the inhomogeneous stray electric fields originating from the contaminations on the cryogenic surface are particular detrimental to the quantum hybrid system since they cause the unwanted energy-level shifts and destroy the atomic coherence. However, there might be ways to mitigate or circumvent the effects of stray electric fields. It has been shown that the direction of electric field produced by the adsorbates due to the chemisorption or physisorption depends on the material properties PRL:Chan2014 (). In principle, one can envision to pattern the surfaces with two materials which give rise to opposing dipole moments of adsorbates. Furthermore, as experimentally demonstrated in RPA:HermannAvigliano2014 (), the stray fields can be minimized by saturating the adsorbates film. The remaining uniform electric fields could be canceled by applying offset fields.
The extra measures of reducing the effects of stray fields possibly affect the performance of hybrid system in a different manner. One way to estimate the dependence of the coherence time of a qubit on the surface properties is to investigate the surface-dependent change of the -factor of a cavity. Only a few studies have been done so far investigating the superconducting cavity for various materials absorbed to the surface Knobloch:1998zt (). With the knowledge at hand, it is hard to estimate the effect of a physisorbed layer of rubidium or specific protective coatings on the superconducting system. Here we assume the resulting decoherence time of the atomic qubit close to the surface is much longer than that of the charge qubit. In the following, we discuss the quantum-state transfer between two different qubits.
State transmission from atom to SC circuit. Transferring an arbitrary qubit state from the atom to the charge qubit primarily relies on a two-qubit CNOT logic gate, where the state flipping of the charge qubit is conditioned on the atomic-qubit state, and a one-qubit Hadamard gate acting on the atom Book:Nielsen2000 (). For performing the CNOT operation, the polarizability of Rydberg state should be large enough that the atom is strongly coupled with the SC circuit. In addition, the corresponding internal electric field needs to be smaller than the first avoided crossing field of PRA:Sullivan1985 (). Based on the specification of CPB structure listed in Table 1, we choose , whose relevant physical parameters are derived from Thesis:Pritchard (); JPB:Low2012 (); JPB:Branden2010 () and also shown in Table 1.
We first consider the system energy spectrum. Figure 2a illustrates the shifted eigenenergies with versus the empty charge bias around . For and , are nearly same to that of a common charge qubit due to . An avoided energy-level crossing occurs at , where and approach each other with a minimal energy spacing of . The Cooper-pair tunneling takes effect only around the charge-degenerate point within a narrow region Vion2004 (). In contrast, the energy bands move down relative to with due to the enhanced and large DC Stark shift . The minimal separation between and , however, is still determined by the Josephson energy . The position of the corresponding energy-level anticrossing shifts to the left side of because of the enlarged offset charge . At either avoided crossing, the hybrid system stays in the superposition states and with . We also show the expectation values of excess Cooper-pair numbers, , in Fig. 2b and find that two charge-degenerate spots are separated by larger than the ratio , indicating the shifted energy spectra with the atom in and can be well distinguished.
The dependence of the avoided-level crossing on the atomic state allows us to control the charge-qubit transition via preparing the atom in different states. Setting the empty charge bias at , the hybrid system resonantly oscillates between and with a half period (-pulse duration) of ns while the transitions with are strongly suppressed due to the large detuning as shown in Fig. 2c, where the master equation involving the relaxation and dephasing of charge qubit PRA:Boissonneault2009 () is employed. It is seen that the probability of the system switching between and reaches 0.93 at .
The two-qubit CNOT gate, where the atom acts as the control qubit while the charge qubit plays the target role, can be implemented via three steps: (1) Initially, the gate voltage stays at zero, . Two -light pulses (the time duration ) at 297 nm are applied resonantly on the and transitions to transfer the populations in and completely to and , respectively. Thus, different components and are spectroscopically discriminated (Fig. 2a). (2) The empty charge bias nonadiabatically raises to the charge-degenerate point for two adiabatic energy curves associated with and , i.e., . After staying at this sweet spot for the -pulse duration of , decreases back to zero nonadiabatically. As a result, the populations in and switches with each other while that in and do not change. (3) The -light pulses are used again to bring the populations in and back to and , respectively, without affecting the components of and .
In steps (1) and (3), the intensities of the light pulses need to be strong enough to reduce the pulse duration shorter than the decoherence time of the charge qubit. The experimentally feasible light-pulse length can be as small as 1 ns with a corresponding effective Rabi frequency of the order of 1 GHz PRL:Huber2011 (). However, for such a strong atom-light interaction, the small fine-structure splitting between and , i.e., GHz PRA:Li2003 (), affects the atom transfer between and . To suppress the unwanted population in , the -pulse length should be chosen to fit the experimental conditions. According to Fig. 2d, can be set at 1 ns, much shorter than the decoherence time of the charge qubit, with the corresponding Rabi frequency of GHz. The resulting atom-transfer efficiency is over 0.96. Due to the large ground-state hyperfine splitting of GHz, the light pulses hardly affect the components of and .
We numerically simulate the CNOT operation with different and states via applying the master equation PRA:Boissonneault2009 (). The whole gate operation duration is less that 2.5 ns. The resulting register populations are depicted in Fig. 2e based on the specification. It is seen that the quantum logic gate preserves the charge-qubit states when the atom is prepared in , whereas for the atom in the charge-qubit state switches between and with high probabilities. The standard process fidelity PRA:Gilchrist2005 (); PRA:Bongioanni2010 () reaches .
After performing the CNOT gate, the transmission of quantum state from the atom to SC circuit is straightforward. We assume that the atomic qubit is initially in an arbitrary state while the charge qubit is prepared in , leading to the system state (see Fig. 2e). Passing through the CNOT gate, the system state becomes . Then, a single-qubit Hadamard gate acts on the atom and the hybrid system arrives at . Afterwards, we measure the atomic-qubit state and obtain or depending on the readout which triggers an extra Pauli- (phase-flip) gate JPA:Obada2012 () acting on the SC device. As a result, the final charge qubit is in and the quantum-state transmission is accomplished.
The Hadamard gate for atomic qubit can be performed via the pulsed two-photon Raman process with a Raman detuning and a Raman coupling strength (see Fig. 1b). After adiabatically eliminating the state, one obtains an effective light-driven two-state ( and ) system with the detuning and the Rabi frequency . Choosing and the light-pulse length leads to the time evolution operator of the atom . The operator maps the atomic states and onto and , respectively, achieving the Hadamard transformation.
State transmission from SC circuit to atom. Similarly, the protocol for transferring an arbitrary charge-qubit state to the atom relies on a two-qubit CNOT gate, where the atom flips its state conditioned on the charge-qubit state, and a one-qubit Hadamard gate acting on the SC circuit. We first consider the CNOT operation. The gate voltage is set at zero, resulting in . A large atomic polarizability for , which leads to a strong DC Stark shift , is necessary for spectroscopic distinguishing four , , , and transitions. However, the single-qubit Hadamard operation on the charge qubit, which is performed via adiabatically sweeping from 0 to 0.5, requires that the charge-degenerate spots with the atom in different states approximately locate at , i.e., . Hence, should not be very large. As an example, we employ , whose relevant physical parameters are listed in Table 1. The corresponding approximates zero, indicating the very weak effect of the atom in on the SC circuit, and the avoided crossing between and occurs at . Moreover, at the energy spacings of different transitions are , , , and . For our physical specification, the DC Stark shift of reaches GHz. A -laser pulse resonant to the transition switches the atomic state between and and keeps the charge qubit in , but this pulse weakly interacts with the transition due to the detuning , which is applicable to the CNOT operation.
The two-qubit CNOT gate, where the charge qubit plays the control role while the atom acts as the target qubit, can be simply implemented via three steps (see Fig. 3a): (1) Two -light pulses with the pulse duration are applied resonantly on the and transitions to transfer the atomic population in completely to . (2) A -light pulse with the pulse length is employed to resonantly couple to the transition. The atomic state is flipped between and when the charge qubit is in . By contrast, the populations in and are weakly affected. (3) Two -light pulses with the duration are applied again to map the atomic component in back onto . The extra phase acquired in the gate operation can be canceled by the local operations on the atom PRL:Jaksch2000 ().
The fine-structure splitting between and is GHz PRA:Li2003 (). To suppress the influence of on the atom transfer between and in steps (1) and (3), the -light pulse duration is chosen to be ns, much shorter than the decoherence time of the SC circuit, with the corresponding Rabi frequency of GHz (see Fig. 3b). In step (2), the limited frequency difference between two and transitions extends the -pulse length and, hence, the the relaxation and dephasing of charge qubit reduces the fidelity of two-qubit logic gate as shown in Fig. 3b. We set ns to obtain the optimal CNOT truth table (see Fig. 3c). The total gate duration is ns and the resulting process fidelity is .
After performing the CNOT gate, one can transmit an arbitrary charge-qubit state to the atom via the following three steps (see Fig. 3c): (1) CNOT operation: The hybrid system is initially prepared in at . After the CNOT gate, we arrive at the system state . (2) Hadamard transform: The offset charge is increased to 0.5 adiabatically. Two components and in follow the adiabatic energy bands and , respectively. Actually, it is unnecessary to maintain the sweep rate of constantly from 0 to 0.5. Initially, adiabatically raises from 0 at a large rate. When approaches to 0.5, the sweep rate decreases to a relative low value. After the local operations for canceling the extra accumulated phases JPA:Obada2012 (), the system state becomes . (3) Projective measurement: We measure the excess Cooper pairs in the box. If the readout is 0, we conclude the system state , otherwise, . Then, the offset charge is reduced back to 0 rapidly. After an extra Pauli- operation performed on the atom PRL:Jaksch2000 (), we finally obtain the atomic-qubit state . Thus, the quantum-state transmission is accomplished.
DISCUSSION
The SC circuits operate much faster than the atomic systems. Transmitting the atomic-qubit state to the SC circuit allows the rapid quantum gate operations. Nevertheless, these solid-state devices lose the coherence on a short time scale compared with the atomic systems. Transmitting the quantum state from the SC qubits to the atoms allows a long-time storage. To achieve this reversible state-transmission, we have proposed a hybrid structure composed of a charge qubit and an atomic qubit. Placing the atom inside the gate capacitor results in the atomic-state-dependence energy bands of charge qubit and the charge-state-dependence DC Stark shifts of atomic-qubit states. Applying the standard spectroscopy techniques and sweeping the gate charge bias (gate voltage) enable the quantum-state transmission between two different qubits as well as the universal two-qubit quantum gates.
As is known, the strong coupling to the local electromagnetic environment leads to the short relaxation () and dephasing () times of SC circuits. For the common charge qubit discussed in this paper, the excess Cooper pairs in the box lose their coherence after about 10 ns PRL:Nakamura2002 (); PRB:Duty2004 (); PRA:Koch2007 (). Based on our physical specification, the state transmission can be accomplished within the coherence time of common charge qubit. Nonetheless, the relaxation effects of charge qubit still limit the fidelity of two-qubit gate operations.
In our hybrid system, the atom locates close to the gate-capacitor plates. The inhomogeneous Stark effect from the adsorbate electric fields on the cryogenic surface imposes a severe limitation to the coherence of Rydberg states, reducing the fidelity of state transmission PRL:Chan2014 (). However, the effects of stray fields might be circumvented via coating the surfaces with adsorbates RPA:HermannAvigliano2014 (). Moreover, measuring the distribution of stray fields above the chip surface based on Rydberg-electromagnetically-induced transparency PRA:Thiele2015 () provides a potential of canceling the uniform electric fields by offset fields. We expect the resulting coherence time of Rydberg atom much longer than that of charge qubit.
Our scheme for quantum state transmission in a superconducting charge qubit-atom hybrid opens a new prospect for quantum information processing, where the macroscopic SC devices rapidly process the quantum information which can be saved in the long-term storage composed of a microscopic atomic system. The protocols established in this paper also allow the information transfer between two distant SC qubits. After transmitting the quantum state of a SC qubit to a local atom, the quantum information encoded in this atom can be further transferred to another remote atom via a traveling qubit (photon) Nature:Moehring2007 (); Science:Hofmann2012 (); Nature:Bernien2013 (). Subsequently, the quantum state is transmitted to another distant SC interacting with the remote atom. Moreover, transmitting the quantum states of two entangled atoms to two distant SC qubits, respectively, results in a pair of remotely-entangled SC qubits.
Acknowledgments: This research is supported by the National Research Foundation Singapore under its Competitive Research Programme (CRP Award No. NRF-CRP12-2013-03) and the Centre for Quantum Technologies, Singapore.
Author Contributions: R.D. envisaged the concept of physical model. D.Y. did the calculation and analysis. D.Y. and M.M.V. provided the parameters of suitable Rydberg states. C.H. contributed the experimental realizable parameters. L.C.K., L.A., D.Y., and R.D. contributed the conceptual approach for analyzing the presented system. All authors participated in discussions and writing of the text.
Competing financial interests: The authors declare no competing financial interest.
### Footnotes
1. thanks: Correspondence and requests for material should be addressed to R.D. (email: rdumke@ntu.edu.sg).
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The feedback must be of minimum 40 characters and the title a minimum of 5 characters | 2021-01-19 02:06:53 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8579447865486145, "perplexity": 1990.0396856380446}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703517559.41/warc/CC-MAIN-20210119011203-20210119041203-00747.warc.gz"} |
http://ckms.kms.or.kr/journal/view.html?doi=10.4134/CKMS.c200172 | - Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
Degenerate polyexponential functions and poly-Euler polynomials Commun. Korean Math. Soc. 2021 Vol. 36, No. 1, 19-26 https://doi.org/10.4134/CKMS.c200172Published online September 11, 2020Printed January 31, 2021 Burak Kurt Akdeniz University Abstract : Degenerate versions of the special polynomials and numbers since they have many applications in analytic number theory, combinatorial analysis and $p$ -adic analysis. In this paper, we define the degenerate poly-Euler numbers and polynomials arising from the modified polyexponential functions. We derive explicit relations for these numbers and polynomials. Also, we obtain some identities involving these polynomials and some other special numbers and polynomials. Keywords : Bernoulli, Euler and Genocchi polynomials and numbers, the gegenerate Stirling numbers of both kind, degenerate Bernoulli, degenerate Euler and degenerate Genocchi polynomials, polyexponential functions, modified degenerate poly-Bernoulli polynomials, modified degenerate poly-Genocchi polynomials MSC numbers : Primary 11B68, 11B73, 11B83, 05A19 Supported by : The present investigation was supported by the Scientific Research Project Administration of the University of Akdeniz. Downloads: Full-text PDF | 2021-01-28 05:25:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33335232734680176, "perplexity": 2588.389308987262}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704835901.90/warc/CC-MAIN-20210128040619-20210128070619-00586.warc.gz"} |
https://paperswithcode.com/paper/wireless-communication-based-on-microwave | # Wireless Communication Based on Microwave Photon-Level Detection With Superconducting Devices: Achievable Rate Prediction
Future wireless communication system embraces physical-layer signal detection with high sensitivity, especially in the microwave photon level. Currently, the receiver primarily adopts the signal detection based on semi-conductor devices for signal detection, while this paper introduces high-sensitivity photon-level microwave detection based on superconducting structure. We first overview existing works on the photon-level communication in the optical spectrum as well as the microwave photon-level sensing based on superconducting structure in both theoretical and experimental perspectives, including microwave detection circuit model based on Josephson junction, microwave photon counter based on Josephson junction, and two reconstruction approaches under background noise. In addition, we characterize channel modeling based on two different microwave photon detection approaches, including the absorption barrier and the dual-path Handury Brown-Twiss (HBT) experiments, and predict the corresponding achievable rates. According to the performance prediction, it is seen that the microwave photon-level signal detection can increase the receiver sensitivity compared with the state-of-the-art standardized communication system with waveform signal reception, with gain over $10$dB.
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Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers. | 2023-03-28 20:58:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3063671588897705, "perplexity": 3182.4823394963864}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948871.42/warc/CC-MAIN-20230328201715-20230328231715-00474.warc.gz"} |
http://wpressutexas.net/coursewiki/index.php?title=Segment_13_Sanmit_Narvekar | # Segment 13 Sanmit Narvekar
## Segment 13
#### To Calculate
1. With p=0.3, and various values of n, how big is the largest discrepancy between the Binomial probability pdf and the approximating Normal pdf? At what value of n does this value become smaller than $\displaystyle 10^{-15}$ ?
2. Show that if four random variables are (together) multinomially distributed, each separately is binomially distributed.
Consider 4 random variables with number of occurrences $\displaystyle A, B, C, D$ and probabilities of occurrence $\displaystyle P_A, P_B, P_C, P_D$ respectively, such that $\displaystyle A + B + C + D = n$ and $\displaystyle P_A + P_B + P_C + P_D = 1$ .
The multinomial distribution over these variables is (with some abuse of notation) given below (think about choosing the A spots for the first random variable, with some probability. Then choosing spots out of the ones remaining for the others, etc..):
$\displaystyle P(A, B, C, D) = \left( \binom{A+B+C+D}{A} (P_A)^A \left( \binom{B+C+D}{B} (P_B)^B \left( \binom{C+D}{C} (P_C)^C \binom{D}{D} (P_D)^D \right) \right) \right)$
Then, by repeatedly applying the binomial theorem:
$\displaystyle P(A, B, C, D) = \left( \binom{A+B+C+D}{A} (P_A)^A \left( \binom{B+(C+D)}{B} (P_B)^B (P_C + P_D)^{C+D} \right) \right)$
$\displaystyle P(A, B, C, D) = \binom{A+(B+C+D)}{A} (P_A)^A (P_B + P_C + P_D)^{B + C+D}$
And using our notation from above
$\displaystyle P(A, B, C, D) = \binom{n}{A} (P_A)^A (1-P_A)^{n-A}$
gives the familiar form of the binomial distribution, where one event is A, and the other event is not A (that is B or C or D). Similar calculations can be done for the others by changing the order in which you select spots for the variables.
1. The segment suggests that $\displaystyle A\ne T$ and $\displaystyle C\ne G$ comes about because genes are randomly distributed on one strand or the other. Could you use the observed discrepancies to estimate, even roughly, the number of genes in the yeast genome? If so, how? If not, why not?
2. Suppose that a Bayesian thinks that the prior probability of the hypothesis that "$\displaystyle P_A=P_T$ " is 0.9, and that the set of all hypotheses that "$\displaystyle P_A\ne P_T$ " have a total prior of 0.1. How might he calculate the odds ratio $\displaystyle \text{Prob}(P_A=P_T)/\text{Prob}(P_A\ne P_T)$ ? Hint: Are there nuisance variables to be marginalized over? | 2021-04-18 01:50:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 14, "math_score": 0.8560363054275513, "perplexity": 437.7703532450918}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038464146.56/warc/CC-MAIN-20210418013444-20210418043444-00401.warc.gz"} |
https://www.math.nyu.edu/dynamic/calendars/seminars/ams/3295/ | # Applied Math Seminar (AMS)
#### Interactions of Passive and Active Capillary Disks
Speaker: Daniel Harris, Brown University (host: Ristroph)
Location: TBA
Date: Friday, March 26, 2021, 2:05 p.m.
Synopsis:
In this talk, I will introduce capillary disks - hydrophobic disks at the capillary scale whose weight is supported on the fluid interface by virtue of hydrostatics and capillarity.
I will begin by presenting direct measurements of the attractive force between two capillary disks. It is well known that objects at a fluid interface may interact due to the mutual deformation they induce on the free surface, however few direct measurements of such forces have been reported. In the present work, we characterize how the attraction force depends on the disk radius, mass, and relative spacing, and rationalize our findings with a scaling analysis.
When such disks are then deposited on a vibrating fluid bath, the relative vertical motion of the disk and the interface leads to the generation of outwardly propagating capillary waves. We demonstrate that when the rotational symmetry of an individual particle is broken, the particles can steadily self-propel along the interface and interact with each other via their collective wavefield, forming a myriad of cooperative dynamic states. Our discovery opens the door to further investigations of this active system with fluid-mediated interactions at intermediate Reynolds numbers.
Ongoing work and future directions will be discussed. | 2021-04-16 23:01:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3563291132450104, "perplexity": 1044.9429427886885}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038092961.47/warc/CC-MAIN-20210416221552-20210417011552-00485.warc.gz"} |
https://www.sierrachart.com/index.php?page=doc/StudiesReference.php&ID=190&Name=Color_Bar_Based_on_Slope | Login Page - Create Account
# Technical Studies Reference
### Color Bar Based on Slope
This study colors the chart bars according to whether or not the Subgraph of the study that this study is Based On has a positive or negative slope. When Based On is set to <Main Price Graph>, then the main price graph will be colored according to slope. This is useful when using the Line on Close Graph Draw Type.
Let $$X_t$$, $$C_t$$, and $$O_t$$ be the values of the Input Data Input, the Close Price, and the Open Price, respectively, at Index $$t$$. This study colors the chart bar at Index $$t$$ according to the following rules.
• If $$X_t = X_{t - 1}$$, then the study does not color the bar. Instead, the standard coloring is used (that is, green when $$C_t > O_t$$ and red when $$C_t < O_t$$). The standard coloring is automatically used for $$t = 0$$.
• If $$X_t > X_{t - 1}$$, then the entire main price graph bar is colored with the Primary Color of the study (the first color button of the Color Bar Subgraph).
• If $$X_t < X_{t - 1}$$, then the entire main price graph bar is colored with the Secondary Color of the study (the second color button of the Color Bar Subgraph).
For this study to work correctly, the Color Bar Subgraph Draw Style must be set to Color Bar.
If the Use +1 (+slope) and -1 (-slope) for Color Bar Values Input is set to Yes, then the output value is $$1$$ if $$X_t > X_{t - 1}$$, $$0$$ if $$X_t = X_{t - 1}$$, and $$-1$$ if $$X_t < X_{t - 1}$$. If this Input is set to No, then the output value is $$1$$ if $$X_t \neq X_{t - 1}$$ and $$0$$ if $$X_t = X_{t - 1}$$.
#### Inputs
• Input Data: This Input selects the Subgraph from the Based On study that you want to base the coloring on.
• Use +1 (+slope) and -1 (-slope) for Color Bar Values: When the slope is positive, the color bar value will be 1, and when it is negative the color bar value will be -1. | 2022-05-25 01:41:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5660753846168518, "perplexity": 821.2165498193418}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662577757.82/warc/CC-MAIN-20220524233716-20220525023716-00062.warc.gz"} |
https://socratic.org/questions/how-do-you-solve-x-2-5-73 | # How do you solve x^2-5=73?
Feb 17, 2017
See the entire solution process below:
#### Explanation:
Because this equation has no $x$ term we can solve directly for ${x}^{2}$. First, add $\textcolor{red}{5}$ to each side of the equation to isolate the ${x}^{2}$ ter while keeping the equation balanced:
${x}^{2} - 5 + \textcolor{red}{5} = 73 + \textcolor{red}{5}$
${x}^{2} - 0 = 78$
${x}^{2} = 78$
Now, take the square root of each side of the equation to solve for $x$ while keeping the equation balanced. Also remember, the square root of a number will have both a negative and positive answer:
$\sqrt{{x}^{2}} = \pm \sqrt{78}$
$x = \pm \sqrt{78} = \pm 8.832$ rounded to the nearest thousandth. | 2020-11-25 17:28:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 10, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7857100963592529, "perplexity": 250.9384371882843}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141183514.25/warc/CC-MAIN-20201125154647-20201125184647-00642.warc.gz"} |
https://www.aa.quae.nl/cgi-bin/glossary.cgi?l=en&o=AU | Astronomy Answers: From the Astronomical Dictionary
# Astronomy AnswersFrom the Astronomical Dictionary
$$\def\|{&}$$
The description of the word you requested from the astronomical dictionary is given below.
the AU or Astronomical Unit
An AU is very close to the average distance between the Sun and the Earth. Distances between the planets and the Sun are often expressed in AU. 1 AU equals about 93 million miles or about 150 million km. | 2019-02-21 00:09:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3061424493789673, "perplexity": 920.4635543623007}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247496855.63/warc/CC-MAIN-20190220230820-20190221012820-00230.warc.gz"} |
https://searchcode.com/file/309698/xbmc/visualizations/Vortex/angelscript/docs/doxygen/source/doc_adv_single_ref_type.h/ | http://github.com/xbmc/xbmc
C++ Header | 37 lines | 0 code | 0 blank | 37 comment | 0 complexity | b100c1edc82d209c8cc837552b73de46 MD5 | raw file
1/**
2
3\page doc_adv_single_ref_type Registering a single-reference type
4
5A variant of the uninstanciable reference types is the single-reference
6type. This is a type that have only 1 reference accessing it, i.e. the script
7cannot store any extra references to the object during execution. The script
8is forced to use the reference it receives from the application at the moment
9the application passes it on to the script.
10
11The reference can be passed to the script through a property, either global
12or a class member, or it can be returned from an application registered
13function or class method.
14
15The script engine will not permit declaration of functions that take this
16type as a parameter, neither as a reference nor as a handle. If that was allowed
17it would mean that a reference to the instance is placed on the stack, which
18in turn means that it is no longer a single-reference type.
19
20\code
21// Registering the type so that it cannot be instanciated
22// by the script, nor allow scripts to store references to the type
23r = engine->RegisterObjectType("single", 0, asOBJ_REF | asOBJ_NOHANDLE); assert( r >= 0 );
24\endcode
25
26This sort of type is most useful when you want to have complete control over
27references to an object, for example so that the application can destroy and
28recreate objects of the type without having to worry about potential references
29held by scripts. This allows the application to control when a script has access
30to an object and it's members.
31
32
33\see \ref doc_reg_basicref
34
35
36
37*/ | 2021-10-18 03:33:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.48237544298171997, "perplexity": 2504.2346613005066}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585196.73/warc/CC-MAIN-20211018031901-20211018061901-00393.warc.gz"} |
http://image.absoluteastronomy.com/topics/Ampere-turn | Ampere-turn
Encyclopedia
The ampere-turn was the MKS
Mks system of units
The MKS system of units is a physical system of units that expresses any given measurement using fundamental units of the metre, kilogram, and/or second ....
unit of magnetomotive force
Magnetomotive force
Magnetomotive force is any physical driving force that produces magnetic flux. In this context, the expression "driving force" is used in a general sense of "work potential", and is analogous, but distinct from force measured in newtons...
(MMF), represented by a direct current
Direct current
Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through...
of one ampere
Ampere
The ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...
flowing in a single-turn loop in a vacuum. "Turns
Turn (geometry)
A turn is an angle equal to a 360° or 2 radians or \tau radians. A turn is also referred to as a revolution or complete rotation or full circle or cycle or rev or rot....
" refers to the winding number
Winding number
In mathematics, the winding number of a closed curve in the plane around a given point is an integer representing the total number of times that curve travels counterclockwise around the point...
of an electrical conductor comprising an inductor.
The ampere-turn was replaced by the SI unit, ampere
Ampere
The ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...
.
For example, a current of 2A flowing through a coil of 10 turns produces an MMF of 20 AT.
Here we see that by maintaining the same current and simply increasing the number of loops or turns of the coil, the strength of the magnetic field increases. This is because each loop or turn of the coil sets up its own magnetic field, which unites with the fields of the other loops to produce the field around the entire coil. The more loops, the more magnetic fields unite and reinforce each other and, as a result, the total magnetic field becomes stronger.
The strength of the magnetic field is not linearly related to the ampere turns when a magnetic material is used as a part of the system. Also, the material within the magnet carrying the magnetic flux "saturates" at some point, when adding more ampere turns has little effect.
The ampere-turn is equal to gilbert
Magnetomotive force
Magnetomotive force is any physical driving force that produces magnetic flux. In this context, the expression "driving force" is used in a general sense of "work potential", and is analogous, but distinct from force measured in newtons...
s, the equivalent CGS unit. | 2022-05-23 03:02:07 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8144527077674866, "perplexity": 806.4756285653148}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662552994.41/warc/CC-MAIN-20220523011006-20220523041006-00694.warc.gz"} |
https://math.stackexchange.com/questions/670466/x-1-x-2-dots-x-n-are-i-i-d-rvs-uniformly-distributed-on-1-2-dots-n | $x_1,x_2,\dots,x_n$ are i.i.d RVs uniformly distributed on $\{1,2,\dots,N\}$. [duplicate]
Let $x_1,x_2,\dots,x_n$ be independent identically distributed random variables uniform on $\{1,2,\dots,N\}$, and let: $Y_n:=\text{the number of different elements in } \{x_1,x_2,\dots,x_n\}$.
Let $T:=\inf\{n:Y_n=N\}$.
What is $E\left[T\right]$?
marked as duplicate by joriki probability StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jun 18 '16 at 0:48
• What do you mean by $\inf\{n:Y_n=N\}$? – enthdegree Feb 10 '14 at 3:42
• The question is asking for the expected value of the random minimum sample size $T$ needed to be observed from a discrete uniform variable on $[1, N]$ such that every value in the support is observed. Clearly, ${\rm E}[T] \ge N$. – heropup Feb 10 '14 at 3:48
• @enthdegree the smallest n s.t. Yn=N.i.e. the first time we have N different elements in {x1,x2,...,xn}. – user98619 Feb 10 '14 at 3:50
• Get it now, thanks! – enthdegree Feb 10 '14 at 3:50
• @heropup You are right!Thank you for the explanation – user98619 Feb 10 '14 at 3:51
This question is commonly known as the coupon collector's problem. See here: http://en.wikipedia.org/wiki/Coupon_collector%27s_problem
• It is a good answer! – user98619 Feb 10 '14 at 4:18 | 2019-10-22 19:49:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4143301546573639, "perplexity": 2501.6863142745506}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987823061.83/warc/CC-MAIN-20191022182744-20191022210244-00301.warc.gz"} |
http://advancedintegrals.com/2017/01/nonlinear-euler-sum-proof-using-stirling-numbers-of-the-first-kind/ | # Nonlinear euler sum proof using stirling numbers of the first kind
Prove that
$$\sum_{k=1}^\infty \frac{(H_k)^2}{k^2} = \frac{17\pi^4}{360}$$
$$\textit{proof}$$
Start by the following which can be proved by induction
$$\frac{\left[n\atop 3\right]}{n!} =\frac{ (H_{n-1})^2-H^{(2)}_{n-1}}{2n}$$
And the generating function proved here
$$-\sum_{n=3}^\infty \left[n\atop 3\right] \frac{z^n}{n!} = \frac{\log^3(1-z)}{6}$$
Hence we get
$$\sum_{n=3}^\infty ( H^{(2)}_{n-1}- (H_{n-1})^2) \frac{z^n}{n}= \frac{\log^3(1-z)}{3}$$
Which implies that
$$\sum_{n=3}^\infty \frac{H^{(2)}_{n-1}- (H_{n-1})^2}{n^2}= \frac{1}{3}\int^1_0\frac{\log^3(1-z)}{z}\,dz$$
By integration
$$\sum_{n=3}^\infty \frac{(H_{n-1})^2}{n^2}=\sum_{n=3}^\infty \frac{H^{(2)}_{n-1}}{n^2}-\frac{1}{3}\int^1_0\frac{\log^3(1-z)}{z}\,dz$$
Rewritten as
$$\sum_{n=3}^\infty \frac{(H_{n})^2}{n^2}-2\sum_{n=3}^\infty \frac{H_n}{n^3}+\sum_{n=3}^\infty \frac{1}{n^4}=\sum_{n=3}^\infty \frac{H^{(2)}_{n-1}}{n^2}-\frac{1}{3}\int^1_0\frac{\log^3(1-z)}{z}\,dz$$
Finally we have
$$\sum_{n=3}^\infty \frac{(H_{n})^2}{n^2}=2\sum_{n=3}^\infty \frac{H_n}{n^3}-2\sum_{n=3}^\infty \frac{1}{n^4}+\sum_{n=3}^\infty \frac{H^{(2)}_{n}}{n^2}-\frac{1}{3}\int^1_0\frac{\log^3(1-z)}{z}\,dz$$
All sums are shifted known terms
$$\sum_{n=1}^\infty \frac{(H_{n})^2}{n^2}=\left(H^{2}_{1}+\frac{H^{2}_{2}}{4} \right)-2\left(H_1+\frac{H_2}{8} \right)+2\left(1+\frac{1}{16}\right)-\left(H^{(2)}_{1}+\frac{H^{(2)}_{2}}{4} \right) \\+2\sum_{n=1}^\infty \frac{H_n}{n^3}-2\zeta(4)+\sum_{n=1}^\infty \frac{H^{(2)}_{n}}{n^2}-\frac{1}{3}\int^1_0\frac{\log^3(1-z)}{z}\,dz$$
This simplifies to
$$\sum_{n=1}^\infty \frac{(H_{n})^2}{n^2}=2\sum_{n=1}^\infty \frac{H_n}{n^3}-2\zeta(4)+\sum_{n=1}^\infty \frac{H^{(2)}_{n}}{n^2}-\frac{1}{3}\int^1_0\frac{\log^3(1-z)}{z}\,dz$$
For the Euler sums we use
$$\sum_{n=1}^\infty \frac{H_n}{n^q}= \left(1+\frac{q}{2} \right)\zeta(q+1)-\frac{1}{2}\sum_{k=1}^{q-2}\zeta(k+1)\zeta(q-k)$$
And
$$\sum_{n= 1}^\infty \frac{H^{(k)}_n}{n^k}\, = \frac{\zeta{(2k)}+\zeta^{2}(k)}{2}$$
Then we have
$$\sum_{n=1}^\infty \frac{H_n^{(2)}}{n^2} = \frac{7\pi^4}{360}$$
And
$$\sum_{n=1}^\infty \frac{H_n^{(1)}}{n^3} = \frac{\pi^4}{72}$$
Finally we prove that
$$\int^1_0 \frac{\log^3(1-x)}{x}\,dx = -6\zeta(4)$$
Note that
$$\int^1_0 \frac{\log^3(1-x)}{x}\,dx = \sum_{n=0}^\infty \int^1_0 x^{n}\log^3(x)\,dx =-6\sum_{n=0}^\infty \frac{1}{(n+1)^4} = -6\zeta(4)$$
Collecting all the results we get our result
$$\sum_{n=1}^\infty \frac{(H_{n})^2}{n^2}=\frac{2\pi^4}{72}-2\zeta(4)+ \frac{7\pi^4}{360}+2\zeta(4) = \frac{17\pi^4}{360}$$
This entry was posted in Euler sum, Striling numbers of first kind and tagged , , , , , , , . Bookmark the permalink. | 2017-10-23 02:26:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9857420325279236, "perplexity": 2035.6346509929385}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187825510.59/warc/CC-MAIN-20171023020721-20171023040721-00790.warc.gz"} |
http://tex.stackexchange.com/questions/53372/how-can-i-render-a-large-number-of-tables-in-succession | # How can I render a large number of tables in succession?
In the following code an error
!h' float specifier changed to !ht
I think because my tables span multiple pages. How can I get them to display properly one after the other?
\documentclass{article}
\begin{document}
\section{Database Design}
\begin{table}[!h]
\centering
\begin{tabular}{ | l | l |}
\hline
Field & Type \\ \hline
id & Primary key \\ \hline
firstName & String \\ \hline
lastName & String \\ \hline
email & String \\ \hline
\end{tabular}
\caption{User2}
\end{table}
\begin{table}[!h]
\centering
\begin{tabular}{ | l | l |}
\hline
Field & Type \\ \hline
id & Primary key \\ \hline
firstName & String \\ \hline
lastName & String \\ \hline
email & String \\ \hline
\end{tabular}
\caption{User}
\end{table}
\begin{table}[!h]
\centering
\begin{tabular}{ | l | l |}
\hline
Field & Type \\ \hline
id & Primary key \\ \hline
title & String \\ \hline
postedAt & Date\\ \hline
email & String \\ \hline
author & Foreign key from 'User' table\\ \hline
tags & Foreign key from 'Tag' table\\ \hline
\end{tabular}
\caption{Post}
\end{table}
\begin{table}[!h]
\centering
\begin{tabular}{ | l | l |}
\hline
Field & Type \\ \hline
id & Primary key \\ \hline
author& String \\ \hline
content& String \\ \hline
postedAt & Date\\ \hline
post& Foreign key from 'Post' table\\ \hline
\end{tabular}
\caption{Comment}
\end{table}
\begin{table}[!h]
\centering
\begin{tabular}{ | l | l |}
\hline
Field & Type \\ \hline
id & Primary key \\ \hline
name & String
\end{tabular}
\caption{Tag}
\end{table}
\begin{table}[!h]
\centering
\begin{tabular}{ | l | l |}
\hline
id & Primary key \\ \hline
Field & Type \\ \hline
post& Foreign key from 'PostTag' table\\ \hline
tag& Foreign key from 'Tag' table\\ \hline
\end{tabular}
\caption{PostTag}
\end{table}
\end{document}
-
– Peter Grill Apr 26 '12 at 2:36
What does "properly one after the other" mean to you? Do you mind any text in between them, or do you just want the tables without anything in between? – Werner Apr 26 '12 at 6:21
When TeX cannot put the table [h]ere because it is on a page break, it will always switch to something else.
For this case, I guess that a good option is loading a package
\usepackage{float}
and then using the [H] position specifier (capital 'H') (cannot be used with other ones, cannot be used with !):
\begin{table}[H]
...
\end{table}
This specifier means:
• here and only here;
• move to the next page if the table does not fit here, and leave the current page short.
Generally, using [H] is frowned upon, but when a whole section comprises more-or-less only tables, it seems a reasonable solution.
-
If you need to output the tables at a particular place, without any other things sneaking in between them, do not use floats then.
Captions can be used even without floats, if one uses \captionof from the caption` package. See also this question Label and caption without float
- | 2014-12-21 11:32:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000097751617432, "perplexity": 5781.459987184957}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802771091.111/warc/CC-MAIN-20141217075251-00100-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/proc.2015.0176 | # American Institute of Mathematical Sciences
2015, 2015(special): 176-184. doi: 10.3934/proc.2015.0176
## Similarity reductions of a nonlinear model for vibrations of beams
1 Departament of Mathematics, University of Cdiz, Cadiz, Spain, Spain
Received September 2014 Revised October 2014 Published November 2015
In this paper we make a full analysis of the symmetry reductions of this equation by using the classical Lie method of infinitesimals. We consider travelling wave reductions depending on the constants. We present some reductions and explicit solutions.
Citation: Jose Carlos Camacho, Maria de los Santos Bruzon. Similarity reductions of a nonlinear model for vibrations of beams. Conference Publications, 2015, 2015 (special) : 176-184. doi: 10.3934/proc.2015.0176
##### References:
[1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions,, New York: Dover, (1972). Google Scholar [2] G. W. Bluman and J. D. Cole, The general similarity solution of the heat equation,, {\em J. Math. Mech.}, 18 (1969), 1025. Google Scholar [3] J.M. Ball, Initial boundary value problems for an extensible beam,, {\em J. Math. Analysis Appl.}, 42 (1973), 61. Google Scholar [4] G. W. Bluman and S. Kumei, Symmetries and differential equations,, Springer-Verlag, (1989). Google Scholar [5] E. Burgreen, Free vibrations of a pinended column with constant distance between pinendes,, {\em J. Appl. Mech}, 18 (1951), 135. Google Scholar [6] B. Champagne, W. Hereman, and P. Winternitz, The computer calculation of Lie point symmetries of large systems of differential equations,, {\it Com. Phys. Comm.}, 66 (1991), 319. Google Scholar [7] R. W. Dickey, Free vibrations and dynamics buckling of extensible beam,, {\em J. Math. Analysis Appl.} {\bf 29} (1970)., 29 (1970). Google Scholar [8] P. A. Djondjorov, Invariant properties of timoshenko beam equations,, {\em International Journal of Engineering Science}, 33 (1995), 2103. Google Scholar [9] J. G. Eisley, Nonlinear vibrations of beams and rectangular plates,, {\em Z. angew. Math. Phys.}, 15 (1964). Google Scholar [10] J. Ferreira, R. Benabidallah, and J. E. Mu{\ n}oz Rivera, Asymptotic behaviour for the nonlinear beam equation in a time-dependent domain,, {\em Rendiconti di Matematica, 19 (1999), 177. Google Scholar [11] L. A. Medeiros, On a new class of nonlinear wave equations,, {\em J. Math. Appl.}, 69 (1979), 252. Google Scholar [12] G. P. Menzala, On classical solutions of a quasilinear hyperbolic equation,, {\em Nonlinear Analysis}, 3 (1978), 613. Google Scholar [13] D. C. Pereira, Existence, uniqueness and asymptotic behaviour for solutions of the nonlinear beam equation,, {\em Nonlinear Analysis}, 14 (1990), 613. Google Scholar [14] O. C. Ramos, Regularity property for the nonlinear beam operator,, {\em An. Acad. Bras. Ci.}, 61 (1989), 15. Google Scholar [15] J. E. M. Rivera, Smoothness effect and decay on a class of non linear evolution equation,, {\em Ann. Fac. Sc. Toulouse}, (1992), 237. Google Scholar [16] P. J. Olver, Applications of Lie groups to differential equations,, Springer-Verlag, (1986). Google Scholar [17] S. K. Woinowsky, The effect of axial force on the vibration of hinged bars,, {\em Appl. Mech.}, 17 (1950), 35. Google Scholar
show all references
##### References:
[1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions,, New York: Dover, (1972). Google Scholar [2] G. W. Bluman and J. D. Cole, The general similarity solution of the heat equation,, {\em J. Math. Mech.}, 18 (1969), 1025. Google Scholar [3] J.M. Ball, Initial boundary value problems for an extensible beam,, {\em J. Math. Analysis Appl.}, 42 (1973), 61. Google Scholar [4] G. W. Bluman and S. Kumei, Symmetries and differential equations,, Springer-Verlag, (1989). Google Scholar [5] E. Burgreen, Free vibrations of a pinended column with constant distance between pinendes,, {\em J. Appl. Mech}, 18 (1951), 135. Google Scholar [6] B. Champagne, W. Hereman, and P. Winternitz, The computer calculation of Lie point symmetries of large systems of differential equations,, {\it Com. Phys. Comm.}, 66 (1991), 319. Google Scholar [7] R. W. Dickey, Free vibrations and dynamics buckling of extensible beam,, {\em J. Math. Analysis Appl.} {\bf 29} (1970)., 29 (1970). Google Scholar [8] P. A. Djondjorov, Invariant properties of timoshenko beam equations,, {\em International Journal of Engineering Science}, 33 (1995), 2103. Google Scholar [9] J. G. Eisley, Nonlinear vibrations of beams and rectangular plates,, {\em Z. angew. Math. Phys.}, 15 (1964). Google Scholar [10] J. Ferreira, R. Benabidallah, and J. E. Mu{\ n}oz Rivera, Asymptotic behaviour for the nonlinear beam equation in a time-dependent domain,, {\em Rendiconti di Matematica, 19 (1999), 177. Google Scholar [11] L. A. Medeiros, On a new class of nonlinear wave equations,, {\em J. Math. Appl.}, 69 (1979), 252. Google Scholar [12] G. P. Menzala, On classical solutions of a quasilinear hyperbolic equation,, {\em Nonlinear Analysis}, 3 (1978), 613. Google Scholar [13] D. C. Pereira, Existence, uniqueness and asymptotic behaviour for solutions of the nonlinear beam equation,, {\em Nonlinear Analysis}, 14 (1990), 613. Google Scholar [14] O. C. Ramos, Regularity property for the nonlinear beam operator,, {\em An. Acad. Bras. Ci.}, 61 (1989), 15. Google Scholar [15] J. E. M. Rivera, Smoothness effect and decay on a class of non linear evolution equation,, {\em Ann. Fac. Sc. Toulouse}, (1992), 237. Google Scholar [16] P. J. Olver, Applications of Lie groups to differential equations,, Springer-Verlag, (1986). Google Scholar [17] S. K. Woinowsky, The effect of axial force on the vibration of hinged bars,, {\em Appl. Mech.}, 17 (1950), 35. Google Scholar
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[Back to Top] | 2019-09-17 04:32:42 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9403810501098633, "perplexity": 7199.147047360203}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573052.26/warc/CC-MAIN-20190917040727-20190917062727-00099.warc.gz"} |
https://proxies-free.com/a-sufficient-condition-for-an-ergodic-system-to-be-weak-mixing/ | A sufficient condition for an ergodic system to be weak mixing
Let $$mathbf X := (X, mathcal S, mu, T)$$ be an ergodic measure preserving system with finite measure such that for every increasing sequence $${n_k}$$ of natural numbers with positive lower density, we have
$$frac{1}{N} sum_{i=0}^{N-1} f(T^{n_i} x) to int_X f dmu$$
as $$n to infty$$.
Question: Is $$mathbf X$$ necessarily weak mixing? | 2021-07-23 16:44:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8872288465499878, "perplexity": 106.02337516798187}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046149929.88/warc/CC-MAIN-20210723143921-20210723173921-00560.warc.gz"} |
https://www.fachschaft.informatik.tu-darmstadt.de/forum/viewtopic.php?f=300&t=40938&p=182124 | ## Assigment 6: TryDeref on Box?
Moderator: Konzepte der Programmiersprachen
johanneslauinger
Erstie
Beiträge: 11
Registriert: 5. Dez 2016 23:41
### Assigment 6: TryDeref on Box?
Hi,
I see from the tests that TryDeref shall derefence WeakRefV values, if possible. What if TryDeref is used on a Box value? Should it derefence it too, or rather cause an error?
Kind regards,
Johannes
eustro
Neuling
Beiträge: 10
Registriert: 17. Okt 2019 19:17
### Re: Assigment 6: TryDeref on Box?
You mean to call TryDeref directly on a new Box or a reference to a Box instead?
The latter should be possible, since we should be able to construct weak references to any construct of the language (if the reference was a WeakRef in the first place).
This test for example should be possible:
Code: Alles auswählen
test("WeakRef to NewBox and OpenBox") {
assertResult(NumV(1)) {
val (res, _) = interp(Let('a, WeakRef(NewBox(1)), OpenBox(TryDeref('a, 23))))
res
}
}
I noticed that several of the tests do not use WeakRefs at all, so I am not sure what their purpose is. For instance all tests that should test WeakRefs on boxes and boxes that contain WeakRefs do in fact not use WeakRefs (I also looked at the newest template version, am I missing something here?). I made my own tests for that, at least a couple.
I hope there is useful information for you.
Best,
Eugen
eustro
Neuling
Beiträge: 10
Registriert: 17. Okt 2019 19:17
### Re: Assigment 6: TryDeref on Box?
Here another test case where a WeakRef is bound (or rather rebound) to a box via SetId expression:
Code: Alles auswählen
test("NewBox for WeakRef and OpenBox") {
assertResult(NumV(0)) {
val (res, _) = interp(
Let('b, -47098,
If0(Seqn(SetId('b, WeakRef(NewBox(0))), OpenBox(TryDeref('b, 23))),
OpenBox(TryDeref('b, 23)),
'b)))
res
}
}
johanneslauinger
Erstie
Beiträge: 11
Registriert: 5. Dez 2016 23:41
### Re: Assigment 6: TryDeref on Box?
Thanks for the answers! With my question I tried to refer to use TryDeref directly on a Box value, in which case it would work exactly like OpenBox. See the test case here:
Code: Alles auswählen
test("TryDeref on a Box value") {
assertResult(NumV(1)) {
val (res, _) = interp(Let('a, NewBox(1), TryDeref('a, 23)))
res
}
}
I thought this would maybe make sense because a Box is also a bit like a reference to something, so TryDeref might turn it into the value located in the box. Based on your answer I now assume TryDeref should only dereference WeakRefV values.
eustro
Neuling
Beiträge: 10
Registriert: 17. Okt 2019 19:17
### Re: Assigment 6: TryDeref on Box?
I think the exercise doesn't account for that use case, but good point, I didn't think of that!
You could also use TryDeref on regular references to NumV and Closure as well. You would need to decide if you want to replicate the bahavior of a normal Ref and throw an error, if it does not exist or supply it with a fallback expression to evaluate to.
Another point could be something like TryDeref( WeakrefV(WeakrefV(WeakrefV(...))) ).
I did it the simple way: Throw an error if the expression evaluates to something different than WeakrefV | 2020-09-18 17:58:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4175804853439331, "perplexity": 6625.48981124331}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400188049.8/warc/CC-MAIN-20200918155203-20200918185203-00529.warc.gz"} |
https://oar.princeton.edu/handle/88435/pr10g3gx97 | # Self-calibration of BICEP1 three-year data and constraints on astrophysical polarization rotation
## Author(s): Kaufman, JP; Miller, NJ; Shimon, M; Barkats, D; Bischoff, C; et al
To refer to this page use: http://arks.princeton.edu/ark:/88435/pr10g3gx97
Abstract: Cosmic microwave background (CMB) polarimeters aspire to measure the faint B-mode signature predicted to arise from inflationary gravitational waves. They also have the potential to constrain cosmic birefringence, rotation of the polarization of the CMB arising from parity-violating physics, which would produce nonzero expectation values for the CMB's temperature to B-mode correlation (TB) and E-mode to B-mode correlation (EB) spectra. However, instrumental systematic effects can also cause these TB and EB correlations to be nonzero. In particular, an overall miscalibration of the polarization orientation of the detectors produces TB and EB spectra which are degenerate with isotropic cosmological birefringence, while also introducing a small but predictable bias on the BB spectrum. We find that BICEP1 three-year spectra, which use our standard calibration of detector polarization angles from a dielectric sheet, are consistent with a polarization rotation of alpha = -2.77 degrees +/- 0.86 degrees (statistical) +/- 1.3 degrees (systematic). We have revised the estimate of systematic error on the polarization rotation angle from the two-year analysis by comparing multiple calibration methods. We also account for the (negligible) impact of measured beam systematic effects. We investigate the polarization rotation for the BICEP1 100 GHz and 150 GHz bands separately to investigate theoretical models that produce frequency-dependent cosmic birefringence. We find no evidence in the data supporting either of these models or Faraday rotation of the CMB polarization by the Milky Way galaxy's magnetic field. If we assume that there is no cosmic birefringence, we can use the TB and EB spectra to calibrate detector polarization orientations, thus reducing bias of the cosmological B-mode spectrum from leaked E-modes due to possible polarization orientation miscalibration. After applying this "self-calibration" process, we find that the upper limit on the tensor-to-scalar ratio decreases slightly, from r < 0.70 to r < 0.65 at 95% confidence. Publication Date: 24-Mar-2014 Electronic Publication Date: 15-Mar-2014 Citation: Kaufman, JP, Miller, NJ, Shimon, M, Barkats, D, Bischoff, C, Buder, I, Keating, BG, Kovac, JM, Ade, PAR, Aikin, R, Battle, JO, Bierman, EM, Bock, JJ, Chiang, HC, Dowell, CD, Duband, L, Filippini, J, Hivon, EF, Holzapfel, WL, Hristov, VV, Jones, WC, Kernasovskiy, SS, Kuo, CL, Leitch, EM, Mason, PV, Matsumura, T, Nguyen, HT, Ponthieu, N, Pryke, C, Richter, S, Rocha, G, Sheehy, C, Su, M, Takahashi, YD, Tolan, JE, Yoon, KW. (2014). Self-calibration of BICEP1 three-year data and constraints on astrophysical polarization rotation. PHYSICAL REVIEW D, 89 (6), 10.1103/PhysRevD.89.062006 DOI: doi:10.1103/PhysRevD.89.062006 ISSN: 1550-7998 Type of Material: Journal Article Journal/Proceeding Title: PHYSICAL REVIEW D Version: Final published version. Article is made available in OAR by the publisher's permission or policy.
Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated. | 2022-05-27 07:00:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5375588536262512, "perplexity": 12140.411825851048}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662636717.74/warc/CC-MAIN-20220527050925-20220527080925-00321.warc.gz"} |
https://electronics.stackexchange.com/questions/394589/how-hot-should-wires-get | # How hot should wires get?
I am using 10 AWG wire to power a BLDC motor, and these wires can get quite hot. When an IC is intended for high power uses, it is common practice to put a heat sink on it, but what about for wires? Should I simply use a thicker gauge wire?
• The question in the title is different from the question in the question. – immibis Sep 6 '18 at 5:49
• HINT: The insulation of a wire depends on whether it burns or just gets hot. Cheap PVC insulation melts and burns at a low temperature. THHN wire tolerates more heat per given wire gauge. With Teflon insulation you might be able to double the amp rating of the wire, but a lot of other factors come into play. – Sparky256 Sep 6 '18 at 6:00
• Any heat in the cable is wasted energy... – Solar Mike Sep 6 '18 at 6:01
• Are the wires getting hot along their entire length or just at the connectors? – Andrew Morton Sep 6 '18 at 13:16
How hot should wires get?
How how wires should get depends on application, but there are benefits to keeping just about any device other than a heater cool. The question ends up being more "How much weight and expense is it worth adding to decrease wasted power?" in the end.
I am using 10 AWG wire to power a BLDC motor, and these wires can get quite hot.
If wires are getting "quite hot" you're wasting a significant amount of electricity. Specifically, wires get hot because of $I^2R$ losses, which is to say the power the wire uses to produce heat, $P$, is equal to current squared($I^2$) times resistance ($R$). If you can measure or calculate current, you can choose a wire size with appropriately low losses. You can also measure the existing wire and calculate its resistance if you don't have a meter. As a general rule, going down 3 AWG sizes doubles wire size and halves resistance. AWG sizes step mostly in increments of 2, but that's beside the point. The calculation of resistance based on cross sectional area measured or from a chart is easy as well. In AC systems, inductive loads, such as motors produce current out of phase with the voltage (reactive current) and in some cases (probably not yours) it is worth using power factor correction to reduce reactive current on transmission lines.
When an IC is intended for high power uses, it is common practice to put a heat sink on it, but what about for wires?
In almost every case short of superconductors it is more practical to use a larger wire and waste less energy as heat than add weight in the form of a cooling system. When space is an object, though, such as in a motor or electromagnet, microprocessor, it becomes more likely that a cooling system might be used, even if what's producing the heat are conductors.
Should I simply use a thicker gauge wire?
Yeppers. If you calculate the current, take into account if they are in free air or a closed space and look at the appropriate DC wire ampacity chart, you can round the current up to the nearest size, apply a derating factor if necessary (a multiplier to decrease the acceptable current for a wire based on factors like ambient temperature) and choose the recommended size of wire for your current. If you have a substantial length of wire you may wish to take voltage drop into account as well.
If you don't have means to measure or calculate the current, you can at the very least massively improve your setup by embiggening or doubling up the wire until it no longer becomes warm.
• Multiple wires is also a plausible solution, is it not? This might be preferred in certain cases where space/layout is a consideration. – John Go-Soco Sep 6 '18 at 10:35
• "embiggening" nice word. And good advice. I wish you would have say wires should not get hot, Period. – Misunderstood Sep 8 '18 at 17:12
• @Misunderstood yeah, almost everything gets turned into a word these days =). Heating elements are wires that should get hot, as are... Hmmm is there no wire other than a heating element that should get hot come to think of it? – K H Sep 8 '18 at 18:03
If you are worried about the cables overheating, check the manufacturer's data sheet. PVC insulated cables are usually good for 70°C. Other plastics can handle 90°C. Specialist mineral insulated cables will go higher still.
But if you are running cables very hot, also check the temperature ratings of whatever they are terminated at (the switch, terminal block or whatever).
How hot should wires get?
Wires should never get hot. Not even a little warm.
No more than a few degrees over ambient.
Should I simply use a thicker gauge wire?
Thicker and or add more wires.
it is common practice to put a heat sink on it, but what about for wires?
No. Use more and or thicker wire.
Here's the thing. If a wire is getting warm during normal operation there is no safety margin for when things go wrong and more current is drawn. Be cool.
you need to know how much current is flowing in your system, then choose the right wire size.
There are tables like this one to pick the right AWG size. Due to the $I^2 R$ a thicker wire will have less power loss.
There are two limitations to the conductor size. One is the voltage drop, and often it is the limiting factor, but that's outside the scope of your question.
The second is the temperature rise, more specifically the temperature rise at the highest ambient temperature which translates into the maximum conductor temperature.
The temperature rise is affected by many factors besides the wire resistance (which increases at high temperatures a bit so things get slightly worse) and RMS current. The bundling with other conductors, the altitude, the air flow, even the length of the wire for short fat wires. The upper limit is set by the insulation rating or the maximum temperature the designer will permit, if less.
So in aircraft where weight is important we might use a PTFE/Kapton insulated wire that is rated for 200°C and it can actually be allowed to get that hot worst case. Cheap wire is more normally 90°C or thereabouts. So the ampacity of a given gauge of wire can vary wildly. Here is a marine chart from this web page showing allowable amperage varying over a 3:1 range (unbundled, and without correction for altitude, both which can reduce the ampacity).
Guidance can be found in charts like the above that assume some standard operating conditions and have some safety factor incorporated, but using nomographs and working it out completely is sometimes required. | 2019-08-19 05:39:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.522544264793396, "perplexity": 1164.8321928020846}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027314667.60/warc/CC-MAIN-20190819052133-20190819074133-00503.warc.gz"} |
http://ams.org/bookstore?fn=20&arg1=fimseries&ikey=FIM-3 | New Titles | FAQ | Keep Informed | Review Cart | Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education
Lectures on Operator Theory and Its Applications
Edited by: Peter Lancaster, University of Calgary, AB, Canada
A co-publication of the AMS and Fields Institute.
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Fields Institute Monographs
1996; 339 pp; hardcover
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ISBN-10: 0-8218-0457-X
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Much of the importance of mathematics lies in its ability to provide theories which are useful in widely different fields of endeavor. A good example is the large and amorphous body of knowledge known as "the theory of linear operators" or "operator theory", which came to life about a century ago as a theory to encompass properties common to matrix, differential, and integral operators. Thus, it is a primary purpose of operator theory to provide a coherent body of knowledge which can explain phenomena common to the enormous variety of problems in which such linear operators play a part. The theory is a vital part of "functional analysis", whose methods and techniques are one of the major advances of twentieth century mathematics and now play a pervasive role in the modeling of phenomena in probability, imaging, signal processing, systems theory, etc., as well as in the more traditional areas of theoretical physics and mechanics.
This book is based on lectures presented at a meeting on operator theory and its applications held at the Fields Institute in the fall of 1994. The purpose of the meeting was to provide introductory lectures on some of the methods being used and problems being tackled in current research involving operator theory.
Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Research mathematicians.
• Lecture Series 1. A. Böttcher, Infinite matrices and projection methods
• Matrix representation of operators
• Three problems for infinite matrices
• The finite section method
• Selfadjoint and compact opeators
• Toeplitz matrices with continuous symbols
• Toeplitz operators: algebraization of stability
• Toeplitz operators: localization
• Block case and higher dimensions
• Banach space phenomena
• Norms of inverses and pseudospectra
• Toeplitz determinants
• More general projection methods
• Bibliography
• Lecture Series 2. A. Dijksma and H. Langer, Operator theory and ordinary differential operators
• Introduction
• Definitizable operators in Kreĭn spaces
• Boundary eigenvalue problems for Sturm-Liouville operators and related holomorphic functions
• Operator representations of holomorphic functions
• Sturm-Liouville operators with indefinite weight
• Interface conditions and singular potentials
• Operator pencils
• Bibliography
• Symbols used in the lecture
• Lecture Series 3. M. A. Dritschel and J. Rovnyak, Operators on indefinite inner product spaces
• Introduction: Preliminaries and notation
• Kreĭn spaces and operators
• Julia operators and contractions
• Extension and completion problems
• The Schur algorithm
• Reproducing kernel Pontryagin spaces and colligations
• Invariant subspaces
• Bibliography
• Lecture Series 4. M. A. Kaashoek, State space theory of rational matrix functions and applications
• Introduction
• Canonical factorization and the state space method
• $$J$$-unitary rational matrix functions
• Analysis of zeros
• Inverse problems involving null pairs
• Analysis of zeros and poles
• Inverse problems involving null-pole triples
• Bibliography
• Index
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http://magnox.ca/umxa0sp/can-you-multiply-radicals-with-different-radicands-f641e9 | That's perfectly fine. Subtraction of radicals follows the same set of rules and approaches as addition—the radicands and the indices must be the same for two (or more) radicals to be subtracted. Radicals with the same index and radicand are known as like radicals. To multiply radicands, multiply the numbers as if they were whole numbers. Look at the two examples that follow. Step One: Simplify the Square Roots (if possible) In this example, radical 3 and radical 15 can not be simplified, so we can leave them as they are for now. Then, we simplify our answer to . Radicals follow the same mathematical rules that other real numbers do. But you might not be able to simplify the addition all the way down to one number. We multiply the radicands to find . Square root, cube root, forth root are all radicals. Mathematically, a radical is represented as x n. This expression tells us that a number x is … As long as the roots of the radical expressions are the same, you can use the Product Raised to a Power Rule to multiply and simplify. It is negative because you can express a quotient of radicals as a single radical using the least common index fo the radicals. How can you multiply and divide square roots? Then, we simplify our answer to . You multiply radical expressions that contain variables in the same manner. You can encounter the radical symbol in algebra or even in carpentry or another trade that involves geometry or calculating relative sizes or distances. So in the example above you can add the first and the last terms: The same rule goes for subtracting. In other words, the square root of any number is the same as that number raised to the 1/2 power, the cube root of any number is the same as that number raised to the 1/3 power, and so on. $\text{3}\sqrt{11}\text{ + 7}\sqrt{11}$. To multiply square roots, first multiply the radicands, or the numbers underneath the radical sign. $x\sqrt[3]{x{{y}^{4}}}+y\sqrt[3]{{{x}^{4}}y}$, $\begin{array}{r}x\sqrt[3]{x\cdot {{y}^{3}}\cdot y}+y\sqrt[3]{{{x}^{3}}\cdot x\cdot y}\\x\sqrt[3]{{{y}^{3}}}\cdot \sqrt[3]{xy}+y\sqrt[3]{{{x}^{3}}}\cdot \sqrt[3]{xy}\\xy\cdot \sqrt[3]{xy}+xy\cdot \sqrt[3]{xy}\end{array}$, $xy\sqrt[3]{xy}+xy\sqrt[3]{xy}$. Multiplying radicals with coefficients is much like multiplying variables with coefficients. An expression with a radical in its denominator should be simplified into one without a radical in its denominator. As long as they have like radicands, you can just treat them as if they were variables and combine like ones together! Just as with "regular" numbers, square roots can be added together. To multiply radicals using the basic method, they have to have the same index. radicals with different radicands cannot be added or subtracted. Example: $$sqrt5*root(3)2$$ The common index for 2 and 3 is the least common multiple, or 6 $$sqrt5= root(6)(5^3)=root(6)125$$ … … Every day at wikiHow, we work hard to give you access to instructions and information that will help you live a better life, whether it's keeping you safer, healthier, or improving your well-being. 5. All tip submissions are carefully reviewed before being published. Multiplying Radicals – Techniques & Examples A radical can be defined as a symbol that indicate the root of a number. wikiHow is where trusted research and expert knowledge come together. Mar 5, 2018 Radicals have one important property that I have not yet mentioned: If two radicals with the same index are multiplied together, the result is just the product of the radicands beneath a single radical of that index. How can you multiply and divide square roots? So in the example above you can add the first and the last terms: The same rule goes for subtracting. Last Updated: June 7, 2019 H ERE IS THE RULE for multiplying radicals: It is the symmetrical version of the rule for simplifying radicals. To multiple squareroot2 by cuberoot2, write it as 2^(1/2)*2^(1/3) . Sample Problem. This type of radical is commonly known as the square root. 5 √ — 7 + √ — 11 − 8 √ — 7 = 5 √ — 7 − 8 √ — 7 + √ — 11 Commutative Property of Addition Step 2: To add or subtract radicals, the indices and what is inside the radical (called the radicand) must be exactly the same. wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. Yes, though it's best to convert to exponential form first. You multiply radical expressions that contain variables in the same manner. If the radicals do not have the same indices, you can manipulate the equation until they do. $\begin{array}{r}2\sqrt[3]{8\cdot 5}+\sqrt[3]{27\cdot 5}\\2\sqrt[3]{{{(2)}^{3}}\cdot 5}+\sqrt[3]{{{(3)}^{3}}\cdot 5}\\2\sqrt[3]{{{(2)}^{3}}}\cdot \sqrt[3]{5}+\sqrt[3]{{{(3)}^{3}}}\cdot \sqrt[3]{5}\end{array}$, $2\cdot 2\cdot \sqrt[3]{5}+3\cdot \sqrt[3]{5}$. Adding and Subtracting Radicals a. There is a more general way to think about this problem (since you might be multiplying two different numbers and hence you would not have a square). Simplify each radical by identifying and pulling out powers of $4$. The radical symbol (√) represents the square root of a number. Although the indices of $2\sqrt[3]{5a}$ and $-\sqrt[3]{3a}$ are the same, the radicands are not—so they cannot be combined. First, multiplications when the indexes of radicals are equal: Example 1: $\sqrt{6} \cdot \sqrt{2} = ?$ Solution: $\sqrt{6} \cdot \sqrt{2} = \sqrt{6 \cdot 2} = \sqrt{12}$ Example 2: $\sqrt{0.6} \cdot \sqrt{5} = ?$ Solution: $\sqrt{0.6} \cdot \sqrt{5}$ $= \sqrt{\frac{6}{10}} \cdot \sqrt{5}$ $= \sqrt{\frac{3}{5}} \cdot \sqrt{5}$ $= \sqrt{\frac{3}{5} \cdot 5} \cdot \sqrt{3}$ And secondly, if you multiply two radicals that hav… Then simplify and combine all like radicals. Within a radical, you can perform the same calculations as you do outside the radical. $5\sqrt{2}+\sqrt{3}+4\sqrt{3}+2\sqrt{2}$. If there is no index number, the radical is understood to be a square root (index 2) and can be multiplied with other square roots. When multiplying radicals. Write an algebraic rule for each operation. In this tutorial, you will learn how to factor unlike radicands before you can add two radicals together. Get wikiHow's Radicals Math Practice Guide. 5. We multiply the radicands to find . If these are the same, then addition and subtraction are possible. Multiply . Give an example of multiplying square roots and an example of dividing square roots that are different from the examples in Exploration 1. This next example contains more addends, or terms that are being added together. One is through the method described above. One helpful tip is to think of radicals as variables, and treat them the same way. What Do Radicals and Radicands Mean? Radicals have one important property that I have not yet mentioned: If two radicals with the same index are multiplied together, the result is just the product of the radicands beneath a single radical of that index. Using the quotient rule for radicals, Rationalizing the denominator. Write an algebraic rule for each operation. When adding radicals with the same radicands you just add the coefficients True or False: You can add radicals with different radicands When dividing radicals you. Can you multiply radicals with the same bases but indexes? Adding Radicals (Basic With No Simplifying). Radicals quantities such as square, square roots, cube root etc. Once we multiply the radicals, we then look for factors that are a power of the index and simplify the radical whenever possible. Multiply . Radicals with the same index and radicand are known as like radicals. Sometimes, you will need to simplify a radical expression before it is possible to add or subtract like terms. These are not like radicals. Multiply . a. the product of square roots b. the quotient of square roots REASONING ABSTRACTLY To be proficient in math, you need to recognize and use counterexamples. Sometimes you may need to add and simplify the radical. It is often helpful to treat radicals just as you would treat variables: like radicals can be added and subtracted in the same way that like variables can be added and subtracted. 6 is the LCM of these two numbers because it is the smallest number that is evenly divisible by both 3 and 2. The answer is $4\sqrt{x}+12\sqrt[3]{xy}$. Click here to review the steps for Simplifying Radicals. Then multiply the two radicands together to get the answer's radicand. % of people told us that this article helped them. If you want to know how to multiply radicals with or without coefficients, just follow these steps. Then, we simplify our answer to . You can add and subtract like radicals the same way you combine like terms by using the Distributive Property. It tells me that when two radicals with different radicands are multiplied, the product can be placed in one radicand. Consider the following example: You can subtract square roots with the same radicand--which is the first and last terms. In the same manner, you can only numbers that are outside of the radical symbols. Write an algebraic rule for each operation. How would I use the root of numbers that aren't a perfect square? We multiply the radicands to find . For tips on multiplying radicals that have coefficients or different indices, keep reading. If the indices or radicands are not the same, then you can not add or subtract the radicals. This finds the largest even value that can equally take the square root of, and leaves a number under the square root symbol that does not come out to an even number. When multiplying radicals the same coefficient and radicands you... just drop the square root symbol. Like the fourth root of 92 * the square root of 92 would be the three fourths root of … 4. An expression with a radical in its denominator should be simplified into one without a radical in its denominator. ... We can use the Product Property of Roots ‘in reverse’ to multiply square roots. Yes, if the indices are the same, and if the negative sign is outside the radical sign. To find the product of radicals with different indices, but the same radicand, apply the following steps: 1. transform the radical to fractional exponents. How To Multiply Radicals. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/5\/5e\/Multiply-Radicals-Step-1-Version-2.jpg\/v4-460px-Multiply-Radicals-Step-1-Version-2.jpg","bigUrl":"\/images\/thumb\/5\/5e\/Multiply-Radicals-Step-1-Version-2.jpg\/aid1374920-v4-728px-Multiply-Radicals-Step-1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":" | 2021-07-29 05:29:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8546838760375977, "perplexity": 395.52258577996577}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153816.3/warc/CC-MAIN-20210729043158-20210729073158-00381.warc.gz"} |
http://openstudy.com/updates/55bab830e4b0746426df0398 | ## peachytea one year ago the volume of this circular cylinder is 588pi cm^3. what is the height of this cylinder? the base of it says the radius is 7
$${ \textit{volume of a cylinder}=\pi r^2 h\qquad \begin{cases} r=radius\to 7\\ h=height \end{cases}\qquad 588=\pi \cdot 7^2\cdot h }$$ solve for "h' to find the height | 2017-01-22 04:25:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5915581583976746, "perplexity": 1050.65728079227}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560281332.92/warc/CC-MAIN-20170116095121-00497-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://www.blaumut.com/benzoin-to-yfmgt/c7c06f-pymc-survival-analysis | We also define $$t_{i, j}$$ to be the amount of time the $$i$$-th subject was at risk in the $$j$$-th interval. Springer Science & Business Media, 2008. These are somewhat interesting (espescially the fact that the posterior of $$\beta_1$$ is fairly well-separated from zero), but the posterior predictive survival curves will be much more interpretable. \end{align*}\end{split}\], $S(t) = \exp\left(-\int_0^s \lambda(s)\ ds\right).$, $\lambda(t) = \lambda_0(t) \exp(\mathbf{x} \beta).$, $\lambda(t) = \lambda_0(t) \exp(\beta_0 + \mathbf{x} \beta) = \lambda_0(t) \exp(\beta_0) \exp(\mathbf{x} \beta).$, $\begin{split}d_{i, j} = \begin{cases} mastectomy. An important, but subtle, point in survival analysis is censoring. One of the fundamental challenges of survival analysis (which also makes is mathematically interesting) is that, in general, not every subject will experience the event of interest before we conduct our analysis. We visualize the observed durations and indicate which observations are censored below. The modular nature of probabilistic programming with PyMC3 should make it straightforward to generalize these techniques to more complex and interesting data set. The survival function of the logistic distribution is. (For example, we may want to account for individual frailty in either or original or time-varying models.). We have really only scratched the surface of both survival analysis and the Bayesian approach to survival analysis. We now sample from the log-logistic model. Log-linear error distribution ($$\varepsilon$$). The fundamental quantity of survival analysis is the survival function; if T is the random variable representing the time to the event in question, the survival function is S (t) = P (T > t). All of the sampling diagnostics look good for this model. We choose a semiparametric prior, where $$\lambda_0(t)$$ is a piecewise constant function. In more concrete terms, if we are studying the time between cancer We now examine the effect of metastization on both the cumulative hazard and on the survival function. Unlike in many regression situations, $$\mathbf{x}$$ should not include a constant term corresponding to an intercept. Tag: python,bayesian,pymc,survival-analysis. Note: Running pip install pymc will install PyMC 2.3, not PyMC3, from PyPI. © Copyright 2018, The PyMC Development Team. Perhaps the most commonly used risk regression model is Cox’s 1 & \textrm{if subject } i \textrm{ died in interval } j \\ Greetings pymc3 developers, I attempted to run the 'survival_analysis' notebook in pymc3/examples but was unsuccessful. \end{cases}.\end{split}$, $$\tilde{\lambda}_0(t) = \lambda_0(t) \exp(-\delta)$$, $$\lambda(t) = \tilde{\lambda}_0(t) \exp(\tilde{\beta}_0 + \mathbf{x} \beta)$$, $$\beta \sim N(\mu_{\beta}, \sigma_{\beta}^2),$$, $$\lambda_j \sim \operatorname{Gamma}(10^{-2}, 10^{-2}).$$, $$\lambda_{i, j} = \lambda_j \exp(\mathbf{x}_i \beta)$$, $$\lambda(t) = \lambda_j \exp(\mathbf{x} \beta_j).$$, $$\beta_1, \beta_2, \ldots, \beta_{N - 1}$$, $$\beta_j\ |\ \beta_{j - 1} \sim N(\beta_{j - 1}, 1)$$, 'Had not metastized (time varying effect)', 'Bayesian survival model with time varying effects'. We illustrate these concepts by analyzing a mastectomy data set from R ’s HSAUR package. Aalen, Odd, Ornulf Borgan, and Hakon Gjessing. Survival and event history analysis: a process point of view. The following plot illustrates this phenomenon using an exponential survival function. The change in our estimate of the cumulative hazard and survival functions due to time-varying effects is also quite apparent in the following plots. The column event indicates whether or not the woman died during the observation period. @AustinRochford included a value for random_seed, so I don't think it's just randomness. where $$F$$ is the CDF of $$T$$. We construct the matrix of covariates $$\mathbf{X}$$. For extra info: alpha here governs an intrinsic correlation between clients, so a higher alpha results in a higher p(x,a), and thus for the same x, a higher alpha means a higher p(x,a). \lambda(t) & = \begin{cases} (2005). Survival Analysis is a set of statistical tools, which addresses questions such as ‘how long would it be, before a particular event occurs’; in other words we can also call it as a ‘time to event’ analysis. This survival function is implemented below. If $$\tilde{\beta}_0 = \beta_0 + \delta$$ and $$\tilde{\lambda}_0(t) = \lambda_0(t) \exp(-\delta)$$, then $$\lambda(t) = \tilde{\lambda}_0(t) \exp(\tilde{\beta}_0 + \mathbf{x} \beta)$$ as well, making the model with $$\beta_0$$ unidentifiable. In the case of our mastectomy study, df.event is one if the subject’s death was observed (the observation is not In this example, the covariates are $$\mathbf{x}_i = \left(1\ x^{\textrm{met}}_i\right)^{\top}$$, where. We see that the hazard rate for subjects whose cancer has metastized is about double the rate of those whose cancer has not metastized. Welcome to "Bayesian Modelling in Python" - a tutorial for those interested in learning how to apply bayesian modelling techniques in python ().This tutorial doesn't aim to be a bayesian statistics tutorial - but rather a programming cookbook for those who understand the fundamental of bayesian statistics and want to learn how to build bayesian models using python. It is mathematically convenient to express the survival function in terms of the hazard rate, $$\lambda(t)$$. Cookbook — Bayesian Modelling with PyMC3 This is a compilation of notes, tips, tricks and recipes for Bayesian modelling that I’ve collected from everywhere: papers, documentation, peppering my more experienced colleagues with questions. Accelerated failure time models incorporate covariates x into the survival function as S (t | β, x) = S 0 (exp (β ⊤ x) ⋅ t), The hazard rate is the instantaneous probability that the event occurs at time $$t$$ given that it has not yet occured. We are nearly ready to specify the likelihood of the observations given these priors. Thanks for bringing that back to my attention. $S(t\ |\ \beta, \mathbf{x}) = S_0\left(\exp\left(\beta^{\top} \mathbf{x}\right) \cdot t\right),$, $Y = \log T = \beta^{\top} \mathbf{x} + \varepsilon.$, \[\begin{split}\begin{align*} PyMC3 is a Python package for Bayesian statistical modeling and probabilistic machine learning which focuses on advanced Markov chain Monte Carlo and variational fitting algorithms. If $$\mathbf{x}$$ includes a constant term corresponding to an intercept, the model becomes unidentifiable. if $$s_j \leq t < s_{j + 1}$$, we let $$\lambda(t) = \lambda_j \exp(\mathbf{x} \beta_j).$$ The sequence of regression coefficients $$\beta_1, \beta_2, \ldots, \beta_{N - 1}$$ form a normal random walk with $$\beta_1 \sim N(0, 1)$$, $$\beta_j\ |\ \beta_{j - 1} \sim N(\beta_{j - 1}, 1)$$. The current development branch of PyMC3 can be installed from GitHub, also using pip: where $$S_0(t)$$ is a fixed baseline survival function. Survival analysis corresponds to a set of statistical approaches used to investigate the time it takes for an event of interest to occur.. Its applications span many fields across medicine, biology, engineering, and social science. Its applications span many fields across medicine, biology, engineering, and social science. This technique is called survival analysis because this method was primarily developed by medical researchers and they were more interested in finding expected lifetime of patients in different … We define indicator variables based on whether or the $$i$$-th suject died in the $$j$$-th interval. If the random variable $$T$$ is the time to the event we are studying, survival analysis is primarily concerned with the survival function. For censored observations, we only know that their true survival time exceeded the total time that they were under observation. His contributions to the community include lifelines, an implementation of survival analysis in Python, lifetimes, and Bayesian Methods for Hackers, an open source book & printed book on Bayesian analysis. 1. This probability is given by the survival function of the Gumbel distribution. Originally authored as a blog post by Austin Rochford on October 2, 2017. From the plots above, we may reasonable believe that the additional hazard due to metastization varies over time; it seems plausible that cancer that has metastized increases the hazard rate immediately after the mastectomy, but that the risk due to metastization decreases over time. On survival time post-mastectomy and whether or not the cancer had metastized prior surgery! Event time regression models in PyMC3 also show the pointwise 95 % high posterior density interval for each function Gumbel! For chosing between them in the last Cox model at the point in survival analysis is censoring science Shopify. To as a blog post that first appeared here random_seed, so i do n't think it 's randomness... Food microbiology likelihood is implemented as should make it straightforward to generalize these techniques more! From a woman diagnosed with breast cancer patient after a mastectomy data set from R s. Weibull model above version of the model we have really only scratched the surface of both survival analysis the... Pymc-Devs.Github.Io/Pymc/… ) might be of interest but i 'm getting nonsense results one example of this is in last! Account for individual frailty in either or original or time-varying models..... To generalize these techniques to more complex and interesting data set whether or not the observation is censored df.event. Analysis example, the likelihood of the distinct advantages of the Gumbel distribution models in involved! 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Borgan, and one for censored observations, we calculate the posterior expected survival functions due to effects!, goodness-of-fit and convergence diagnostics we are nearly ready to specify the likelihood the! From GitHub, also using pip: Bayesian Modelling in Python using PyMC3 for concern about poor mixing in.! ( T\ ): Bayesian Modelling in Python GP ) can be installed from GitHub, also pip. S WWS 509 course notes. ) available in Ibrahim et al post illustrates a approach... Will admit that i have had a hard time building the docs of view, we only know their... S WWS 509 course notes. ) @ AustinRochford included a value for,. Censored obsevation is that the subject ’ s proportional hazards model most commonly risk! It straightforward to generalize these techniques to more complex and interesting data from... With the online commerce leader Shopify implementing parametric survival regression models in PyMC3 involved some fairly complex numpy and. | 2021-10-19 18:45:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6829215884208679, "perplexity": 1555.9467897837624}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585280.84/warc/CC-MAIN-20211019171139-20211019201139-00498.warc.gz"} |
https://www.mathgenealogy.org/id.php?id=186895 | ## Marysol Navarro-Burruel
Dissertation: The $A_\infty$ property of elliptic measures for operators with coefficients supported in Whitney-type cubes | 2022-05-18 06:18:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24204042553901672, "perplexity": 8889.010856853842}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662521152.22/warc/CC-MAIN-20220518052503-20220518082503-00404.warc.gz"} |
https://huggingface.co/rafalposwiata/deproberta-large-v1 | # DepRoBERTa
DepRoBERTa (RoBERTa for Depression Detection) - language model based on RoBERTa-large and further pre-trained on depressive posts from Reddit.
Model was part of the winning solution for the Shared Task on Detecting Signs of Depression from Social Media Text at LT-EDI-ACL2022.
More information can be found in the following paper: OPI@LT-EDI-ACL2022: Detecting Signs of Depression from Social Media Text using RoBERTa Pre-trained Language Models.
If you use this model, please cite:
@inproceedings{poswiata-perelkiewicz-2022-opi,
title = "{OPI}@{LT}-{EDI}-{ACL}2022: Detecting Signs of Depression from Social Media Text using {R}o{BERT}a Pre-trained Language Models",
author = "Po{\'s}wiata, Rafa{\l} and Pere{\l}kiewicz, Micha{\l}",
booktitle = "Proceedings of the Second Workshop on Language Technology for Equality, Diversity and Inclusion",
month = may,
year = "2022",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2022.ltedi-1.40",
doi = "10.18653/v1/2022.ltedi-1.40",
pages = "276--282",
}
Mask token: <mask> | 2023-03-22 21:57:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2848460078239441, "perplexity": 13711.937737613101}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296944452.97/warc/CC-MAIN-20230322211955-20230323001955-00494.warc.gz"} |
https://docs.haqq.network/guides/validators/faq.html | # # Validator FAQ
Check the FAQ for running a validator on Haqq
## # General Concepts
### # What is a validator?
Haqq is powered by Tendermint (opens new window) Core, which relies on a set of validators to secure the network. Validators run a full node and participate in consensus by broadcasting votes which contain cryptographic signatures signed by their private key. Validators commit new blocks in the blockchain and receive revenue in exchange for their work. They also participate in on-procotol treasury governance by voting on governance proposals. A validator's voting influence is weighted according to their total stake.
### # What is "staking"?
Haqq is a public Proof-of-Stake (PoS) blockchain, meaning that validator's weight is determined by the amount of staking tokens (ISLM) bonded as collateral. These staking tokens can be staked directly by the validator or delegated to them by ISLM holders.
Any user in the system can declare its intention to become a validator by sending a create-validator transaction. From there, they become validators.
The weight (i.e. total stake or voting power) of a validator determines wether or not it is an active validator, and also how frequently this node will have to propose a block and how much revenue it will obtain. Initially, only the top 125 validators with the most weight will be active validators. If validators double-sign, or are frequently offline, they risk their staked tokens (including ISLMs delegated by users) being "slashed" by the protocol to penalize negligence and misbehavior.
### # What is a full node?
A full node is a program that fully validates transactions and blocks of a blockchain. It is distinct from a light client node that only processes block headers and a small subset of transactions. Running a full node requires more resources than a light client but is necessary in order to be a validator. In practice, running a full-node only implies running a non-compromised and up-to-date version of the software with low network latency and without downtime.
Of course, it is possible and encouraged for any user to run full nodes even if they do not plan to be validators.
### # What is a delegator?
Delegators are ISLM holders who cannot, or do not want to run validator operations themselves. Users can delegate ISLMs to a validator and obtain a part of its revenue in exchange (for more detail on how revenue is distributed, see What is the incentive to stake? and What is a validator's commission? sections below).
Because they share revenue with their validators, delegators also share responsibility. Should a validator misbehave, each of its delegators will be partially slashed in proportion to their stake. This is why delegators should perform due-diligence on validators before delegating, as well as diversifying by spreading their stake over multiple validators.
Delegators play a critical role in the system, as they are responsible for choosing validators. Be aware that being a delegator is not a passive role. Delegators are obligated to remain vigilant and actively monitor the actions of their validators, switching should they fail to act responsibly.
## # Becoming a Validator
### # How to become a validator?
Any participant in the network can signal their intent to become a validator by creating a validator and registering its validator profile. To do so, the candidate broadcasts a create-validator transaction, in which they must submit the following information:
• Validator's PubKey: Validator operators can have different accounts for validating and holding liquid funds. The PubKey submitted must be associated with the private key with which the validator intends to sign prevotes and precommits.
• Validator's Address: haqqvaloper1- address. This is the address used to identify your validator publicly. The private key associated with this address is used to bond, unbond, and claim rewards.
• Validator's name (also known as the moniker)
• Validator's website (optional)
• Validator's description (optional)
• Initial commission rate: The commission rate on block provisions, block rewards and fees charged to delegators.
• Maximum commission: The maximum commission rate which this validator will be allowed to charge.
• Commission change rate: The maximum daily increase of the validator commission.
• Minimum self-bond amount: Minimum amount of ISLM the validator needs to have bonded at all times. If the validator's self-bonded stake falls below this limit, its entire staking pool will be unbonded.
• Initial self-bond amount: Initial amount of ISLM the validator wants to self-bond.
Copy haqqd tx staking create-validator \ --amount=1000000000000aISLM \ --pubkey=\$(haqqd tendermint show-validator) \ --moniker=<your_moniker_name> \ --chain-id=<chain_id> \ --commission-rate="0.10" \ --commission-max-rate="0.20" \ --commission-max-change-rate="0.01" \ --min-self-delegation="1000000" \ --gas="auto" \ --gas-prices="0.025aISLM" \ --from=<key_name> \ --node https://rpc.tm.testedge.haqq.network:443
Once a validator is created and registered, ISLM holders can delegate ISLMs to it, effectively adding stake to its pool. The total stake of a validator is the sum of the ISLM self-bonded by the validator's operator and the ISLM bonded by external delegators.
Only the top 125 validators with the most stake are considered the active validators, becoming bonded validators. If ever a validator's total stake dips below the top 125, the validator loses its validator privileges (meaning that it won't generate rewards) and no longer serves as part of the active set (i.e doesn't participate in consensus), entering unbonding mode and eventually becomes unbonded.
## # Validator keys and states
### # What are the different types of keys?
In short, there are two types of keys:
• Tendermint Key: This is a unique key used to sign block hashes. It is associated with a public key haqqvalconspub.
• Generated when the node is created with haqqd init.
• Get this value with haqqd tendermint show-validator e.g. haqqvalconspub1zcjduc3qcyj09qc03elte23zwshdx92jm6ce88fgc90rtqhjx8v0608qh5ssp0w94c
• Application keys: These keys are created from the application and used to sign transactions. As a validator, you will probably use one key to sign staking-related transactions, and another key to sign oracle-related transactions. Application keys are associated with a public key haqqpub- and an address haqq-. Both are derived from account keys generated by haqqd keys add.
A validator's operator key is directly tied to an application key, but uses reserved prefixes solely for this purpose: haqqvaloper and haqqvaloperpub
### # What are the different states a validator can be in?
After a validator is created with a create-validator transaction, it can be in three states:
• bonded: Validator is in the active set and participates in consensus. Validator is earning rewards and can be slashed for misbehaviour.
• unbonding: Validator is not in the active set and does not participate in consensus. Validator is not earning rewards, but can still be slashed for misbehaviour. This is a transition state from bonded to unbonded. If validator does not send a rebond transaction while in unbonding mode, it will take three weeks for the state transition to complete.
• unbonded: Validator is not in the active set, and therefore not signing blocks. Unbonded validators cannot be slashed, but do not earn any rewards from their operation. It is still possible to delegate ISLM to this validator. Un-delegating from an unbonded validator is immediate.
Delegators have the same state as their validator.
Delegations are not necessarily bonded. ISLM can be delegated and bonded, delegated and unbonding, delegated and unbonded, or liquid.
### # What is "self-bond"? How can I increase my "self-bond"?
The validator operator's "self-bond" refers to the amount of ISLM stake delegated to itself. You can increase your self-bond by delegating more ISLM to your validator account.
### # Is there a faucet?
If you want to obtain coins for the testnet, you can do so by using the faucet.
### # Is there a minimum amount of ISLM that must be staked to be an active (bonded) validator?
There is no minimum. The top 125 validators with the highest total stake (where total stake = self-bonded stake + delegators stake) are the active validators.
### # How will delegators choose their validators?
Delegators are free to choose validators according to their own subjective criteria. That said, criteria anticipated to be important include:
• Amount of self-bonded ISLM: Number of ISLMs a validator self-bonded to its staking pool. A validator with higher amount of self-bonded ISLM has more skin in the game, making it more liable for its actions.
• Amount of delegated ISLMs: Total number of ISLM delegated to a validator. A high stake shows that the community trusts this validator, but it also means that this validator is a bigger target for hackers. Validators are expected to become less and less attractive as their amount of delegated ISLM grows. Bigger validators also increase the centralization of the network.
• Commission rate: Commission applied on revenue by validators before it is distributed to their delegators
• Track record: Delegators will likely look at the track record of the validators they plan to delegate to. This includes seniority, past votes on proposals, historical average uptime and how often the node was compromised.
Apart from these criteria, there will be a possibility for validators to signal a website address to complete their resume. Validators will need to build reputation one way or another to attract delegators. For example, it would be a good practice for validators to have their setup audited by third parties. Note though, that the Haqq team will not approve or conduct any audit itself.
## # Responsibilites
### # Do validators need to be publicly identified?
No, they do not. Each delegator will value validators based on their own criteria. Validators will be able(and are advised) to register a website address when they nominate themselves so that they can advertise their operation as they see fit. Some delegators may prefer a website that clearly displays the team running the validator and their resume, while others might prefer anonymous validators with positive track records. Most likely both identified and anonymous validators will coexist in the validator set.
### # What are the responsiblities of a validator?
Validators have three main responsibilities:
• Be able to constantly run a correct version of the software: validators need to make sure that their servers are always online and their private keys are not compromised.
• Provide oversight and feedback on correct deployment of community pool funds: the Haqq protocol includes the a governance system for proposals to the facilitate adoption of its currencies. Validators are expected to hold budget executors to account to provide transparency and efficient use of funds.
Additionally, validators are expected to be active members of the community. They should always be up-to-date with the current state of the ecosystem so that they can easily adapt to any change.
### # What does staking imply?
Staking ISLM can be thought of as a safety deposit on validation activities. When a validator or a delegator wants to retrieve part or all of their deposit, they send an unbonding transaction. Then, ISLM undergo a three weeks unbonding period during which they are liable to being slashed for potential misbehaviors committed by the validator before the unbonding process started.
Validators, and by association delegators, receive block provisions, block rewards, and fee rewards. If a validator misbehaves, a certain portion of its total stake is slashed (the severity of the penalty depends on the type of misbehavior). This means that every user that bonded ISLM to this validator gets penalized in proportion to its stake. Delegators are therefore incentivized to delegate to validators that they anticipate will function safely.
### # Can a validator run away with its delegators' ISLM?
By delegating to a validator, a user delegates staking power. The more staking power a validator has, the more weight it has in the consensus and processes. This does not mean that the validator has custody of its delegators' ISLM. By no means can a validator run away with its delegator's funds.
Even though delegated funds cannot be stolen by their validators, delegators are still liable if their validators misbehave. In such case, each delegators' stake will be partially slashed in proportion to their relative stake.
### # How often will a validator be chosen to propose the next block? Does it go up with the quantity of ISLM staked?
The validator that is selected to mine the next block is called the proposer, the "leader" in the consensus for the round. Each proposer is selected deterministically, and the frequency of being chosen is equal to the relative total stake (where total stake = self-bonded stake + delegators stake) of the validator. For example, if the total bonded stake across all validators is 100 ISLM, and a validator's total stake is 10 ISLM, then this validator will be chosen 10% of the time as the proposer.
To understand more about the proposer selection process in Tendermint BFT consensus, read more in their official docs (opens new window).
## # Incentives
### # What is the incentive to stake?
Each member of a validator's staking pool earns different types of revenue:
• Block rewards: Native tokens of applications run by validators (e.g. ISLMs on Haqq) are inflated to produce block provisions. These provisions exist to incentivize ISLM holders to bond their stake, as non-bonded ISLMs will be diluted over time.
• Transaction fees: Haqq maintains a whitelist of token that are accepted as fee payment. The initial fee token is the ISLM.
This total revenue is divided among validators' staking pools according to each validator's weight. Then, within each validator's staking pool the revenue is divided among delegators in proportion to each delegator's stake. A commission on delegators' revenue is applied by the validator before it is distributed.
### # What is the incentive to run a validator ?
Validators earn proportionally more revenue than their delegators because of commissions.
Validators also play a major role in governance. If a delegator does not vote, they inherit the vote from their validator. This gives validators a major responsibility in the ecosystem.
### # What is a validator's commission?
Revenue received by a validator's pool is split between the validator and its delegators. The validator can apply a commission on the part of the revenue that goes to its delegators. This commission is set as a percentage. Each validator is free to set its initial commission, maximum daily commission change rate and maximum commission. Haqq enforces the parameter that each validator sets. These parameters can only be defined when initially declaring candidacy, and may only be constrained further after being declared.
### # How are block provisions distributed?
Block provisions (rewards) are distributed proportionally to all validators relative to their total stake (voting power). This means that even though each validator gains ISLMs with each provision, all validators will still maintain equal weight.
Let us take an example where we have 10 validators with equal staking power and a commission rate of 1%. Let us also assume that the provision for a block is 1000 ISLMs and that each validator has 20% of self-bonded ISLM. These tokens do not go directly to the proposer. Instead, they are evenly spread among validators. So now each validator's pool has 100 ISLMs. These 100 ISLMs will be distributed according to each participant's stake:
• Commission: 100*80%*1% = 0.8 ISLMs
• Validator gets: 100\*20% + Commission = 20.8 ISLMs
• All delegators get: 100\*80% - Commission = 79.2 ISLMs
Then, each delegator can claim its part of the 79.2 ISLMs in proportion to their stake in the validator's staking pool. Note that the validator's commission is not applied on block provisions. Note that block rewards (paid in ISLMs) are distributed according to the same mechanism.
### # How are fees distributed?
Fees are similarly distributed with the exception that the block proposer can get a bonus on the fees of the block it proposes if it includes more than the strict minimum of required precommits.
When a validator is selected to propose the next block, it must include at least ⅔ precommits for the previous block in the form of validator signatures. However, there is an incentive to include more than ⅔ precommits in the form of a bonus. The bonus is linear: it ranges from 1% if the proposer includes ⅔rd precommits (minimum for the block to be valid) to 5% if the proposer includes 100% precommits. Of course the proposer should not wait too long or other validators may timeout and move on to the next proposer. As such, validators have to find a balance between wait-time to get the most signatures and risk of losing out on proposing the next block. This mechanism aims to incentivize non-empty block proposals, better networking between validators as well as to mitigate censorship.
Let's take a concrete example to illustrate the aforementioned concept. In this example, there are 10 validators with equal stake. Each of them applies a 1% commission and has 20% of self-bonded ISLM. Now comes a successful block that collects a total of 1005 ISLMs in fees. Let's assume that the proposer included 100% of the signatures in its block. It thus obtains the full bonus of 5%.
We have to solve this simple equation to find the reward $R$ for each validator:
$9R ~ + ~ R ~ + ~ 5\%(R) ~ = ~ 1005 ~ \Leftrightarrow ~ R ~ = ~ 1005 ~/ ~10.05 ~ = ~ 100$
• For the proposer validator:
• The pool obtains $R ~ + ~ 5\%(R)$: 105 ISLMs
• Commission: $105 ~ * ~ 80\% ~ * ~ 1\%$ = 0.84 ISLMs
• Validator's reward: $105 ~ * ~ 20\% ~ + ~ Commission$ = 21.84 ISLMs
• Delegators' rewards: $105 ~ * ~ 80\% ~ - ~ Commission$ = 83.16 ISLMs (each delegator will be able to claim its portion of these rewards in proportion to their stake)
• The pool obtains $R$: 100 ISLMs
• Commission: $100 ~ * ~ 80\% ~ * ~ 1\%$ = 0.8 ISLMs
• Validator's reward: $100 ~ * ~ 20\% ~ + ~ Commission$ = 20.8 ISLMs
• Delegators' rewards: $100 ~ * ~ 80\% ~ - ~ Commission$ = 79.2 ISLMs (each delegator will be able to claim its portion of these rewards in proportion to their stake)
### # What are the slashing conditions?
If a validator misbehaves, its bonded stake along with its delegators' stake and will be slashed. The severity of the punishment depends on the type of fault. There are 3 main faults that can result in slashing of funds for a validator and its delegators:
• Double-signing: If someone reports on chain A that a validator signed two blocks at the same height on chain A and chain B, and if chain A and chain B share a common ancestor, then this validator will get slashed on chain A.
• Downtime: If a validator misses more than 95% of the last 10.000 blocks, they will get slashed by 0.01%.
• Unavailability: If a validator's signature has not been included in the last X blocks, the validator will get slashed by a marginal amount proportional to X. If X is above a certain limit Y, then the validator will get unbonded.
• Non-voting: If a validator did not vote on a proposal, its stake could receive a minor slash.
Note that even if a validator does not intentionally misbehave, it can still be slashed if its node crashes, looses connectivity, gets DDoSed, or if its private key is compromised.
### # Do validators need to self-bond ISLMs
No, they do not. A validators total stake is equal to the sum of its own self-bonded stake and of its delegated stake. This means that a validator can compensate its low amount of self-bonded stake by attracting more delegators. This is why reputation is very important for validators.
Even though there is no obligation for validators to self-bond ISLM, delegators should want their validator to have self-bonded ISLM in their staking pool. In other words, validators should have skin-in-the-game.
In order for delegators to have some guarantee about how much skin-in-the-game their validator has, the latter can signal a minimum amount of self-bonded ISLM. If a validator's self-bond goes below the limit that it predefined, this validator and all of its delegators will unbond.
### # How to prevent concentration of stake in the hands of a few top validators?
For now the community is expected to behave in a smart and self-preserving way. When a mining pool in Bitcoin gets too much mining power the community usually stops contributing to that pool. Haqq will rely on the same effect initially. In the future, other mechanisms will be deployed to smoothen this process as much as possible:
• Penalty-free re-delegation: This is to allow delegators to easily switch from one validator to another, in order to reduce validator stickiness.
• UI warning: Wallets can implement warnings that will be displayed to users if they want to delegate to a validator that already has a significant amount of staking power.
## # Technical Requirements
### # What are hardware requirements?
Validators should expect to provision one or more data center locations with redundant power, networking, firewalls, HSMs and servers.
We expect that a modest level of hardware specifications will be needed initially and that they might rise as network use increases. Participating in the testnet is the best way to learn more.
### # What are software requirements?
In addition to running an Haqq node, validators should develop monitoring, alerting and management solutions.
### # What are bandwidth requirements?
Haqq has the capacity for very high throughput compared to chains like Ethereum or Bitcoin.
As such, we recommend that the data center nodes only connect to trusted full nodes in the cloud or other validators that know each other socially. This relieves the data center node from the burden of mitigating denial-of-service attacks.
Ultimately, as the network becomes more used, one can realistically expect daily bandwidth on the order of several gigabytes.
### # What does running a validator imply in terms of logistics?
A successful validator operation will require the efforts of multiple highly skilled individuals and continuous operational attention. This will be considerably more involved than running a bitcoin miner for instance.
### # How to handle key management?
Validators should expect to run an HSM that supports ed25519 keys. Here are potential options:
The Haqq team does not recommend one solution above the other. The community is encouraged to bolster the effort to improve HSMs and the security of key management.
### # What can validators expect in terms of operations?
Running effective operation is the key to avoiding unexpectedly unbonding or being slashed. This includes being able to respond to attacks, outages, as well as to maintain security and isolation in your data center.
### # What are the maintenance requirements?
Validators should expect to perform regular software updates to accommodate upgrades and bug fixes. There will inevitably be issues with the network early in its bootstrapping phase that will require substantial vigilance.
### # How can validators protect themselves from Denial-of-Service attacks?
Denial-of-service attacks occur when an attacker sends a flood of internet traffic to an IP address to prevent the server at the IP address from connecting to the internet.
An attacker scans the network, tries to learn the IP address of various validator nodes and disconnect them from communication by flooding them with traffic.
One recommended way to mitigate these risks is for validators to carefully structure their network topology in a so-called sentry node architecture.
Validator nodes should only connect to full-nodes they trust because they operate them themselves or are run by other validators they know socially. A validator node will typically run in a data center. Most data centers provide direct links the networks of major cloud providers. The validator can use those links to connect to sentry nodes in the cloud. This shifts the burden of denial-of-service from the validator's node directly to its sentry nodes, and may require new sentry nodes be spun up or activated to mitigate attacks on existing ones.
Sentry nodes can be quickly spun up or change their IP addresses. Because the links to the sentry nodes are in private IP space, an internet based attacked cannot disturb them directly. This will ensure validator block proposals and votes always make it to the rest of the network.
It is expected that good operating procedures on that part of validators will completely mitigate these threats.
For more on sentry node architecture, see this (opens new window). | 2023-03-27 10:46:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 10, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2501642405986786, "perplexity": 4761.382862017376}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948620.60/warc/CC-MAIN-20230327092225-20230327122225-00076.warc.gz"} |
http://acomasx.com/break-even-analysis-how-to-calculate-break-even-point/ | ## How to Calculate Break Even Point: The Break Even Formula
The textbook formula for calculating your break even point in units of number of guests for a given period of time is:
### $\fn_jvn \large \text{Break Even}= \left ( \frac{ \text{Total Fixed Costs}}{\text{Avg Revenue per Guest}-\text{Variable Cost per Guest}} \right )$
I call this textbook, because it is the universal way to calculate any business’s break even point. We measure “At how many units sold, will my business break even and start turning a profit?” In our industry, our units are the guest counts (or number of “covers”) themselves. Our unit price is essentially the dollar amount of our “guest average.”
This isn’t always the easiest way to look at things, and that’s mostly because of the difficulty I’ve seen in obtaining the “variable cost per guest” component. Some restaurants will have worked out their estimated margins on food dishes and drinks based on an expanded analysis of recipes and cost of ingredients. However, I don’t usually see a restaurant’s entire chart of accounts neatly categorized into fixed vs variable costs in order to accurately conduct complete break even analysis.
As an alternative, I sometimes like using the following variation of the formula. You only need 3 values: Total sales, total fixed costs, and total variable costs.
$\fn_jvn \LARGE \text{Break Even = Total Fixed Costs}\ \div\ \left ( \frac{\text{Total Sales} -\text{Total Variable Costs}}{\text{Total Sales}} \right)$
This allows you to quickly calculate a restaurant’s break even point (in sales dollars) as soon as you have categorized your fixed vs variable costs for any given period of time. All you have to do is gather basic accounting reports from a high level, without yet factoring in guest counts or \$ averages per guest.
Let’s break this down a bit to see how I derived that.
You can look at break even (in dollars) as, “For a given period of time, at what volume in sales did my total contribution margin break even my bottom line, offsetting my total fixed costs, after which point each additional dollar earned went straight to contributing to my net income (profits)?”
Break Even is equal to Total Fixed Costs divided by the Contribution Margin Ratio (aka “The percentage of each sales dollar that is available to cover my fixed costs and profits.”)
$\fn_jvn \large \text{Contribution Margin}= \text{Total Sales}\ -\ \text{Total Variable Costs}$
$\fn_jvn \large \text{Contribution Margin Ratio}= \left ( \frac{\text{Contribution Margin}}{\text{Total Sales}} \right )$
$\fn_jvn \large \text{Contribution Margin Ratio}= \left ( \frac{\text{Total Sales}-\text{Total Variable Costs}}{\text{Total Sales}} \right )$
$\fn_jvn \LARGE \text{Break Even = Total Fixed Costs}\ \div\ \left ( \frac{\text{Total Sales} -\text{Total Variable Costs}}{\text{Total Sales}} \right)$
First off, this is especially helpful for combining multiple months together. Sometimes, you are only looking at P&L (Profit and Loss) statements for a longer period of time, working on identifying any financial trends for that period. Also, it can be difficult to summarize some fixed costs that don’t always occur every month.
With this formula, we simply remove the guest count component to answer the question, “At what point did I break even and start accumulating profit to my bottom line?”
Let’s look at an example: Last quarter, let’s say you…
• Introduced a new menu and slightly raised prices.
• Printed new menus which only happens a few times per year.
• Started using new vendors that you negotiated into contract pricing.
• Brought on a new restaurant management team.
• Invested in a new kiosk system which will now cost you a fixed monthly amount, saving you a significant amount of money in labor every day.
As a result, we should use the last 3 months of accounting data to reset our way of measuring our break even. It is a good idea to use a moving average of these expenses and sales figures. Using moving averages allows you to account for the quirks of all the miscellaneous expenses which still impact your bottom line, while still updating your historical numbers with the most recent month’s closing figures. | 2019-02-20 16:28:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42077553272247314, "perplexity": 1787.5530939515106}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247495147.61/warc/CC-MAIN-20190220150139-20190220172139-00475.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/algebra-1-common-core-15th-edition/chapter-7-exponents-and-exponential-functions-chapter-review-page-475/10 | ## Algebra 1: Common Core (15th Edition)
We have $x^{0}$$y^{2}.We are given x=2 and y=-3 so we substitute them into the expression: 2^{0}$$(-3)^{2}$.Since any number raised to 0 is 1 we have 1$\times$$(-3)^{2}$ . -3 squared is 9 so we have 1$\times$9=9.The answer is 9 | 2022-05-26 10:12:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.45158207416534424, "perplexity": 3572.1966186991385}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662604794.68/warc/CC-MAIN-20220526100301-20220526130301-00040.warc.gz"} |
https://www.doubtnut.com/question-answer-physics/a-charged-particle-going-around-in-a-circle-can-be-considered-to-be-a-current-loopa-particle-of-mass-642612153 | Home
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# A charged particle going around in a circle can be considered to be a current loop.A particle of mass m carrying charge q is moving in a plane with speed v , under the influence of magnetic field B. The magnetic momnet of this moving particle :
Updated On: 27-06-2022
Text Solution
(mv^(2) vec(B))/(2 B^(2))(mv^(2) vec(B))/(2 pi B^(2))(mv^(2) vec(B))/(B^(2)) -(mv^(2) vec(B))/(2 B^(2))
Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
Transcript
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square B to b square into you could check for the option hello Sodi will be the correct option minus A square B B to b square simple | 2022-12-08 13:29:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5760623812675476, "perplexity": 350.41389854366844}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711336.41/warc/CC-MAIN-20221208114402-20221208144402-00062.warc.gz"} |
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# Superconductivity and strong correlations in moiré flat bands
## Abstract
Strongly correlated systems can give rise to spectacular phenomenology, from high-temperature superconductivity to the emergence of states of matter characterized by long-range quantum entanglement. Low-density flat-band systems play a vital role because the energy range of the band is so narrow that the Coulomb interactions dominate over kinetic energy, putting these materials in the strongly-correlated regime. Experimentally, when a band is narrow in both energy and momentum, its filling may be tuned in situ across the whole range, from empty to full. Recently, one particular flat-band system—that of van der Waals heterostructures, such as twisted bilayer graphene—has exhibited strongly correlated states and superconductivity, but it is still not clear to what extent the two are linked. Here, we review the status and prospects for flat-band engineering in van der Waals heterostructures and explore how both phenomena emerge from the moiré flat bands.
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## Acknowledgements
We thank K. Hejazi and C. Liu for assistance with preparation of Fig. 1c. L.B. acknowledges support by the NSF CMMT program under award no. DMR-1818533; the US Department of Energy, Office of Science, Basic Energy Sciences under award no. DE-FG02-08ER46524 and the UCSB NSF Quantum Foundry through Q-AMASE-i program award no. DMR-1906325. A.F.Y. acknowledges the support of the US Department of Energy, Office of Science, Basic Energy Sciences under award no. DE-SC0020043 and the UCSB NSF Quantum Foundry through Q-AMASE-i program award no. DMR-1906325. C.R.D. acknowledges the support of the Pro-QM EFRC funded by the US Department of Energy, Office of Science, Basic Energy Sciences under award no. DE-SC0019443. D.K.E. acknowledges support from the Ministry of Economy and Competitiveness of Spain through the ‘Severo Ochoa’ program for Centres of Excellence in R&D (SE5-0522), Fundació Privada Cellex, Fundació Privada Mir-Puig, the Generalitat de Catalunya through the CERCA program, the H2020 Programme under grant agreement no. 820378, Project: 2D·SIPC and the La Caixa Foundation.
## Author information
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### Corresponding authors
Correspondence to Leon Balents or Dmitri K. Efetov or Andrea F. Young.
## Ethics declarations
### Competing interests
The authors declare no competing interests.
Peer review information Nature Physics thanks Emanuel Tutuc and Oskar Vafek for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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Balents, L., Dean, C.R., Efetov, D.K. et al. Superconductivity and strong correlations in moiré flat bands. Nat. Phys. 16, 725–733 (2020). https://doi.org/10.1038/s41567-020-0906-9
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• Issue Date: | 2021-09-19 19:19:14 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9471912980079651, "perplexity": 12131.854982857292}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056900.32/warc/CC-MAIN-20210919190128-20210919220128-00216.warc.gz"} |
https://psychopy.org/api/microphone.html | # psychopy.microphone - Capture and analyze sound¶
(Available as of version 1.74.00; Advanced features available as of 1.77.00)
Deprecated Use Microphone for new projects.
## Overview¶
AudioCapture() allows easy audio recording and saving of arbitrary sounds to a file (wav format). AudioCapture will likely be replaced entirely by AdvAudioCapture in the near future.
AdvAudioCapture() can do everything AudioCapture does, and also allows onset-marker sound insertion and detection, loudness computation (RMS audio “power”), and lossless file compression (flac). The Builder microphone component now uses AdvAudioCapture by default.
## Audio Capture¶
psychopy.microphone.switchOn(sampleRate=48000, outputDevice=None, bufferSize=None)[source]
You need to switch on the microphone before use, which can take several seconds. The only time you can specify the sample rate (in Hz) is during switchOn().
Considerations on the default sample rate 48kHz:
DVD or video = 48,000
CD-quality = 44,100 / 24 bit
human hearing: ~15,000 (adult); children & young adult higher
human speech: 100-8,000 (useful for telephone: 100-3,300)
Google speech API: 16,000 or 8,000 only
Nyquist frequency: twice the highest rate, good to oversample a bit
pyo’s downsamp() function can reduce 48,000 to 16,000 in about 0.02s (uses integer steps sizes). So recording at 48kHz will generate high-quality archival data, and permit easy downsampling.
outputDevice, bufferSize: set these parameters on the pyoSndServer
before booting; None means use pyo’s default values
class psychopy.microphone.AdvAudioCapture(name='advMic', filename='', saveDir='', sampletype=0, buffering=16, chnl=0, stereo=True, autoLog=True)[source]
Class extends AudioCapture, plays marker sound as a “start” indicator.
Has method for retrieving the marker onset time from the file, to allow calculation of vocal RT (or other sound-based RT).
See Coder demo > input > latencyFromTone.py
Parameters
name :
Stem for the output file, also used in logging.
filename :
optional file name to use; default = ‘name-onsetTimeEpoch.wav’
saveDir :
Directory to use for output .wav files. If a saveDir is given, it will return ‘saveDir/file’. If no saveDir, then return abspath(file)
sampletypebit depth
pyo recording option: 0=16 bits int, 1=24 bits int; 2=32 bits int
bufferingpyo argument
Controls the buffering argument for pyo if necessary
chnlint (default=0)
which audio input channel to record (default=0)
stereobool or nChannels (default = True)
how many channels to record
compress(keep=False)[source]
Compress using FLAC (lossless compression).
getLoudness()[source]
Return the RMS loudness of the saved recording.
getMarkerInfo()[source]
Returns (hz, duration, volume) of the marker sound. Custom markers always return 0 hz (regardless of the sound).
getMarkerOnset(chunk=128, secs=0.5, filename='')[source]
Return (onset, offset) time of the first marker within the first secs of the saved recording.
Has approx ~1.33ms resolution at 48000Hz, chunk=64. Larger chunks can speed up processing times, at a sacrifice of some resolution, e.g., to pre-process long recordings with multiple markers.
If given a filename, it will first set that file as the one to work with, and then try to detect the onset marker.
playMarker()[source]
Plays the current marker sound. This is automatically called at the start of recording, but can be called anytime to insert a marker.
playback(block=True, loops=0, stop=False, log=True)
Plays the saved .wav file, as just recorded or resampled. Execution blocks by default, but can return immediately with block=False.
loops : number of extra repetitions; 0 = play once
stop : True = immediately stop ongoing playback (if there is one), and return
record(sec, filename='', block=False)[source]
Starts recording and plays an onset marker tone just prior to returning. The idea is that the start of the tone in the recording indicates when this method returned, to enable you to sync a known recording onset with other events.
resample(newRate=16000, keep=True, log=True)
Re-sample the saved file to a new rate, return the full path.
Can take several visual frames to resample a 2s recording.
The default values for resample() are for Google-speech, keeping the original (presumably recorded at 48kHz) to archive. A warning is generated if the new rate not an integer factor / multiple of the old rate.
To control anti-aliasing, use pyo.downsamp() or upsamp() directly.
reset(log=True)
Restores to fresh state, ready to record again
setFile(filename)[source]
Sets the name of the file to work with.
setMarker(tone=19000, secs=0.015, volume=0.03, log=True)[source]
Sets the onset marker, where tone is either in hz or a custom sound.
The default tone (19000 Hz) is recommended for auto-detection, as being easier to isolate from speech sounds (and so reliable to detect). The default duration and volume are appropriate for a quiet setting such as a lab testing room. A louder volume, longer duration, or both may give better results when recording loud sounds or in noisy environments, and will be auto-detected just fine (even more easily). If the hardware microphone in use is not physically near the speaker hardware, a louder volume is likely to be required.
Custom sounds cannot be auto-detected, but are supported anyway for presentation purposes. E.g., a recording of someone saying “go” or “stop” could be passed as the onset marker.
stop(log=True)
Interrupt a recording that is in progress; close & keep the file.
Ends the recording before the duration that was initially specified. The same file name is retained, with the same onset time but a shorter duration.
The same recording cannot be resumed after a stop (it is not a pause), but you can start a new one.
uncompress(keep=False)[source]
Uncompress from FLAC to .wav format.
## Speech recognition¶
Google’s speech to text API is no longer available. AT&T, IBM, and Wit.ai have a similar (paid) service.
## Misc¶
Functions for file-oriented Discrete Fourier Transform and RMS computation are also provided.
psychopy.microphone.wav2flac(path, keep=True, level=5)[source]
Lossless compression: convert .wav file (on disk) to .flac format.
If path is a directory name, convert all .wav files in the directory.
keep to retain the original .wav file(s), default True.
level is compression level: 0 is fastest but larger,
8 is slightly smaller but much slower.
psychopy.microphone.flac2wav(path, keep=True)[source]
Uncompress: convert .flac file (on disk) to .wav format (new file).
If path is a directory name, convert all .flac files in the directory.
keep to retain the original .flac file(s), default True.
psychopy.microphone.getDft(data, sampleRate=None, wantPhase=False)[source]
Compute and return magnitudes of numpy.fft.fft() of the data.
If given a sample rate (samples/sec), will return (magn, freq). If wantPhase is True, phase in radians is also returned (magn, freq, phase). data should have power-of-2 samples, or will be truncated.
psychopy.microphone.getRMS(data)[source]
Compute and return the audio power (“loudness”).
Uses numpy.std() as RMS. std() is same as RMS if the mean is 0, and .wav data should have a mean of 0. Returns an array if given stereo data (RMS computed within-channel).
data can be an array (1D, 2D) or filename; .wav format only. data from .wav files will be normalized to -1..+1 before RMS is computed.
Back to top | 2022-10-05 20:54:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18629948794841766, "perplexity": 13869.646916234478}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337668.62/warc/CC-MAIN-20221005203530-20221005233530-00686.warc.gz"} |
https://www.physicsforums.com/threads/probablity-question-confused-on-the-pdf.633103/ | # Probablity question (confused on the pdf)
## Homework Statement
[itex]
$f(x)=\begin{cases} 7(4)^{-i} & x\in(\frac{1}{2^{i}},\frac{1}{2^{i-1}}],i=1,2,3,...\\ 0 & 0\geq x,x>1 \end{cases}$ (please excuse the poor latex)
## The Attempt at a Solution
the problem i'm having is say x=3/4. then according to the pdf, shouldn't P(x)=7*(4^-1)=7/4>1. i mean, shouldn't it be bounded by 1? when i integrate this out, i get 1, like i should, so i'm not sure what mistake i'm making.
## Answers and Replies
Related Calculus and Beyond Homework Help News on Phys.org
what is the actual question? Maybe I'm missing it, but it seems like you just posted an equation without any description of what you are trying to do
jbunniii
Science Advisor
Homework Helper
Gold Member
Why do you expect that a pdf must be bounded by 1? Consider a random variable that is uniformly distributed over the interval [0, 1/2]. Is that pdf bounded by 1?
well, the actual problem is show that this function is a pdf. so i need to show that it integrates to 1, which it does, but i believe i also need to show that it's bounded by 0 and 1 for all x in the domain, which is the problem i'm having a hard time with.
oh, got it. duh. thank you. | 2020-01-17 18:27:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6992338299751282, "perplexity": 319.01468990388076}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250590107.3/warc/CC-MAIN-20200117180950-20200117204950-00517.warc.gz"} |
https://knowledgebase.psyquation.com/en/expected-drawdown/ | # Expected Drawdown
Expected Maximal Drawdown over the period of T days is computed by the following formula (which depends on the sign of the mean daily log-returns):
Functions Qn and Qp do not have simple analytical expressions. Below you can see charts of Qn and Qp for different values of μ and σ
For the journey, the time horizon T is 252 days | 2021-07-27 01:57:13 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8930191397666931, "perplexity": 746.6338232621248}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046152168.38/warc/CC-MAIN-20210727010203-20210727040203-00696.warc.gz"} |
http://mathhelpforum.com/business-math/188465-help-writing-formula-word-problem.html | Math Help - Help with writing a formula from a word problem.
1. Help with writing a formula from a word problem.
A finance company will lend you $1000 for a finance charge of$20 plus simple interest at 1% per month. This mean you will pay 1% of $1000, or$10 per month plus the $20 finance charge. Find a formula for F if F is the finance charge and M is the number of months before you repay the loan. Isn't F already given as$20? How am I suppose to do this!?
2. Re: Help with writing a formula from a word problem.
i agree that is a badly worded question. are you sure you copied it exactly?
3. Re: Help with writing a formula from a word problem.
I suspect that "F" is to be the total finance charge- that is the total amount you pay above paying back the original $1000. Since you are paying$10 per month toward the \$1000, it will take you 100 months to repay the loan. What is the total finance charge you will have paid in those 100 months?
(Notice that the monthly finance charge is twice your payment toward the loan!) | 2015-04-21 14:16:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2261652648448944, "perplexity": 961.9006186438988}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246641468.77/warc/CC-MAIN-20150417045721-00118-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://www.csam.or.kr/journal/view.html?uid=1820&vmd=Full | TEXT SIZE
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The Bivariate Kumaraswamy Weibull regression model: a complete classical and Bayesian analysis
Juliana B. Fachini-Gomesa, Edwin M. M. Ortegab, Gauss M. Cordeiroc, Adriano K. Suzuki1,d
aDepartment of Statistics, University of Brasilia, Brazil;
bDepartment of Exact Sciences, University of São Paulo, Brazil;
cDepartment of Statistics, Federal University of Pernambuco, Brazil;
dDepartment of Applied Mathematics and Statistics, University of São Paulo, Brazil
Correspondence to: 1Department of Applied Mathematics and Statistics, University of São Paulo, Avenida Trabalhador São-carlense, 400 - Centro CEP: 13566-590, São Carlos-SP, Brazil. E-mail: suzuki@icmc.usp.br
Received March 20, 2018; Revised June 23, 2018; Accepted August 14, 2018.
Abstract
Bivariate distributions play a fundamental role in survival and reliability studies. We consider a regression model for bivariate survival times under right-censored based on the bivariate Kumaraswamy Weibull (Cordeiro et al., Journal of the Franklin Institute, 347, 1399–1429, 2010) distribution to model the dependence of bivariate survival data. We describe some structural properties of the marginal distributions. The method of maximum likelihood and a Bayesian procedure are adopted to estimate the model parameters. We use diagnostic measures based on the local influence and Bayesian case influence diagnostics to detect influential observations in the new model. We also show that the estimates in the bivariate Kumaraswamy Weibull regression model are robust to deal with the presence of outliers in the data. In addition, we use some measures of goodness-of-fit to evaluate the bivariate Kumaraswamy Weibull regression model. The methodology is illustrated by means of a real lifetime data set for kidney patients.
Keywords : Bayesian inference, bivariate failure time, censored data, diagnostics, survival analysis
1. Introduction
Statistical applications for the time of occurrence of an event of interest generally use the exponential, Weibull, gamma, log-normal and log-logistic distributions. However, there has been growing interest in new distributions to model skewness, kurtosis and different types of hazard rates. Among them, we cite the exponentiated Weibull (Mudholkar et al., 1995) and beta modified Weibull (Silva et al., 2010) distributions. More recently, Cordeiro et al. (2010) introduced the Kumaraswamy Weibull (KwW) distribution from the generator defined by Cordeiro and de Castro (2011). By considering more than one response variable in the experiment, Cordeiro et al. (2010) proposed the bivariate Kumaraswamy Weibull (BKwW) distribution based on the construction of the bivariate Weibull (Hougaard, 1986) distribution.
In practice, regressor variables associated with the response variable of each observation are always presented; however, statistical analysis always gives consideration to models that account for all the information existing in the observations. Due to these factors, this work extends the well-known KwW distribution to include covariates by means of the scale parameter leading to the BKwW regression model. The inferential part is conducted using the asymptotic distribution of the maximum likelihood estimators (MLEs) subject to restrictions on parameters. To implement this method, we use the adjusted barrier function (Lange, 1999). Situations with small samples may present difficult results to justify. We explore the use of a Bayesian method as an alternative to classic analysis. Markov chain Monte Carlo (MCMC) methods are used to develop a Bayesian analysis for the regression model.
After fitting the data, it is important to check model assumptions and conduct a robustness study to detect influential or extreme observations that can cause distortions in the results of the analysis. Influence diagnostics is an important step in the analysis of a data set, since it provides an indication of bad model fit or influential observations. Cook (1986) proposed a diagnostic approach named local influence to assess the effect of small perturbations in the model and/or data on parameter estimates. Several authors have applied the local influence method in more general regression models than the normal regression model. Some authors have also investigated the assessment of local influence in survival analysis models. For instance, Ortega et al. (2013) proposed the log-beta Weibull regression model with application to predict recurrence of prostate cancer, Hashimoto et al. (2013) adapted local influence methods to log-generalized gamma regression model for interval-censored data, Ortega et al. (2015) considered the problem of assessing local influence in a power series beta Weibull regression model to predict breast carcinoma and da Cruz et al. (2016) explored global and local influence methods to the log-odd log-logistic Weibull regression model with censored data. For the BKwW regression model, we propose a similar method to detect influential subjects by considering the global and local influence and Bayesian case influence.
The article is organized as follows. In Section 2, we present the BKwW regression model and some properties of the marginal distributions. In Section 3, we examine the performance of the likelihood function by computing the maximum likelihood, while the estimated equations are considered under parameter constraints and derive several diagnostic measures by considering the normal curvatures of local influence under various perturbation schemes. In Section 4, we consider a Bayesian approach and influence diagnostics for the BKwW regression model. In Section 5, we conduct various simulation studies to evaluate the behavior of the estimators in the BKwW regression model. In Section 6, we present a reanalysis of the dataset from patients of a renal insufficiency study reported by McGilchrist and Aisbett (1991). Finally, Section 7 provides some conclusions remark.
2. A bivariate KwW regression model
In practice, the majority of studies involve covariates related to survival times. Regression models can be formulated in various ways. In survival analysis, the class of parametric regression models and Cox regression model are well-known. However, we adopt a reparameterization of the BKwW (Cordeiro et al., 2010) distribution to define a new regression model. The bivariate Kumaraswamy (BKw) cumulative distribution is defined by
$F(t1,t2)=1-[1-G(t1,t2)a]b, t1,t2>0,$
where a > 0 and b > 0 are additional shape parameters, and G(t1, t2) is an arbitrary joint cumulative distribution function (cdf). We also consider the bivariate Weibull (Hougaard, 1986) distribution due to its evident applicability and popularity in the literature. Its cdf G(t1, t2) is given by
$G(t1,t2)=exp {-[(λ1 t1)c1α+(λ2 t2)c2α]α}-exp [-(λ1 t1)c1]-exp [-(λ2 t2)c2]+1.$
Let T1 and T2 be two non-negative random variables denoting the survival times of two components of a system. We define a bivariate random variable T = (T1, T2)T having a BKwW distribution. Its cumulative distribution (for tk > 0, k = 1, 2) follows from equations (2.1) and (2.2) as
$F(t1,t2)=1-{1-[exp {-[(λ1 t1)c1α+(λ2 t2)c2α]α}-exp [-(λ1 t1)c1]-exp [-(λ2 t2)c2]+1]a}b,$
where a > 0, b > 0, and ck > 0 are shape parameters, λk > 0 is a scale parameter and 0 < α ≤ 1 is an association parameter between T1 and T2. We propose the reparameterization λk = exp(−μk) and ck = σk−1, for which −∞ < μk < ∞ and 0 < σk < ∞. We introduce a vector of regressor variables x = (x0, x1, …, xp)T and the linear structure μ = xTβ, where β = (β0, β1, …, βp)T is the unknown parameter vector associated with the covariates. Therefore, the reparameterization can be expressed as: λk = exp(−xTβk) = exp[−(β0k x0 + β1k x1 + · · · + βpk xp)] and ck = 1/σk, for k = 1, 2. The BKwW regression model is defined by
$F(t1,t2∣x)=1-[1-{exp [-{[exp (-xTβ1) t1]1σ1α+[exp (-xTβ2) t2]1σ2α}α]-exp {-[exp (-xTβ1) t1]1σ1}-exp {-[exp (-xTβ2) t2]1σ2}+1}a]b,$
with probability density function (pdf) given by
$f(t1,t2∣x)=abGa-2(t1,t2∣x) [A(t1,t2∣x)+B(t1,t2∣x)+C(t1,t2∣x)][1-Ga(t1,t2∣x)]1-b,$
where the functions A(·), B(·), C(·), and G(·) are given in the Appendix.
To illustrate some possible shapes of the pdf, we set the parameter values μ1 = 4.5, σ1 = 1.5, μ2 = 5, σ2 = 1.5, a = 1.5, b = 0.9, and take α = 0.99 (when the lifetimes, t1 and t2, are independent), α = 0.50 (when there is some dependency between the lifetimes t1 and t2), and α = 0.01 (when the lifetimes, t1 and t2, are highly dependent), respectively. Figure 1 displays the plots of the pdf.
The corresponding marginal pdfs f(tk|x) and marginal cdfs F(tk|x) are given by
$f(tk∣x)=a bσk[exp (-xTβk)]1σk tk1σk-1 exp {-[exp (-xTβk) tk]1σk}×{1-exp {-[exp (-xTβk) tk]1σk}}a-1{1-[1-exp {-[exp (-xTβk) tk]1σk}]a}b-1$
and
$F(tk∣x)=1-{1-[1-exp {-[exp (-xTβk) tk]1σk}]a}b,$
respectively, for k = 1, 2.
If |z| < 1 and b is real non-integer, the power series
$(1-z)b-1=∑i=0∞(-1)i(b-1i) zi$
holds, where the binomial coefficient is defined for any real number. Let Tk be a random variable with pdf (2.5) for k = 1, 2. We consider here only the general case: the parameters a and b are real non-integers. By applying (2.7) to (2.5) and expanding the binomial term, the marginal density function of Tk reduces to
$f(tk∣x)=∑r=0∞wrgλr,k,ck(tk∣x),$
where gλr,(k),ck (x) denotes the Weibull density function with shape parameter ck = σk−1 and scale parameter λr,k = (r + 1)σk exp(−xTβk) and the coefficients wr are given by
$wr=a br+1∑j=0∞(-1)j+r (b-1j) ((j+1)a-1r).$
Equation (2.8) reveals that the marginal density function of Tk is an infinite linear combination of Weibull densities. We can easily check using computer software that $∑r=0∞wr=1$ as expected. Thus, the ordinary, inverse and factorial moments and generating function of Tk can be obtained from an infinite weighted linear combination of those quantities for Weibull distributions.
The quantile function of Tk is readily obtained by inverting (2.6) as
$tk=(1λk) [-log {1-[1-(1-u)1b]1a}]σk,$
where λk = exp(−xTβk) and u is uniform on the unit interval (0, 1).
The survival function associated with (2.3) can be expressed as
$S(t1,t2∣x)=1-F(t1∣x)-F(t2∣x)+F(t1,t2∣x),$
where the functions F(t1, t2|x) and F(t1|x), F(t2|x) are defined in (2.3) and (2.6), respectively. Consequently, the joint survival function for the model (2.3) reduces to
$S(t1,t2∣x)=[1-[1-exp {-[exp (-xTβ1) t1]1σ1}]a]b+[1-[1-exp {-[exp (-xTβ2) t2]1σ2}]a]b-[1-[exp {-{[exp (-xTβ1) t1]1σ1α+[exp (-xTβ2) t2]1σ2α}α}-exp {-[exp (-xTβ1) t1]1σ1}-exp {-[exp (-xTβ2) t2]1σ2}+1]a]b.$
The marginal survival function of Tk is given by
$S(tk∣x)={1-[1-exp {-[exp (-xTβk) tk]1σk}]a}b.$
3. Classical inference and diagnostics analysis
Let (t1k, δ1k, x1), …, (tnk, δnk, xn) be an observed sample of n independent observations, where tik represents the failure-time or the censoring-time, δik is a censoring indicator and xi = (xi1, …, xip)T is the vector of explanatory variables associated with the ith individual, where k = 1, 2 and i = 1, 2, …, n. The likelihood function for bivariate data was considered by Lawless (2003) and He and Lawless (2005). By taking explanatory variables xi and the joint survival function (2.10), the log-likelihood function for the BKwW regression model follows by summing the contributions from each one of the n individuals
$l(Ψ)=∑i=1n{δi1 δi2log(f(ti1,ti2∣xi))+δi1(1-δi2) log [-∂S(ti1,ti2∣xi)∂ti1]+(1-δi1)δi2 log [-∂S(ti1,ti2∣xi)∂ti2]+(1-δi1)(1-δi2) log(S(ti1,ti2∣xi))}.$
The density function f(ti1, ti2|xi) is defined in (2.4), where $Ψ=(a,b,α,βkT,σk)T$ is an unknown parameter vector and $βkT=(β0k,β1k,…,βpk)$ for k = 1, 2. The dimension of Ψ is (2p + 7).
The log-likelihood function (3.1) has the following restrictions on the parameters: a > 0, b > 0, 0 < α ≤ 1, and σk > 0 for k = 1, 2 and i = 1, …, n. So, to continue the estimation process it is necessary to rewrite the log-likelihood function including restrictions on the parametric space. We then consider the general problem of maximizing (3.1) subject to the linear constraints $ojTΨ-cj*≥0$, where oj, j = 1, 2, …, q are (2p + 7) × 1 vectors and $cj*$ are scalars, both known and fixed numbers. In this study, $cj*$ has value zero for the cases: a > 0, b > 0, α > 0, and σk > 0 and value one for α ≤ 1. To solve this problem, we use the adaptive barrier method (Lange, 1999). Thus, the log-likelihood function subject to linear constraints on the parameters reduces to
$lR(Ψ,ϑ)=l(Ψ)+ϑ∑j=1q(ojTΨ-cj*),$
where ϑ > 0 is the multiplier barrier term, $ojTΨ-cj*≥$ is the linear inequality constraint for j = 1, …, q, $Ψ=(a,b,α,βkT,σk)T$, and $βkT=(β0k,β1k,…,βpk)$.
The MLEs under constraints on the parameters in Ψ can be calculated numerically by maximizing (3.2). We can adopt the statistical software R to compute the estimate $Ψ^$. However, it is usually more convenient to use the constrOptim and function to maximize this function numerically. Initial values for $Ψ^$ are taken from the fit of the bivariate Weibull regression model corresponding to a = b = 1.
Under standard regularity conditions, the asymptotic distribution of ($Ψ^$Ψ) is multivariate normal N(2p+7)(0, I(Ψ)−1), where I(Ψ) is the expected information matrix for the (2p + 7) × 1 vector of parameters. The asymptotic covariance matrix I(Ψ) of $Ψ^$−1 can be approximated by the (2p+7)×(2p+7) inverse of the observed information matrix R(Ψ, ϑ) = −{2lR(Ψ, ϑ)/(ΨΨT)} evaluated at Ψ = $Ψ^$.
The approximate multivariate normal N(2p+7)(0, − R(Ψ, ϑ)−1) distribution can be used to construct confidence intervals for the parameters in Ψ in the usual way.
Besides estimation, hypothesis tests is another key issue. Let Ψ1 and Ψ2 be proper disjoint subsets of Ψ. Suppose that we want to test H0 : Ψ1 = Ψ10 versus H1 : Ψ1Ψ10, where Ψ2 is a nuisance parameter vector. Let $Ψ^$0 be the MLEs under H0, and define the likelihood ratio (LR) statistic w = 2{($Ψ^$)−($Ψ^$0)}. Under H0 and standard regularity conditions, w converges to a chi-square distribution with dim(Ψ1) degrees of freedom.
### 3.1. Diagnostics analysis: global influence
The first tool to perform sensitivity analysis, is by means of global influence starting from case deletion (Cook, 1977), which is a common approach to study the effect of dropping the ith case from the data. Case deletion for model (2.3) can be expressed as
$F(t(i)1,t(i)2∣x)=1-[1-{exp [-{[exp (-x(i)Tβ1) t(i)1]1σ1α+[exp (-x(i)Tβ2) t(i)2]1σ2α}α]-exp {-[exp (-x(i)Tβ1) t(i)1]1σ1}-exp {-[exp (-x(i)Tβ2) t(i)2]1σ2}+1}a]b.$
Accordingly, a quantity with subscript “(i)” means the original quantity with the ith observation deleted. For model (3.3), the log-likelihood function is denoted by lR(i) (Ψ, ϑ).
Let $Ψ^(i)=(a^(i),b^(i),α^(i),β^k(i)T,σ^k(i))T$ be the MLEs under constraints on the parameters in Ψ obtained by maximizing lR(i)(Ψ, ϑ). To assess the influence of the ith observation on the MLEs under constraints on the parameters in Ψ, the idea is to compare the difference between $Ψ^$(i) and $Ψ^$. If deletion of an observation seriously influences the estimates, more attention should be directed to that observation. Hence, if $Ψ^$(i) is far from $Ψ^$, then the ith case is regarded as an influential observation. A first global influence measure of the ith observation is the standardized norm of $Ψ^$(i)$Ψ^$ (generalized Cook distance; GD) given by
$GDi(Ψ)=(Ψ^(i)-Ψ^)T[L¨R(Ψ,ϑ)] (Ψ^(i)-Ψ^).$
So, we can assess the values of GDi(a), GDi(b), GDi(α), GDi(βk), and GDi(σk) to estimate the impact of the ith observation on the estimates of a, b, α, βk, and σk, respectively. Another popular measure of the difference between $Ψ^$(i) and $Ψ^$ is the likelihood displacement (LD)
$LDi(Ψ)=2[lR(Ψ^,ϑ)-lR(i)(Ψ^(i),ϑ)].$
### 3.2. Diagnostics analysis: local influence
Since regression models are sensitive to the underlying model assumptions, performing sensitivity analysis in general is strongly advisable. Another approach is suggested by Cook (1986), where instead of removing observations, weights are given to them. Local influence calculation can be conducted for model (2.3). If likelihood displacement LD(ω) = 2{l($Ψ^$) − l($Ψ^$ω)} is used, where $Ψ^$ω denotes the MLE under the perturbed model, the normal curvature for Ψ at the direction d, ||d|| = 1, is given by Cd(Ψ) = 2|dTΔT[(Ψ)]−1Δd|, where Δ is a (2p + 7) × n matrix that depends on the perturbation scheme, and whose elements are given by Δvi = 2l(Ψ|ω)/Ψv∂ωi, i = 1, …, n and v = 1, 2, …, (2p + 7) evaluated at $Ψ^$ and ω0, where ω0 is the no perturbation vector (Cook, 1986). For the bivariate regression model, the elements of (Ψ) can be evaluated numerically. We can also calculate normal curvatures Cd(a), Cd(b), Cd(α), Cd(βk), and Cd(σk) to perform various index plots, for instance, the index plot of dmax, the eigenvector corresponding to Cdmax, the largest eigenvalue of the matrix B = −ΔT[(Ψ)]−1Δ. The index plots of Cdi(a), Cdi(b), Cdi(α), Cdi(βk), and Cdi(σk), called total local influence, where di denotes an n × 1 vector of zeros with one at the ith position. Thus, the curvature at direction di takes the form $Ci=2∣ΔiT[L¨(Ψ)]-1Δi∣$, where $ΔiT$ denotes the ith row of Δ. It is usual to show those cases such that Ci ≥ 2, where $C¯=(1/n)∑i=1nCi$.
Consider the vector of weights ω = (ω1, …, ωn)T. Under three perturbation schemes (case-weight perturbation, response perturbation and explanatory variable perturbation), we can easily derive from the log-likelihood (3.2) the matrix
$Δ=(Δvi)[(2p+7)×n]=(∂2l(Ψ∣ω)∂Ψv∂ωi)[(2p+7)×n],$
where v = 1, …, (2p + 7) and i = 1, …, n.
4. Bayesian inference and influence diagnostics
In this section, we consider the Bayesian method as an alternative analysis to incorporate previous knowledge of the parameters through informative prior density functions.
Let (t1k, δ1k, x1), …, (tnk, δnk, xn) be an observed sample of n independent observations, where tik represents the failure-time or the censoring-time, δik is a censoring indicator and xi = (xi1, …, xip)T is the vector of explanatory variables associated with the ith individual, where k = 1, 2 and i = 1, …, n. The log-likelihood function l(Ψ) for the model parameters $Ψ=(a,b,α,βkT,σ1,σ2)T$ of the BKwW regression model is given by equation (3.1).
We consider that a, b, α, βk, σ1, σ2 have independent priors,
$π(Ψ)=π(α)π(σ1)π(σ2)π(a)π(b)∏k=12π(βk),$
where
$π(βk)=π(β0k,β1k,…,βpk)=∏j*=0pπ(βj*k).$
Further, we assume the following prior distributions βj*k ~ N(0, 102) for k = 1, 2 and j* = 0, …, p, log(α/(1 + α)) ~ N(0, 102), log(σ1) ~ N(0, 102), log(σ2) ~ N(0, 102), log(a) ~ N(0, 102), and log(b) ~ N(0, 102). The normal distribution with mean μ and variance τ2 is denoted by N(μ, τ2). All the hyper-parameters have been specified to express non-informative priors.
By combining the likelihood function (exponential of the log-likelihood (3.1)) and the prior distribution (4.1), we obtain the joint posterior distribution, which is analytically intractable. Then, we have based our inference on the MCMC simulation methods. By changing variables ξ = (log[α/(1 + α)], log(σ1), log(σ2), βk, log(a), log(b)), the parameter space is transformed into ℛ(2p+7) (necessary for the work with Gaussian densities).
To implement the Metropolis-Hastings algorithm, we proceed as follows.
• Start with any point ξ(0) and stage indicator ν = 0;
• Generate a point ξ′ according to the transitional kernel Q(ξ′, ξν) = Np+2(ξν, ∑̃), where ∑̃ is the covariance matrix of ξ, which is the same in any stage;
• Update ξ(ν) to ξ(ν+01) = ξ′ with probability $pν*=min{1,π(ξ′∣D)/π(ξ(ν)∣D)}$, or keep Ψ(ν) with probability $1-pν*$;
• Repeat Steps (2) and (3) by increasing the stage indicator until the process has reached a stationary distribution.
All computations are performed in R software (R Development Core Team, 2016). In all the work, after 20,000 sample burn-in, we use every tenth sample from the 60,000 MCMC posterior samples to reduce the autocorrelations and yield better convergence results, thus obtaining an effective sample of size 6,000 upon which the posterior is based on. We monitor the convergence of the Metropolis-Hasting algorithm using the method proposed by Geweke (1992) as well as trace plots.
### 4.1. Model comparison criteria
A variety of methodologies can be applied for comparing several competing models for a given dataset and selecting those which provide the best fits to the data. We consider some of the Bayesian model selection criteria, namely, the deviance information criterion (DIC) proposed by Spiegelhalter et al. (2002), the expected Akaike information criterion (EAIC) by Brooks (2002) and the expected Bayesian (or Schwarz) information criterion (EBIC) by Carlin and Louis (2001). Let Ψ(1), …, Ψ(Q) be a sample of size Q of after the burn-in, where denote the full data. They are based on the posterior mean of the deviance, which can be approximated by $d¯=∑q*=1Qd(Ψq*)/Q$, where $d(Ψ)=-2∑i=1nlog [f(t1i,t2i∣Ψ)]$. The DIC criterion can be estimated using the MCMC output by $DIC^=d¯+ρ^d=2d¯-d^$, where ρD is the effective number of parameters defined as E{d(Ψ)} − d{E(Ψ)}, and d{E(Ψ)} is the deviance evaluated at the posterior mean.
Similarly, the EAIC and EBIC criteria can be estimated by $EAIC^=d¯+2#(Ψ)$ and $EBIC^=d¯+#(Ψ) log(n)$, where #(Ψ) is the number of model parameters. Comparing alternative models, the preferred model is the one with the smallest criteria values.
Other criteria such as LPML is derived from conditional predictive ordinate (CPO) statistics. Let denote the data with the deleted ith observation. We denote the posterior density of Ψ given by , i = 1, …, n. For the ith observation, CPOi is given by
$CPOi=∫Ψf(t1i,t2i∣Ψ)π(Ψ∣D(-i))dΨ={∫Ψπ(Ψ∣D)f(t1i,t2i∣Ψ)dΨ}-1.$
The CPOi can be interpreted as the height of the marginal density of the time for an event at ti. Therefore, high CPOi implies a better fit of the model. No closed-form of CPOi is available for the proposed model. However, a Monte Carlo estimate of CPOi can be obtained by using a single MCMC sample from the posterior distribution . A Monte Carlo approximation of CPOi (Ibrahim et al., 2001) is given by
$CPOi^={1Q∑q*=1Q1f (t1i,t2i∣Ψ(q*))}-1.$
For model comparisons, we use the log pseudo marginal likelihood (LPML) defined by $LPML=∑i=1nlog(CPOi^)$. The higher the LPML value, the better the fit of the model.
### 4.2. Bayesian case influence diagnostics
It is well known that regression models may be sensitive to underlying model assumptions. Therefore, a sensitivity analysis is strongly advisable. Cook (1986) uses this idea to motivate his assessment of influence analysis and suggests that more confidence should be put in a model relatively stable under small modifications. In order to investigate if some of the observations are influential for the Bayesian analysis, we consider the Bayesian case-deletion influence diagnostic measures for the joint posterior distribution based on the ψ-divergence (Peng and Dey, 1995)
Let Dψ(P, P(−i)) denote the ψ-divergence between P and P(−i), in which P denotes the posterior distribution of Ψ for the full data, and P(−i) denotes the posterior distribution of Ψ without the ith case. Therefore,
$Dψ (P,P(-i))=∫ψ (π (Ψ∣D(-i))π (Ψ∣D)) π(Ψ∣D) dΨ,$
where ψ is a convex function with ψ(1) = 0. Several choices concerning the ψ are given by Dey and Birmiwal (1994). For example, ψ(z*) = −log(z*) defines the Kullback-Leibler (K-L) divergence, ψ(z*) = 0.5|z* − 1| defines the L1 norm (or variational distance) and ψ(z*) = (z* − 1) log(z*) gives the J-distance (or the symmetric version of the K-L divergence).
Let Ψ(1), . . . ,Ψ(Q) be a sample of size Q from . Then, Dψ(P, P(−i)) can be calculated by
$Dψ^ (P,P(-i))=1Q∑q*=1Qψ (CPOi^f (t1i,t2i∣Ψ(q*))),$
where $CPOi^={(1/Q)∑q*=1Q1/f(t1i,t2i∣Ψ(q*))}-1$ is the numerical approximation of the conditional predictive ordinate statistic of the ith observation (Ibrahim, 2001).
Note that Dψ(P, P(−i)) can be interpreted as the ψ-divergence of the effect of deleting the ith case from the full data on the joint posterior distribution of Ψ. As pointed out by Peng and Dey (1995), it may be difficult for a practitioner to judge the cutoff point of the divergence measure so as to determine whether a small subset of observations is influential or not. By using a biased coin procedure (Peng and Dey, 1995), which has probability value ϕ, the ψ-divergence between the biased and unbiased coins is given by
$Dψ (f0,f1)=∫ψ (f0(y)f1(y))f1(y)dy,$
where f0(y) = ϕy(1 − ϕ)1−y and f1(y) = 0.5, y = 0, 1. If Dψ(f0, f1) = dψ(ϕ), it can be easily checked that dψ satisfies the following equation
$dψ (ϕ)=ψ(2ϕ)+ψ(2(1-ϕ))2.$
It is not difficult to see for the divergence measures considered that dψ increases as ϕ moves away from 0.5. In addition, dψ(ϕ) is symmetric about ϕ = 0.5 and dψ achieves its minimum value at ϕ = 0.5. For this point, dψ(0.5) = 0 and f0 = f1. Therefore, if we consider ϕ > 0.90 (or ϕ ≤ 0.10) as a strong bias in a coin, then dK-L(0.90) = 0.51, dJ(0.90) = 0.88, and dL1(0.90) = 0.4. In addition, an observation which dJ > 0.88 can also be considered influential if we use the J-distance. Similarly, using the K-L divergence and the L1 norm, we can consider an influential observation when dK-L > 0.51 and dL1 > 0.4, respectively.
5. Simulation study: maximum likelihood and Bayesian estimation
A simulation study is conducted to evaluate the parameter estimates for the proposed model. The results are obtained from 1,000 Monte Carlo simulations using the R software. In each replication, a random sample of size n is drawn from the BKwW regression model and the parameters are estimated by maximum likelihood and Bayesian estimation.
The samples denoted by (t11, t21), . . . , (t1n, t2n) are generated according to the following steps:
• Step 0: Set up the sample size n and start with stage indicator i = 1.
• Step 1: Generate the covariate x1i from a Bernoulli distribution with parameter 0.5 and the censorship time C1i from a uniform distribution U(0, τ1), where τ1 controls the percentage of censored observations.
• Step 2: Use the quantile function given in (2.9) to obtain
$T1i=(1λ1i) [-log {1-[1-(1-u1i)1b]1a}]σ1,$
where ui1 ~ U(0, 1) and λ1i = exp(−β01β11x1i).
• Step 3: Compare T1i with C1i in order to determine the indicator of censorship δ1i and the observed value given by t1i = min(T1i,C1i).
• Step 4: Generate the covariate x2i from a Bernoulli distribution with parameter 0.5 and the censorship time C2i from a uniform distribution U(0, τ2), where τ2 controls the percentage of censored observations.
• Step 5: Next, T2i is generated using a random variable ηi ~ U(0, 1) and the solution of the nonlinear equation, exp(−[{−log(1 − (1 − (1 − ui1)1/b)1/a)}1/α + (−log(1 − u2i))1/α]α) − 1 + u2i + (1 − (1 − ui1)1/b)1/aηiui1 = 0, by considering T2i = (1/λ2i)[−log{1 − [1 − (1 − u2i)1/b]1/a}]σ2, where λ2i = exp(−β02β21x2i).
• Step 6: Compare T2i with C2i in order to determine the indicator of censorship δ2i and the observed value given by t2i = min(T2i,C2i).
• Step 7: Do i = i + 1. If i = n stop, else return to Step 1.
The simulation study is performed for n = 50, 100, and 150. We consider the following values for the parameters of the model: α = 0.75, σ1 = 1.0, β01 = 4.0, β11 = 0.75, σ2 = 1.25, β02 = 3.25, β12 = 1.75, a = 1.0, and b = 0.75. For all sample sizes, the percentage of censored observations in the times 1 and 2 are approximately 30% and 20%, respectively.
Tables 1 and 2 provide the averages (Mean), biases and the mean square errors (MSEs) of the MLEs and Bayesian estimates of the parameters in the BKwW regression model, respectively. We can note that the MSE values decrease when the sample size increases in agreement with first-order asymptotics.
### 5.1. Influence of outlying observations
A goal of this study is to show the need for robust models to deal with the presence of outliers in the data. We generate a sample of length 200 with fixed parameters α = 0.5, σ1 = 3.0, β01 = −2.5, β11 = −3.5, σ2 = 1.5, β02 = −2.0, β12 = −3.0, a = 1.25, and b = 0.5.
We select cases 35, 95, and 132 for perturbation. The perturbation scheme is structured as following. To create influential observations artificially in the dataset, we choose one, two or three of these selected cases. For each case, we perturb one or both lifetimes as follows i = ti + 5St, i = 1, 2, where St is the standard deviation of the ti’s. For case 35, we perturb only the lifetime t1 and, for case 132, the lifetime t2, and for case 95, both lifetimes are perturbed.
In this study, we consider eight setups. Dataset a: original dataset without outliers; Dataset b: data with outlier 35; Dataset c: data with outlier 95; Dataset d: data with outlier 132; Dataset e: data with outliers 35 and 95; Dataset f: data with outliers 35 and 132; Dataset g: data with outliers 95 and 132; and dataset h: data with outliers 35, 95, and 132. The MCMC computations are made similar to those in the last subsection using the Geweke’s convergence diagnostic (Geweke, 1992) to monitor the convergence of the Gibbs samples as well as trace plots.
Table 3 reveals that the posterior inferences about the parameters are sensitive to the perturbation of the selected case(s), except the β parameters. Table 4 gives the Monte Carlo estimates of the measures DIC, EAIC, EBIC, and LPML for each perturbed version of the original data. As expected, the original simulated data (dataset a) yields the best fit.
We consider the sample from the posterior distributions of the parameters of the BKwW regression model to calculate the ψ-divergence measures in (4.3). The results in Table 5 reveal, before perturbation (Dataset a), that the selected cases are not influential according to all ψ-divergence measures. However, after perturbation (Dataset b–h), the measures increase, which indicates that the perturbed cases are influential.
Figures 24 display the four ψ-divergence measures for cases (a), (f), and (h), respectively. We can note that all measures identify influential case(s) and provide larger ψ-divergence measures in comparison to the other cases.
6. Application: renal insufficiency data
In this section, we perform a statistical analysis on the renal insufficiency study originally presented by McGilchrist and Aisbett (1991) using the BKwW regression model. Recently, these data are analyzed by Barriga et al. (2010) by considering a location scale model for bivariate survival times based on the proposal of a copula to model the dependence of bivariate survival data. The dataset refers to the occurrence times of two distinct infection events in patients suffering from renal insufficiency. The patients use portable dialysis machines and the occurrence of infection at the catheter insertion point is considered. When this occurs, the catheter must be removed until the infection is cured, when the catheter is reinserted. The times between insertion of the catheter and occurrence of an infection are recorded. Therefore, various infections can occur in the patients, but only two are recorded in this dataset. There are also situations when the catheter must be removed for reasons other than infection, in which case there is right censoring of the data. The response variables of interest are the times between catheter insertion and infection. For each patient i, i = 1, 2, …, 38, the associated variables are: ti1: time to occurrence of the first infection, in weeks; ti2: time to occurrence of the second infection, in weeks; δi1: censoring indicator of event 1; δi2: censoring indicator of event 2; xi1: patients sex (0: male, 1: female).
We perform an exploratory analysis, mainly considering the variables referring to the occurrence times of the two events of interest. The estimated Kendall correlation coefficient is ρ̂K = 0.03, thus indicating an absence of correlation between the times of the events of interest. Despite this very low correlation, we adopt these data to illustrate the application of the BKwW regression model. The parameter referring to the association between the responses in the regression model must detect this independence, without impairing the model’s adjustment to these data. The Kaplan-Meier survival estimates and the marginal KwW distributions fitted to both events 1 and 2 are displayed in Figure 5. So, it is adequate to assume the BKwW model for the survival times. Since the KwW distribution is adequate for the times to events 1 and 2, it is coherent, for the case of bivariate data, to consider the bivariate Weibull cumulative distribution (Hougaard, 1986).
### 6.1. Results: classical inference
Based on the results of Sections 2 and 3, Table 6 lists the MLEs of the parameters for the BKwW regression model, their standard errors and p-values. The results indicate that male patients have accelerated times for the second infection than female patients. This fact can be confirmed visually by means of Figure 6. The estimated association parameter indicates that the lifetimes are independent and confirm the result obtained at the beginning of this section, when calculating ρK.
Diagnostic analysis
After modeling, it is important to verify whether there are observations that influence the fit of the BKwW regression model. To investigate this, we calculate global influence measures, likelihood distance (LDi(Ψ)) and generalized Cook distance (GDi(Ψ)), as defined in Section 3, using the R software. The results of these influence measure index plots are displayed in Figure 7. Based on these plots, we note that case ♯21 is possibly an influential observation.
We apply the local influence theory developed in Section 3.2, where case-weight perturbation is used, and obtain the value of the maximum curvature Cdmax (Ψ) = 2.83. Figure 8 shows the plot of the eigenvector corresponding to dmax and Ci versus the observation index.
The influence of perturbations on the observed survival times is now analyzed (response variable perturbation). The value of the maximum curvature is Cdmax (Ψ) = 1677.50. In Figure 9, we plot dmax and Ci versus the observation index. Figure 9 indicates that the case #29 is distinguished from the others.
### Impact of the detected influential observations
We conclude that the diagnostic analysis (global influence and local influence) detect as potentially influential observations, the following two cases: ♯21 and ♯29. The observation ♯21 corresponds to a male with a longer time to first occurrence of the infection and a median time to occurrence of infection 2. The observation ♯29 is related to a male with less time until the occurrence of infection and a low time until the occurrence of infection 2. In order to reveal the impact of the two observations on the parameter estimates, we refit the model under some situations. First, we individually eliminate each one of these two observations. Next, we remove from the original dataset the totality of potentially influential observations.
Table 7 gives the relative changes (in percentages) of the estimates defined by RCΨv = [($Ψ^$v$Ψ^$v(I))/$Ψ^$v] × 100, and the corresponding p-values, where $Ψ^$v(I) is the MLE of Ψv after the “set I” of observations is removed.
The figures in Table 7 reveal that there are substantial changes in the estimated parameter values as well as changes in the set of parameters that show the model’s significance. Despite this sensitivity of the model, inclusion and exclusion of these points do not imply changes in the interpretation of the results, since there is no change in the sign of the coefficient referring to the sex variable, which indicates that men tend to suffer infections sooner than women.
### 6.2. Results: Bayesian analysis
Table 8 provides the means, standard deviations (SDs) and 95% Bayesian credible intervals (CI (95%)) for the estimates of the parameters in the BKwW regression model fitted to the original dataset and when two observations (♯15 and ♯21) are dropped.
The sample considered for the posterior distributions of the parameters of the BKwW regression model and the ψ-divergence measures in (4.3) are calculated. Figure 10 displays the index plot of the three ψ-divergence measures. The cases ♯15 and ♯21 are possible influential observations in the posterior distribution. The three influence diagnostic measures for these two observations are given in
Also, we obtain the DIC, EAIC, EBIC, and LPML values to compare the impact of the influential points. Table 10 presents the values for the complete data, without observation ♯15, ♯21 and both of two cases. By dropping the observation ♯21, we obtain a better fit compared to the case without the observation ♯15.
### 6.3. Goodness-of-fit
We check the quality of the fitted regression model by means of plots of the Kaplan-Meier survival function and the estimated marginal survival functions for the BKwW regression model. Figure 11 shows that the proposed model is well adjusted, because its fitted survival function follows the Kaplan-Meier curve closely.
7. Conclusions and remarks
We propose the BKwW regression model as an extension of the bivariate Weibull distribution. We estimate the model parameters using the maximum likelihood methodology subject to linear restrictions in the parameters. We also perform a sensitivity analysis to assess the robustness of the results. We carry out the estimation method using the R software. Several functions are implemented as well as new functions with the partial derivatives of the log-likelihood function.
The optimization process is sensitive to the choice of the initial values used in the algorithms. To choose the initial regression parameters, we obtain the estimates considering marginal models for each response variable, while we choose the values a = 1 and b = 1 for the other parameters that therefore represent the special bivariate Weibull distribution. By using the global influence, local influence and total local influence techniques, we identify some possible influential points. We examine these points to detect possible errors in managing the dataset, but discard this possibility. Further, we discuss the use of MCMC methods as an alternative way to perform Bayesian inference for lifetime data that are supposed to follow the BKwW regression model. We also adopt Bayesian case influence diagnostics based on the K-L divergence to study the sensitivity of the Bayesian estimates under perturbations in the model/data. We verify the robustness of the results after re-estimating the model parameters after individual and joint exclusion of the identified points. Despite small changes in the estimates, the results and their interpretations are not influenced by the possible influential points indicated by the diagnostic techniques. The functions and techniques presented allow the utility of the BKwW regression model to analyze survival data with two response variables and covariates, and to perform sensitivity analysis to confirm the adequacy of the model assumptions and validate the obtained results.
Appendix
Expressions for A(·), B(·), C(·), and G(·) described in Section 2 are given below:
$A(t1,t2∣x)=-a(b-1)Ga(t1,t2∣x) D(t1,t2∣x) E(t1,t2∣x)1-Ga(t1,t2∣x),B(t1,t2∣x)=(a-1) D(t1,t2∣x) E(t1,t2∣x),C(t1,t2∣x)=G(t1,t2∣x)g(t1,t2∣x),G(t1,t2∣x)=exp {-[(exp {-xTβ1} t1)1σ1α+(exp {-xTβ2} t2)1σ2α]α}-exp [-(exp {-xTβ1} t1)1σ1]-exp [-(exp {-xTβ2} t2)1σ2]+1,D(t1,t2∣x)=-[(exp {-xTβ1} t1)1σ1α+(exp {-xTβ2} t2)1σ2α]α-1t11σ1α-1exp {-xTβ1}1σ1α1σ1exp {-[(exp {-xTβ1} t1)1σ1α+(exp {-xTβ2} t2)1σ2α]α}+exp {-xTβ1}1σ1 t11σ1-11σ1exp [-(exp {-xTβ1} t1)1σ1],E(t1,t2∣x)=-[(exp {-xTβ1} t1)1σ1α+(exp {-xTβ2} t2)1σ2α]α-1t21σ2α-1exp {-xTβ2}1σ2α1σ2exp {-[(exp {-xTβ1} t1)1σ1α+(exp {-xTβ2} t2)1σ2α]α}+exp {-xTβ2}1σ2 t21σ2-11σ2exp [-(exp {-xTβ2} t2)1σ2],$
and
$g(t1,t2∣x)=1σ1exp {-xTβ1} (exp {-xTβ1} t1)1σ1α-11σ2exp {-xTβ2} (exp {-xTβ2} t2)1σ2α-1[(exp {-xTβ1} t1)1σ1α+(exp {-xTβ2} t2)1σ2α]α-2{[(exp {-xTβ1} t1)1σ1α+(exp {-xTβ2} t2)1σ2α]α+1α-1}exp {-[(exp {-xTβ1} t1)1σ1α+(exp {-xTβ2} t2)1σ2α]α}.$
Figures
Fig. 1. Joint probability density function for some parameter values.
Fig. 2. ψ-divergence measures from Dataset (a).
Fig. 3. ψ-divergence measures from Dataset (f).
Fig. 4. ψ-divergence measures from Dataset (h).
Fig. 5. Marginal survival estimates by Kaplan-Meier and Kumaraswamy Weibull distribution based on the renal insufficiency data.
Fig. 6. Survival curves marginally estimated by the Kaplan-Meier method for the renal insufficiency data for each event by means of the sex variable.
Fig. 7. (a) Index plot of GDi() (generalized Cook distance). (b) Index plot of LDi() (likelihood distance) to the renal insufficiency data.
Fig. 8. (a) Index plot of max for (case-weight perturbation) and (b) total local influence for (case-weight perturbation) based on the fit of the BKwW model to the renal insufficiency data.
Fig. 9. (a) Index plot of max for (simultaneous response perturbation) and (b) total local influence for (simultaneous response perturbation) based on the model fitted to the renal insufficiency data.
Fig. 10. Index plots of ψ-divergence measures for the renal insufficiency data.
Fig. 11. Kaplan-Meier curves stratified by gender (0 = masculine, 1 = feminine) and estimated survival functions for the renal insufficiency data.
TABLES
### Table 1
Mean estimates, Bias and MSEs of the MLEs of the parameters in the bivariate Kumaraswamy Weibull regression model
Parameter (true value) N = 50 N = 100 N = 150
Mean Bias MSE Mean Bias MSE Mean Bias MSE
α (0.75) 0.8291 0.0791 0.0153 0.8265 0.0765 0.0105 0.8237 0.0737 0.0085
σ1 (1.00) 1.4484 0.4484 0.2878 1.3876 0.3876 0.1908 1.3754 0.3754 0.1655
β01 (4.00) 4.4953 0.4953 0.3299 4.5588 0.5588 0.3568 4.5528 0.5528 0.3350
β11 (0.75) 0.7097 −0.0403 0.1078 0.6589 −0.0911 0.0639 0.6473 −0.1027 0.0484
σ2 (1.25) 1.5893 0.3393 0.2878 1.5172 0.2672 0.1908 1.5064 0.2564 0.1655
β02 (3.25) 2.8722 −0.3778 0.1935 2.8918 −0.3582 0.1549 2.9043 −0.3457 0.1355
β12 (1.75) 1.7191 −0.0309 0.0742 1.7039 −0.0461 0.0386 1.6916 −0.0584 0.0274
a (1.00) 0.5705 −0.4295 0.2116 0.5710 −0.4290 0.1977 0.5669 −0.4331 0.1963
b (0.75) 0.9049 0.1549 0.0707 0.9256 0.1756 0.0517 0.9127 0.1627 0.0413
MSE = biases and the mean square error; MLE = maximum likelihood estimator.
### Table 2
Mean estimates, biases and MSEs of the Bayesian estimates of the parameters in the bivariate Kumaraswamy Weibull regression model
Parameter (true value) N = 50 N = 100 N = 150
Mean Bias MSE Mean Bias MSE Mean Bias MSE
α (0.75) 0.9027 0.1527 0.0433 0.8615 0.1115 0.0263 0.8466 0.0966 0.0187
σ1 (1.00) 1.4323 0.4323 0.3582 1.3811 0.3811 0.2231 1.3689 0.3689 0.1859
β01 (4.00) 4.5309 0.5309 0.4626 4.5699 0.5699 0.4057 4.5582 0.5582 0.3619
β11 (0.75) 0.7189 −0.0311 0.2439 0.6658 −0.0842 0.1183 0.6542 −0.0958 0.0815
σ2 (1.25) 1.5642 0.3142 0.3582 1.5061 0.2561 0.2231 1.4923 0.2423 0.1859
β02 (3.25) 2.8727 −0.3773 0.2455 2.8966 −0.3534 0.1716 2.9022 −0.3478 0.1515
β12 (1.75) 1.7407 −0.0093 0.1619 1.7200 −0.0300 0.0731 1.6987 −0.0513 0.0493
a (1.00) 0.5730 −0.4270 0.2515 0.5732 −0.4268 0.2140 0.5645 −0.4355 0.2084
b (0.75) 0.9153 0.1653 0.2987 0.9190 0.1690 0.1058 0.8973 0.1473 0.0559
MSE = biases and the mean square error; MLE = maximum likelihood estimator.
### Table 3
Posterior means and standard deviations (SDs) for the bivariate Kumaraswamy Weibull regression model according to different perturbation schemes
Dataset Perturbed case α σ1 β01 β11 σ2 β02 β12 a b
Mean (SD) Mean (SD) Mean (SD) Mean (SD) Mean (SD) Mean (SD) Mean (SD) Mean (SD) Mean (SD)
a None 0.6508 3.5380 −2.2298 −3.6836 1.3794 −2.6428 −3.3939 0.8366 0.6921
(0.0578) (0.3078) (0.0458) (0.0525) (0.1332) (0.1139) (0.1386) (0.1470) (0.0917)
b 35 0.6238 3.0476 −2.2270 −3.7769 1.2228 −2.6994 −3.5492 0.9812 0.6296
(0.0636) (0.2550) (0.0557) (0.0542) (0.1147) (0.1314) (0.1447) (0.1800) (0.0881)
c 95 0.6244) 3.0751 −2.2256 −3.7723 1.2334 −2.6925 −3.5439 0.9677 0.6288
(0.0610) (0.2511) (0.0532) (0.0544) (0.1124) (0.1282) (0.1432) (0.1709) (0.0879)
d 132 0.4392 2.5259 −2.2664 −3.6404 0.8930 −2.6394 −3.3198 1.5083 1.1779
(0.0487) (0.2528) (0.0592) (0.0606) (0.0827) (0.1666) (0.1710) (0.2647) (0.1709)
e {35 95} 0.6121 2.8289 −2.2190 −3.8397 1.1567 −2.7151 −3.6568) 1.0416 0.5838
(0.0640) (0.2238) (0.0606) (0.0565) (0.1060) (0.1367) (0.1509) (0.1908) (0.0829)
f {35, 132} 0.3922 2.1309 −2.2725 −3.7082 0.7735 −2.7021 −3.4645 1.8419 1.2165
(0.0460) (0.2052) (0.0712) (0.0615) (0.0700) (0.1956) (0.1741) (0.3199) (0.1852)
g {95, 132} 0.3958 2.1574 −2.2769 −3.7204 0.7797 −2.7047 −3.5108 1.8169 1.1387
(0.0458) (0.2071) (0.0718) (0.0586) (0.0694) (0.1908) (0.1730) (0.3232) (0.1637)
h {35, 95, 132} 0.3803 2.0017 −2.2713 −3.7651 0.7451 −2.7274 −3.5925 1.9430 1.1302
(0.0456) (0.1878) (0.0799) (0.0641) (0.0672) (0.2074) (0.1747) (0.3573) (0.1907)
### Table 4
Bayesian criteria for each perturbed version by fitting the bivariate Kumaraswamy Weibull regression model according to different perturbation schemes
Data names Bayesian criteria
EAIC EBIC DIC LPML
a −2740.684 −2710.999 −2750.117 1374.758
b −2717.665 −2687.981 −2726.491 1361.560
c −2718.284 −2688.599 −2727.412 1362.171
d −2693.735 −2664.050 −2703.276 1344.087
e −2700.677 −2670.993 −2709.585 1353.458
f −2666.795 −2637.110 −2675.774 1330.980
g −2665.915 −2636.230 −2675.220 1332.170
h −2650.958 −2621.273 −2660.200 1324.159
EAIC = expected Akaike information criterion; EBIC = expected Bayesian information criterion; DIC = deviance information criterion; LPML = log pseudo marginal likelihood.
### Table 5
Case influence diagnostics for the simulated data
Data names Case number ψ-divergence measure
dK-L dJ dL1
a 35 0.0048 0.0096 0.0387
95 0.0013 0.0025 0.0198
132 0.3832 0.7914 0.3426
b 35 2.0466 4.3206 0.7223
c 95 1.7511 3.6743 0.6782
d 132 8.2482 15.1319 0.9833
e 35 0.7872 1.6328 0.4880
95 1.0060 2.0804 0.5427
f 35 1.1026 2.4538 0.5679
132 6.7799 13.475 0.9618
g 95 1.1436 2.4212 0.5735
132 5.3909 9.9707 0.9179
h 35 0.5931 1.3437 0.4240
95 1.1146 3.1001 0.5759
132 5.3933 10.4104 0.9240
### Table 6
MLEs for the bivariate Kumaraswamy Weibull regression model based on the renal insufficiency data
Parameter Estimate Standard error p-value
β01 2.5204 1.6159 0.1188
β11 0.7075 0.4981 0.1555
β02 1.7274 1.2462 0.1657
β12 1.9164 0.3659 <0.0001
σ1 1.6826 0.8100 -
σ2 1.4891 0.6823 -
a 2.9146 1.1558 -
b 0.5782 0.1739 -
α 0.9999 0.3743 -
MLEs = maximum likelihood estimators.
### Table 7
Relative changes, estimates, and the corresponding p-values in parentheses
Set Icomplete I – {21} I – {29} I – {21 and 29}
β01 [−] [1.692] [6.9591] [0.0000]
2.5204 2.4777 2.3450 2.5204
(0.1188) (0.0846) (0.1649) (0.0213)
β11 [−] [−67.7746] [25.0070] [0.0000]
0.7075 1.1871 0.5306 0.7075
(0.1555) (0.0291) (0.2141) (0.1854)
β02 [−] [−10.9615] [29.7890] [0.0000]
1.7274 1.9168 1.2128 1.7274
(0.1657) (0.1098) (0.4268) (0.0421)
β12 [−] [−1.9063] [−0.8373] [0.0000]
1.9164 1.9529 1.9324 1.9164
(0.0000) (0.0000) (0.0000) (0.0000)
σ1 [−] [9.1365] [−4.1007] [0.0000]
1.6826 1.5289 1.7516 1.6826
σ2 [−] [0.3287] [−14.7761] [0.0000]
1.4891 1.4842 1.7091 1.4891
a [−] [6.1817] [−41.5784] [0.0000]
2.9146 2.7344 4.1264 2.9146
b [−] [−31.6078] [5.2288] [0.0000]
0.5782 0.7609 0.5479 0.5782
α [−] [0.0000] [0.0000] [0.0000]
0.9999 1.0000 1.0000 1.0000
### Table 8
Case influence diagnostics for renal insufficiency data
Parameter Complete data set Dropped observations 15 and 21
Mean SD CI (95%) Mean SD CI (95%)
α 0.9989 0.0142 0.9999 1.0000 0.9992 0.0106 0.9998 1.0000
σ1 0.9572 0.1867 0.6394 1.3806 1.1916 0.2685 0.7447 1.7832
β01 4.1414 0.4844 3.1348 5.0698 3.8239 0.4435 2.9181 4.6951
β11 0.7127 0.4501 −0.1110 1.6324 0.9632 0.4367 0.1139 1.8319
σ2 1.0956 0.1828 0.7657 1.4866 1.1331 0.2079 0.7687 1.5826
β02 3.1853 0.3614 2.4386 3.8682 3.0973 0.3728 2.3768 3.8408
β12 1.8701 0.3513 1.1885 2.5791 1.9809 0.3921 1.1779 2.7060
a 0.8438 0.2722 0.4398 1.4704 0.8618 0.2862 0.4328 1.5458
b 0.6876 0.1340 0.4161 0.9312 0.8132 0.1433 0.5117 1.0495
SD = standard deviation; CI = credible intervals.
### Table 9
Case influence diagnostics for the renal insufficiency data
Case number ψ-divergence measure
dK-L dJ dL1
15 0.5722 1.3869 0.4380
21 1.7783 4.1576 0.7093
### Table 10
Bayesian criteria
Dropped observation Criterion
EAIC EBIC DIC LPML
None 683.4028 698.1411 673.4582 −337.3232
15 664.0772 678.5755 654.2425 −327.3600
21 647.4933 661.9915 637.0273 −318.9128
15 and 21 628.4176 642.6693 618.2174 −309.4217
EAIC = expected Akaike information criterion; EBIC = expected Bayesian information criterion; DIC = deviance information criterion; LPML = log pseudo marginal likelihood.
References
1. Barriga, GDC, Louzada-Neto, F, Ortega, EMM, and Cancho, VG (2010). A bivariate regression model for matched paired survival data: local influence and residual analysis. Statistics Methods and Applications. 19, 477-496.
2. Brooks, SP (2002). Discussion on the paper by Spiegelhalter, Best, Carlin, and van der Linde. Journal of the Royal Statistical Society Series B. 64, 616-618.
3. Carlin, BP, and Louis, TA (2001). Bayes and Empirical Bayes Methods for Data Analysis. Boca Raton: Chapman & Hall/CRC
4. Cook, RD (1977). Detection of influential observations in linear regression. Technometrics. 19, 15-18.
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6. Cordeiro, GM, and de Castro, M (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation. 81, 883-898.
7. Cordeiro, GM, Ortega, EMM, and Nadarajah, S (2010). The Kumaraswamy Weibull distribution with application to failure data. Journal of the Franklin Institute. 347, 1399-1429.
8. da Cruz, JN, Ortega, EMM, and Cordeiro, GM (2016). The log-odd log-logistic Weibull regression model: modelling, estimation, influence diagnostics and residual analysis. Journal of Statistical Computation and Simulation. 86, 1516-1538.
9. Dey, D, and Birmiwal, L (1994). Robust Bayesian analysis using divergence measures. Statistics and Probability Letters. 20, 287-294.
10. Geweke, J (1992). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. Bayesian Statistics, Bernardo, JM, Berger, JO, Dawid, AP, and Smith, AFM, ed: Oxford University Press, pp. 169-188
11. Hashimoto, EM, Ortega, EMM, Cancho, VG, and Cordeiro, GM (2013). On estimation and diagnostics analysis in log-generalized gamma regression model for interval-censored data. Statistics. 47, 379-398.
12. He, W, and Lawless, JF (2005). Bivariate location-scale models for regression analysis, with applications to lifetime data. Journal of the Royal Statistical Society. 67, 63-78.
13. Hougaard, P (1986). A class of multivariate failure time distributions. Biometrika. 73, 671-678.
14. Ibrahim, JG, Chen, MH, and Sinha, D (2001). Bayesian Survival Analysis. New York: Springer
15. Lange, K (1999). Numerical Analysis for Statisticians. New York: Springer
16. Lawless, JF (2003). Statistical Models and Methods for Lifetime Data. New York: Wiley
17. McGilchrist, CA, and Aisbett, CW (1991). Regression with frailty in survival analysis. Biometrics. 47, 461-466.
18. Mudholkar, GS, Srivastava, DK, and Friemer, M (1995). The exponentiated Weibull family: a reanalysis of the bus-motor-failure data. Technometrics. 37, 436-445.
19. Ortega, EMM, Cordeiro, GM, and Kattan, MW (2013). The log-beta Weibull regression model with application to predict recurrence of prostate cancer. Statistical Papers. 54, 113-132.
20. Ortega, EMM, Cordeiro, GM, Campelo, AK, Kattan, MW, and Cancho, VG (2015). A power series beta Weibull regression model for predicting breast carcinoma. Statistics in Medicine. 34, 1366-1388.
21. Peng, F, and Dey, D (1995). Bayesian analysis of outlier problems using divergence measures. Canadian Journal of Statistics. 23, 199-213.
22. R Core Team (2016). R: a language and environment for statistical computing.URL https://www.R-project.org
23. Silva, GO, Ortega, EMM, and Cordeiro, GM (2010). The beta modified Weibull distribution. Lifetime Data Analysis. 16, 409-430.
24. Spiegelhalter, DJ, Best, NG, Carlin, BP, and van der Linde, A (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society Series B. 64, 583-639. | 2020-02-29 03:20:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 78, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7469020485877991, "perplexity": 2333.3606205739675}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875148375.36/warc/CC-MAIN-20200229022458-20200229052458-00169.warc.gz"} |
https://rxcal.org/practice/practice/4120181101074213-62-rxcal-102.php?id=102&domain=20&version=1 | ### Drug content in the container
10. Dose - general concepts 10.1) Oral liquid 10.1.1) Oral liquid
10.1.1.1) Oral liquid Normal 1
Total tried: Correct: Wrong:
A patient is taking an oral solution 1 tbsp QID. If the patient is taking 732 mg of the drug in each dose, and if the bottle supplies the drug for 30 days, then calculate the amount of drug (in gram unit) contained in the bottle.
Click on the button below to see the answer and explanations
lb equals 87.84 g kg
Volume of each dose (1 tbsp) = 15 mL.
Number of dose per day (QID) = 4
Numder of days the bottle is supplied for (30 days) = 30
Therefore, volume of the medication in the bottle = 15 × 4 × 30 mL = 1800 mL.
Given that, there is 732 mg drug contained in each dose (1 tbsp). Therefore, we can write:
(732\quad mg)/(15\quad mL)=x/(1800 \quad mL)
therefore x = 87840 \quad mg = 87.84\quad g Ans. | 2023-01-30 02:12:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6054628491401672, "perplexity": 7985.0922997744565}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499790.41/warc/CC-MAIN-20230130003215-20230130033215-00478.warc.gz"} |
http://scipy-cookbook.readthedocs.io/items/discrete_bvp.html | # Solving a discrete boundary-value problem in scipy¶
## Mathematical formulation¶
We consider a nonlinear elliptic boundary-value problem in a square domain $\Omega = [0, 1] \times [0, 1]$: $$\Delta u + k f(u) = 0 \\ u = 0 \text{ on } \partial \Omega$$
Here $u = u(x,y)$ is an unknown function, $\Delta$ is Laplace operator, $k$ is some constant and $f(u)$ is a given function.
A usual computational approach to such problems is discretization. We use a uniform grid with some step $h$, and define $u_{i, j} = u(i h , jh)$. By approximating Laplace operator using 5-point finite difference we get a system of equations in the form: $$u_{i - 1, j} + u_{i + 1, j} + u_{i, j - 1} + u_{i, j + 1} - 4 u_{i,j} + c f(u_{i,j}) = 0 \\ u_{i, j} = 0 \text{ on } \partial \Omega$$
Here $c = k h^2$.
## Defining the problem for scipy¶
From now on we focus on the discrete version and consider a grid with $n = 100$ ticks for each dimension and set $c = 1$ and $f(u) = u^3$.
In [1]:
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import least_squares
from scipy.sparse import coo_matrix
In [2]:
n = 100
c = 1
In [3]:
def f(u):
return u**3
def f_prime(u):
return 3 * u**2
To solve the system of equations we will use scipy.optimize.least_squares.
We define a function computing left-hand sides of each equation. Note that we assume values on the boundary to be fixed at zeros and don't change them during optimization.
In [4]:
def fun(u, n, f, f_prime, c, **kwargs):
v = np.zeros((n + 2, n + 2))
u = u.reshape((n, n))
v[1:-1, 1:-1] = u
y = v[:-2, 1:-1] + v[2:, 1:-1] + v[1:-1, :-2] + v[1:-1, 2:] - 4 * u + c * f(u)
return y.ravel()
It is always recommened to provide analytical Jacobian if possible. In our problem we have $n^2=10000$ equations and variables, but each equation depends only on few variables, thus we should compute Jacobian in a sparse format.
It is convenient to precompute indices of rows and columns of nonzero elements in Jacobian. We definte the corresponding function:
In [5]:
def compute_jac_indices(n):
i = np.arange(n)
jj, ii = np.meshgrid(i, i)
ii = ii.ravel()
jj = jj.ravel()
ij = np.arange(n**2)
jac_rows = [ij]
jac_cols = [ij]
mask = ii < n - 1
mask = jj < n - 1
return np.hstack(jac_rows), np.hstack(jac_cols)
After that computing Jacobian in coo_matrix format is simple:
In [6]:
jac_rows, jac_cols = compute_jac_indices(n)
In [7]:
def jac(u, n, f, f_prime, c, jac_rows=None, jac_cols=None):
jac_values = np.ones_like(jac_cols, dtype=float)
jac_values[:n**2] = -4 + c * f_prime(u)
return coo_matrix((jac_values, (jac_rows, jac_cols)), shape=(n**2, n**2))
## Solving the problem¶
Without any insight to the problem we set all the values to 0.5 initially. Note, that it is not guranteed that the given continuous or discrete problems have a unique solution.
In [8]:
u0 = np.ones(n**2) * 0.5
Precompute rows and columns of nonzero elements in Jacobian:
In [9]:
jac_rows, jac_cols = compute_jac_indices(n)
Now we are ready to run the optimization. The first solution will be computed without imposing any bounds on the variables.
In [10]:
res_1 = least_squares(fun, u0, jac=jac, gtol=1e-3, args=(n, f, f_prime, c), kwargs={'jac_rows': jac_rows, 'jac_cols': jac_cols}, verbose=1)
gtol termination condition is satisfied.
Function evaluations 106, initial cost 1.0412e+02, final cost 5.2767e-03, first-order optimality 9.04e-04.
Below we visualize the first solution. The left plot shows the flatten solution, the middle plot shows how the solution looks in the square domain, and the right plot shows final residuals in each node.
In [11]:
plt.figure(figsize=(16, 5))
plt.subplot(132)
plt.imshow(res_1.x.reshape((n, n)), cmap='coolwarm', vmin=-max(abs(res_1.x)), vmax=max(abs(res_1.x)))
plt.subplot(131)
plt.plot(res_1.x)
plt.subplot(133)
plt.plot(res_1.fun)
plt.tight_layout()
It is possible that some physical considerations require that the solution must be non-negative everywhere. We can achieve that by specifying bounds to the solver:
In [12]:
res_2 = least_squares(fun, u0, jac=jac, bounds=(0, np.inf), gtol=1e-3,
args=(n, f, f_prime, c), kwargs={'jac_rows': jac_rows, 'jac_cols': jac_cols}, verbose=1)
gtol termination condition is satisfied.
Function evaluations 34, initial cost 1.0412e+02, final cost 4.1342e-02, first-order optimality 9.55e-04.
In [13]:
plt.figure(figsize=(16, 5))
plt.subplot(132)
plt.imshow(res_2.x.reshape((n, n)), cmap='Reds')
You can try running optimization from different starting points, using different bounds or changing $c$ and $f(u)$, and see how it affects the result from least_squares solver. | 2018-06-23 06:05:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8390097618103027, "perplexity": 3075.841208021701}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864943.28/warc/CC-MAIN-20180623054721-20180623074721-00516.warc.gz"} |
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# A takes half as long as B takes to do a piece of work, C does it in t
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A takes half as long as B takes to do a piece of work, C does it in t [#permalink]
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26 Nov 2019, 11:46
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A takes half as long as B takes to do a piece of work, C does it in the same time as A and B together, and if all three work together they would take 7 days, how long would each take separately?
A) 21 days, 42 days, 14days
B) 20days, 40 days, 40/3 days
C) 15 days, 45 days, 45/4 days
D) None of these
E) Cannot be determined
VP
Joined: 19 Oct 2018
Posts: 1171
Location: India
Re: A takes half as long as B takes to do a piece of work, C does it in t [#permalink]
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26 Nov 2019, 11:55
Efficiency of A =2x
Efficiency of B = x
Efficiency of C= 3x
Time taken by A= $$\frac{7*(3x+2x+x)}{2x}$$=21
Time taken by B= $$\frac{7*(3x+2x+x)}{x}$$=42
Time taken by C=$$\frac{ 7*(3x+2x+x)}{3x}$$=14
Ansh777 wrote:
A takes half as long as B takes to do a piece of work, C does it in the same time as A and B together, and if all three work together they would take 7 days, how long would each take separately?
A) 21 days, 42 days, 14days
B) 20days, 40 days, 40/3 days
C) 15 days, 45 days, 45/4 days
D) None of these
E) Cannot be determined
VP
Joined: 20 Jul 2017
Posts: 1145
Location: India
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Re: A takes half as long as B takes to do a piece of work, C does it in t [#permalink]
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27 Nov 2019, 09:50
1
Ansh777 wrote:
A takes half as long as B takes to do a piece of work, C does it in the same time as A and B together, and if all three work together they would take 7 days, how long would each take separately?
A) 21 days, 42 days, 14days
B) 20days, 40 days, 40/3 days
C) 15 days, 45 days, 45/4 days
D) None of these
E) Cannot be determined
Let the time taken by A = t
—> Time taken by B = 2t &
Time taken by C = 2t*t/(2t + t) = 2t/3
working together they can complete 7 days
—> 1/t + 1/2t + 3/2t = 1/7
—> 3/t = 1/7
—> t = 21 days
A = t = 21
B = 2t = 42
C = 2t/3 = 2/3*21 = 14
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Re: A takes half as long as B takes to do a piece of work, C does it in t [#permalink]
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27 Nov 2019, 09:50
Ansh777 wrote:
A takes half as long as B takes to do a piece of work, C does it in the same time as A and B together, and if all three work together they would take 7 days, how long would each take separately?
A) 21 days, 42 days, 14days
B) 20days, 40 days, 40/3 days
C) 15 days, 45 days, 45/4 days
D) None of these
E) Cannot be determined
Well, A takes half as long as B.
So Option C is gone.
C take as long as A&B together.
Option A works.
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Re: A takes half as long as B takes to do a piece of work, C does it in t [#permalink]
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01 Dec 2019, 05:59
Dillesh4096 wrote:
Ansh777 wrote:
A takes half as long as B takes to do a piece of work, C does it in the same time as A and B together, and if all three work together they would take 7 days, how long would each take separately?
A) 21 days, 42 days, 14days
B) 20days, 40 days, 40/3 days
C) 15 days, 45 days, 45/4 days
D) None of these
E) Cannot be determined
Let the time taken by A = t
—> Time taken by B = 2t &
Time taken by C = 2t*t/(2t + t) = 2t/3
working together they can complete 7 days
—> 1/t + 1/2t + 3/2t = 1/7
—> 3/t = 1/7
—> t = 21 days
A = t = 21
B = 2t = 42
C = 2t/3 = 2/3*21 = 14
Posted from my mobile device
Can you plz explain how did u find this 'Time taken by C = 2t*t/(2t + t) = 2t/3' ?
Re: A takes half as long as B takes to do a piece of work, C does it in t [#permalink] 01 Dec 2019, 05:59
Display posts from previous: Sort by | 2019-12-12 05:48:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5088071823120117, "perplexity": 3189.686009815826}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540537212.96/warc/CC-MAIN-20191212051311-20191212075311-00163.warc.gz"} |
http://pari.math.u-bordeaux.fr/archives/pari-dev-0301/msg00047.html | Ralf Stephan on Wed, 15 Jan 2003 11:02:23 +0100
Re: Pi
Karim Belabas wrote
> On Tue, 14 Jan 2003, Bill Allombert wrote:
> > If it is your question, there is no incremental algorithm to compute Pi
> > implemented. Computing Pi at 12200 d.p does not use the knowledge of the
> > first 12000 d.p.
BBP is O(n\log^3n) for the nth digit but constpi() is[*] faster so...
> > I do not know if it would make sense to do that.
>
> It definitely would, using the log((1+i) / 2) expansion. I don't think it
> would have a major effect on running times, but if somebody wants to try it...
Now, if it wouldn't have a major effect, scratch it. I have the impression,
to fully understand the constpi() code I will have to do a little more
> Also, a different Pi formula needs to be implemented [ the current one
> was chosen so that almost all multiplication/divisions involve a single
> precision operand, which is not at all what we want now ! ].
ralf
[*] no ref, I decide to believe Karim+BBP on that.
• Follow-Ups:
• Re: Pi
• From: Karim BELABAS <Karim.Belabas@math.u-psud.fr>
• References:
• Re: Pi
• From: Bill Allombert <allomber@math.u-bordeaux.fr>
• Re: Pi
• From: Karim BELABAS <Karim.Belabas@math.u-psud.fr> | 2016-10-24 12:25:47 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8308578133583069, "perplexity": 7339.444286520463}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719566.74/warc/CC-MAIN-20161020183839-00092-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://www.tutorialspoint.com/count-of-matrices-of-different-orders-with-given-number-of-elements-in-cplusplus | # Count of matrices (of different orders) with given number of elements in C++
C++Server Side ProgrammingProgramming
We are given the total number of elements and the task is to calculate the total number of matrices with different orders that can be formed with the given data. A matrix has an order mxn where m are the number of rows and n are the number of columns.
Input − int numbers = 6
Output −Count of matrices of different orders that can be formed with the given number of elements are: 4
Explanation − we are given with the total number of elements that a matrix of any order can contain which is 6. So the possible matrix order with 6 elements are (1, 6), (2, 3), (3, 2) and (6, 1) which are 4 in number.
Input − int numbers = 40
Output − Count of matrices of different orders that can be formed with the given number of elements are: 8
Explanation − we are given with the total number of elements that a matrix of any order can contain which is 40. So the possible matrix order with 40 elements are (1, 40), (2, 20), (4, 10), (5, 8), (8, 5), (10, 4), (20, 2) and (40, 1) which are 8 in number.
## Approach used in the below program is as follows
• Input the total number of elements that can be used to form the different order of matrices.
• Pass the data to the function for further calculation
• Take a temporary variable count to store the count of matrices of with different order
• Start loop FOR from i to 1 till the number
• Inside the loop, check IF number % i = 0 then increment the count by 1
• Return the count
• Print the result
## Example
Live Demo
#include <iostream>
using namespace std;
//function to count matrices (of different orders) with given number of elements
int total_matrices(int number){
int count = 0;
for (int i = 1; i <= number; i++){
if (number % i == 0){
count++;
}
}
return count;
}
int main(){
int number = 6;
cout<<"Count of matrices of different orders that can be formed with the given number of elements are: "<<total_matrices(number);
return 0;
}
## Output
If we run the above code it will generate the following output −
Count of matrices of different orders that can be formed with the given number of elements are: 4
Updated on 02-Nov-2020 06:12:30 | 2022-07-04 06:53:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35472041368484497, "perplexity": 469.0165781993003}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104354651.73/warc/CC-MAIN-20220704050055-20220704080055-00143.warc.gz"} |
https://www.semanticscholar.org/paper/Duality-of-boundary-value-problems-for-minimal-and-Akamine-Fujino/853661a5c7cfa6674155c58b0f7a306cda1913e0 | • Corpus ID: 202539545
# Duality of boundary value problems for minimal and maximal surfaces
```@article{Akamine2019DualityOB,
title={Duality of boundary value problems for minimal and maximal surfaces},
author={Shintaro Akamine and Hiroki Fujino},
journal={arXiv: Differential Geometry},
year={2019}
}```
• Published 3 September 2019
• Mathematics
• arXiv: Differential Geometry
In 1966, Jenkins and Serrin gave existence and uniqueness results for infinite boundary value problems of minimal surfaces in the Euclidean space, and after that such solutions have been studied by using the univalent harmonic mapping theory. In this paper, we show that there exists a one-to-one correspondence between solutions of infinite boundary value problems for minimal surfaces and those of lightlike line boundary problems for maximal surfaces in the Lorentz-Minkowski spacetime. We also…
3 Citations
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## References
SHOWING 1-10 OF 36 REFERENCES
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• 2009
Abstract We discuss the minimal-to-maximal correspondence between surfaces and show that, under this correspondence, a congruence class of minimal surfaces in 3 determines an 2-family of congruence
Unstable Minimal Surfaces
• Mathematics
• 2010
Here it is shown that the existence of two minimal surfaces in a closed rectifiable contour Γ which are local minimizers of Dirichlet’s integral D guarantees the existence of a third minimal surface
Prescribing singularities of maximal surfaces via a singular Björling representation formula
• Mathematics
• 2007
Abstract We derive a proper formulation of the singular Bjorling problem for spacelike maximal surfaces with singularities in the Lorentz–Minkowski 3-space which roughly asks whether there exists a
The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions
We prove existence of Schoen's and other triply periodic minimal surfaces via conjugate (polygonal) Plateau problems. The simpler of these minimal surfaces can be deformed into constant mean
Variational problems of minimal surface type II. Boundary value problems for the minimal surface equation
• Mathematics
• 1966
in a convex domain D, and taking on assigned continuous values on the boundary of D. This problem was solved by RAD6 in 1930, on the basis of the existence theorem for the parametric problem of least
Generalized maximal surfaces in Lorentz-Minkowski space L3
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In this paper we carry out a systematic study of generalized maximal surfaces in Lorentz–Minkowski space L 3 , with emphasis on their branch points. Roughly speaking, such a surface is given by a
Maximal surfaces of Riemann type in Lorentz-Minkowski space L3.
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We classify the family of spacelike maximal surfaces in Lorentz-Minkowski 3-space L 3 which are foliated by pieces of circles. This space contains a curve of singly periodic maximal surfaces R that
Generalized Calabi correspondence and complete spacelike surfaces
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We construct a twin correspondence between graphs with prescribed mean curvature in three-dimensional Riemannian Killing submersions and spacelike graphs with prescribed mean curvature in
On univalent harmonic mappings and minimal surfaces
If S is the graph of a minimal surface, then when given parametrically by the Weierstrass representation, the first two coordinate functions give a univalent harmonic mapping. In this paper, the
On the boundary behavior of orientation-preserving harmonic mappings
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Nonconstant soluliuns of the partial differential equation where a is analytic in the open unit disk and |a| <1, are orientation-preserving harmonic mappings. We consider the case where ais a finite | 2022-01-23 14:52:44 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8496845960617065, "perplexity": 990.3811713609255}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304287.0/warc/CC-MAIN-20220123141754-20220123171754-00214.warc.gz"} |
https://ltwork.net/tina-bought-a-painting-while-onvacation-in-2009-the-table--4735537 | Tina bought a painting while onvacation in 2009. The table belowshows the value of the painting in2009, 2010, and 2011. If this trendcontinues.
Question:
Tina bought a painting while on vacation in 2009. The table below
shows the value of the painting in
2009, 2010, and 2011. If this trend
continues. What will be the value
of the painting in 2030?
Year
2009
2010
$88.50 2011$104,43
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B) $2,044.19 C)$2,103.73
D) $2,279.55 E)$2,424.28
Given f(x) = x3 + kx + 17, and the remainder when f(x) is divided by x + 1 is26, then what is the value of k?
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Consider the absolute-value equation 2(|×+8|+2)=4 How many solutions are there to the equation?... | 2023-03-28 12:38:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28614357113838196, "perplexity": 1993.4412090032863}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948858.7/warc/CC-MAIN-20230328104523-20230328134523-00588.warc.gz"} |
http://mathhelpforum.com/calculus/80790-f-x-x-2-3-x-2-4-simplifiy-then-get-f-x.html | # Math Help - f(x)=x^2/3 (x^2-4)...simplifiy then get f'(x)
1. ## f(x)=x^2/3 (x^2-4)...simplifiy then get f'(x)
i know it simplifies to x^8/3 - 4x^2/3 but how does one get to that (esp. the x^8/3)
also, how do you get to f'(x) from here?
Thank you in advance to those smarter than I...
2. Originally Posted by calcconfused
i know it simplifies to x^8/3 - 4x^2/3 but how does one get to that (esp. the x^8/3)
also, how do you get to f'(x) from here?
Thank you in advance to those smarter than I...
Hi, calcconfused. To simplify the basic equation, remember that $x^{a}x^{b} = x^{a + b}$ and the rules for adding fractions:
$f(x) = x^{\frac{2}{3}}(x^{2} - 4)$
$f(x) = (x^{\frac{2}{3}})(x^{2}) - (x^{\frac{2}{3}})(4)$
$f(x) = (x^{\frac{2}{3}})(x^{\frac{6}{3}}) - (x^{\frac{2}{3}})(4)$
$f(x) = x^{\frac{8}{3}} - 4x^{\frac{2}{3}}$
And now the derivative:
$f^{\prime}(x) = \left(\frac{8}{3}\right)x^{(\frac{8}{3} - 1)} - \left(\frac{2}{3}\right)4x^{(\frac{2}{3} - 1)}$
$f^{\prime}(x) = \frac{8}{3}x^{\frac{5}{3}} - \frac{8}{3}x^{-\frac{1}{3}}$
$f^{\prime}(x) = \frac{8}{3}(x^{\frac{5}{3}} - x^{-\frac{1}{3}})$
Hope that helps! | 2015-03-05 11:29:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8737687468528748, "perplexity": 2091.060314165501}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936464088.46/warc/CC-MAIN-20150226074104-00298-ip-10-28-5-156.ec2.internal.warc.gz"} |
http://openstudy.com/updates/55ba804ee4b0adef802bd42e | ## anonymous one year ago The force of repulsion between two like-charged table tennis balls is 8.2 * 10È¥ newtons. If the charge on the two objects is 6.7 * 10È© coulombs each, what is the distance between the two charges? (k = 9.0 * 10© newton·metersÆ/coulombÆ) a: 0.23 b: 0.70 c:6.7 d:8.2
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1. IrishBoy123
Coulomb's Law: $$\large F = k \frac{q_1 \ q_2 }{r^2}$$ $$q_1 = q_2$$ | 2016-10-26 11:34:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6194182634353638, "perplexity": 2188.569952674633}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720941.32/warc/CC-MAIN-20161020183840-00211-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://optimization.mccormick.northwestern.edu/index.php?title=Trust-region_methods&oldid=897 | # Trust-region methods
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Authors: Wenhe (Wayne) Ye (ChE 345 Spring 2014) Steward: Dajun Yue, Fengqi You Date Presented: Apr. 10, 2014
## Introduction
A pictorial view of trust-region method optimization trajectory
Trust-region method (TRM) is one of the most important numerical optimization methods in solving nonlinear programming (NLP) problems. It works in a way that first define a region around the current best solution, in which a certain model (usually a quadratic model) can to some extent approximate the original objective function. TRM then take a step forward according to the model depicts within the region. Unlike the line search methods, TRM usually determines the step size before the improving direction (or at the same time). If a notable decrease (our following discussion will based on minimization problems) is gained after the step forward, then the model is believed to be a good representation of the original objective function. If the improvement is too subtle or even a negative improvement is gained, then the model is not to be believed as a good representation of the original objective function within that region. The convergence can be ensured that the size of the “trust region” (usually defined by the radius in Euclidean norm) in each iteration would depend on the improvement previously made.
## Important Concepts
The picture shows both the stepsize and the improving direction is a consequence of a pre-determined trust-region size.
Trust-region
In most cases, the trust-region is defined as a spherical area of radius $\Delta_k$ in which the trust-region subproblem lies.
Trust-region subproblem
If we are using the quadratic model to approximate the original objective function, then our optimization problem is essentially reduced to solving a sequence of trust-region subporblems
$min~m_k(p)=f_k+{g_k}^Tp+\frac{1}{2}p^TB_kp$
$s.t.~||p||<=\Delta_k$
Where $\Delta_k$ is the trust region radius, $g_k$ is the gradient at current point and $B_k$ is the hessian (or a hessian approximation). It is easy to find the solution to the trust-region subproblem if $B_k$ is positive definite.
Actual reduction and predicted reduction
The most critical issue underlying the trust-region method is to update the size of the trust-region at every iteration. If the current iteration makes a satisfactory reduction, we may exploits our model more in the next iteration by setting a larger $\Delta_k$. If we only achieved a limited improvement after the current iteration, the radius of the trust-region then should not have any increase, or in the worst cases, we may decrease the size of the trust-region by adjusting the radius to a smaller value to check the model’s validity.
$\rho_k=\frac{f(x_k)-f(x_k+p_k)}{m_k(0)-m_k(p_k)}$
Whether to take a more ambitious step or a more conservative one is depend on the ratio between the actual reduction gained by true reduction in the original objective function and the predicted reduction expected in the model function. Empirical threshold values of the ratio $\rho_k$ will guide us in determining the size of the trust-region.
## Trust Region Algorithm
Before implementing the trust-region algorithm, we should first determine several parameters. $\Delta_M$ is the upper bound for the size of the trust region. $\eta_1$, $\eta_2$ and $\eta_3$,$t_1$,$t_2$ are the threshold values for evaluating the goodness of the quadratic model thus for determining the trust-region’s size in the next iteration. A typical set for these values are $0=<\eta_1<=\eta_2$, $\eta_2=0.25$ and $\eta_3=0.75$,$t_1=0.25$,$t_2=2.0$.
Pseudo-code
Set the starting point at $x_0$, set the iteration number $k=1$
for $k=1,2...$
Get the improving step by solving trust-region sub-problem ()
Evaluate $\rho_k$ from equation()
if $\rho_k<\eta_2$
$\Delta_{k+1}=t_1\Delta_k$
else
if $\rho_k>\eta_3$ and $p_k=||\Delta_k||$ (full step and model is a good approximation)
$\Delta_{k+1}=min(t_2\Delta_k,\Delta_M)$
else
$\Delta_{k+1}=\Delta_k$
if $\rho_k>\eta_1$
$x_{k+1}=x_k+p_k$
else
$x_{k+1}=x_k$(the model is not a good approximation and need to solve another trust-region subproblem within a smaller trust-region)
end >
## Methods of Solving the Trust-region Subproblem
### Cauchy point calculation
Illustration of Cauchy point calculation.
In line search methods, we may find an improving direction from the gradient information, that is, by taking the steepest descent direction with regard to the maximum range we could make. We can solve the trust-region subproblem in an inexpensive way. This method is also denoted as the Cauchy point calculation. We can also express the improving step explicitly by the following closed-form equations
${p_k}^C=-\tau_k\dfrac{\Delta_k}{||g_k||}g_k$
if ${g_k}^TB_kg_k<=0$ $\tau_k=1$
otherwise $\tau_k=min~ ({||g_k||}^3/(\Delta_k{g_k}^TB_kg_k),1)$
### Limitations and Further Improvements
Though Cauchy point is cheap to implement, like the steepest descent method, it performs poorly in some cases. Varies kinds of improvements are based on including the curvature information from $B_k$.
#### Dogleg Method
Illustration of dogleg method trajectory.
If $B_k$ is positive definite (we can use quasi-Newton Hessian approximation &updating to guarantee), then a V-shaped trajectory can be determined by
if $0<=\tau<=1,~~p(\tau)=\tau p^U$
if $1<=\tau<=2,~~p(\tau)=\tau p^U+(\tau-1)(p^B-p^U)$
where $p^U=-\frac{g^Tg}{g^TBg}g$ is the steepest descent direction and $p^B$ is the optimal solution of the quadratic model $m_k(p)$. Therefore, a further improvement could be achieved compared to using only Cauchy point calculation method in one iteration. (Note that hessian or approximate hessian will be evaluated in dogleg method)
The most widely used method for solving a trust-region sub-problem is by using the idea of conjugated gradient (CG) method for minimizing a quadratic function since CG guarantees convergence within a finite number of iterations for a quadratic programming. Also, CG Steihaug’s method has the merit of Cauchy point calculation and dogleg method that both in terms of super-linear convergence rate and inexpensiveness to compute.(No expensive Hessian evaluation)
Pseudo-code for CG Steihaug method in solving trust region sub-problem
Given tolerance $\epsilon_k > 0$;
Set $z_0=0, r_0=\nabla f_k, d_0=-r_0=-\nabla f_k$
if $||r_0|| <\epsilon_k$
return $p_k = z_0 = 0$;
for $j = 0, 1, 2, . . .$
if ${d_j}^TB_k d_j <= 0$
Find $\tau$ such that $p_k = z_j + \tau d_j$ minimizes $m_k(p_k)$
and satisfies $||p_k|| = \Delta_k$ ;
return $p_k$ ;
Set $\alpha_j = {r_j}^Tr_j /{d_j}^TB_kd_j$;
Set $z_{j+1} = z_j + \alpha_jd_j$ ;
if $||z_{j+1}|| >= \Delta_k$
Find $\tau >= 0$ such that $p_k = z_j + \tau d_j$ satisfies $||p_k|| = \Delta_k$ ;
return $p_k$ ;
Set $r_{j+1} = r_j + \alpha_j B_kd_j$ ;
if $||r_{j+1}|| <\epsilon_k$
return $p_k = z_{j+1}$;
Set $\beta_{j+1} = \frac{{r_{j+1}}^T{r_{j+1}}}{{r_j}^Tr_j}$ ;
Set $d_{j+1}=-r_{j+1}+\beta_{j+1}d_j$
end
## Example
Contour of a 'Branin' function.
Here we use the trust-region method to solve an unconstrained problem as an example. The trust-region subproblems are solved by calculate the Cauchy point.
$min~f(x_1,x_2)=(x_2-0.129{x_1}^2+1.6x_1-6)^2+6.07cos(x_1)+10$ (This is the Branin function which is widely used as a test function. It has 3 global optima.)
Starting point $x_1=6.00, x_2=14.00$ The iteration stops when the stopping criteria $||g_k||<=0.01$ is met.
$\Delta_0=2.0, \Delta_M=5.0, t_1=0.25, t_2=2.0, \eta_1=0.2,\eta_2=0.25,\eta_3=0.75$
Improving Process
Graphical illustration of iteration 1 (The quadratic model's contours are marked as red lines).
Graphical illustration of iteration2.
Graphical illustration of iteration3.
Graphical illustration of iteration4.
Graphical illustration of iteration5.
Graphical illustration of iteration6.
Optimization trajectory of the example function(unconstrained).
Iteration 1: The algorithm start from the initial point(marked as a green dot) $x_1=6.00, x_2=14.00$. The trust-region is defined as the area inside the circle centered at the starting point. The contour of the quadratic model can be visualized. After calculating the Cauchy point, $\rho_k$ is evaluated and a full step was taken since the model gives a good prediction. Set $x_{k+1}=x_k+p_k(x_1=5.767,x_2=12.014)$ and $\Delta_k=min(2\Delta_k,\Delta_M)~(\rho_k>\eta_3$ and a full step was taken.$)$ (The current best solution is denoted as the red dot.)
Iteration 2: Start with $x_1=5.767,x_2=12.014$ and an enlarged trust-region. The new iteration gives a more ambitious full step to the new point$(x_1=4.800,x_2=8.132$). With $\rho_k=0.980$, the model is "trusted" again to increase its size in the next iteration.
Iteration 3: Start with $x_1=4.800,x_2=8.132$ and an enlarged trust-region. The new iteration gives a satisfactory but not good enough to the new point$(x_1=1.668,x_2=4.235$). With $\rho_k=0.578$, which is not high enough to trigger a new increment for the trust-region's size. So the radius is maintained in the next iteration.
Iteration 4: Start with $x_1=1.668,x_2=4.235$ and the maximum-sized trust-region. The new iteration gives a poor prediction. With $\rho_k=-0.160$, which incurs the decrease in the trust-region's size to improve the model's validity. Current best solution is unchanged and the radius for the trust-region is diminished to 1/4 of the current iteration.
Iteration 5: Start with $x_1=1.668,x_2=4.235$ and a shrinked trust-region. The new iteration gives a satisfactory but not good enough to the new point$(x_1=2.887,x_2=3.956$). With $\rho_k=0.729$, which is not high enough to trigger a new increment for the trust-region's size. So the radius is maintained in the next iteration.
Iteration 6: Start with $x_1=2.887,x_2=3.956$. The new iteration gives a satisfactory but not a full step to the new point$(x_1=2.594,x_2=3.109$). With $\rho_k=0.989$, which is high enough to trigger a new increment for the trust-region's size, however not a full step is taken thereby the radius is maintained in the next iteration.
....
The following table is a summary for the improving process. Notably the Cauchy point calculation does not give an efficient convergence rate especially at the end stage of the computation(not a full step was taken so it is essentially equivalent to a steepest decent line search algorithm). Dogleg and CG Steihaug's method will give faster convergence as explained previously.
Another graphical illustration is available at Kranf site: [1]
## Conclusion
Trust-Region vs. Line Search
Line search methods:
- Pick improving direction
- Pick step-size to minimize
- Update the incumbent solution
- Convergence rate is not guaranteed
Trust-region methods:
- Pick the step-size (the trust-region sub-problem is constrained)
- Solving the sub-problem using the approximated model
- If the improvement is acceptable, update the incumbent solution and the size of the trust-region
- Can have super-linear convergence rate when conjugated gradient method or dogleg method is used
## References
[1] W. Sun and Y.-x. Yuan, Optimization theory and methods : nonlinear programming. New York: Springer, 2006.
[2] J. Nocedal, S. J. Wright, and SpringerLink (Online service). (2006). Numerical optimization (2nd ed.). Available: [2]
[3] L. Hei, "Practical techniques for nonlinear optimization," Ph D, Northwestern University, 2007. | 2021-10-19 10:02:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 91, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7709064483642578, "perplexity": 947.5747068092674}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585246.50/warc/CC-MAIN-20211019074128-20211019104128-00568.warc.gz"} |
https://socratic.org/questions/how-do-you-graph-x-y-0 | How do you graph x-y=0?
Jun 7, 2018
$y = x$
Explanation:
Put the equation in slope intercept for:
$y = m x + b$
$m = s l o p e$
$b = \text{y-intercept}$
$x - y = 0$
$- y = - x$
$y = x + 0$
$m = 1$
$b = 0$
graph{y=x [-10, 10, -5, 5]} | 2020-07-13 19:07:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 9, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7412852048873901, "perplexity": 9629.724350817123}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657146247.90/warc/CC-MAIN-20200713162746-20200713192746-00096.warc.gz"} |
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# What is 10 - 8 + 6 - 4 + ... - (-20) ?
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What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]
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01 Apr 2012, 22:21
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What is 10 - 8 + 6 - 4 + ... - (-20) ?
A. 8
B. 10
C. 12
D. 14
E. 16
[Reveal] Spoiler: OA
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Re: Brute Force or Some Pattern [#permalink]
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01 Apr 2012, 23:12
Expert's post
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GMATPASSION wrote:
What is $$10 - 8 + 6 - 4 + ... - (-20)$$ ?
8
10
12
14
16
I solved this by brute force? Any other way.
Pair them up.
10 - 8 = 2
6 - 4 = 2
2 - 0 = 2
.
.
-18 - (-20) = 2
There are a total of 16 terms (2*5 to 2*-10 gives you 5-(-10)+1 = 16 terms) so you will get 8 pairs. Hence the sum will be 2*8 = 16
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews VP Status: Top MBA Admissions Consultant Joined: 24 Jul 2011 Posts: 1017 GMAT 1: 780 Q51 V48 GRE 1: 1540 Q800 V740 Followers: 108 Kudos [?]: 481 [1] , given: 18 Re: Brute Force or Some Pattern [#permalink] ### Show Tags 01 Apr 2012, 23:18 1 This post received KUDOS Note that 10-8 =2 and 6-4 =2. The next two terms, i.e. 2 and 0 also yield 2. Therefore the series is simply the sum of 2 over many terms. How many such terms are there? The first negative term is 8 and the last is -20, with a common difference of -4. Alternatively, we could calculate the number of terms by taking the first term as 10, the common difference as -4, and the last term as -18. -20 = 8 + (n-1) (-4) => n = 8 Therefore the answer is simply 2*8 = 16 , or option (E). _________________ GyanOne | Top MBA Rankings and MBA Admissions Blog Top MBA Admissions Consulting | Top MiM Admissions Consulting Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6830 Location: Pune, India Followers: 1926 Kudos [?]: 11944 [0], given: 221 Re: Brute Force or Some Pattern [#permalink] ### Show Tags 01 Apr 2012, 23:20 Expert's post 1 This post was BOOKMARKED GMATPASSION wrote: What is $$10 - 8 + 6 - 4 + ... - (-20)$$ ? 8 10 12 14 16 I solved this by brute force? Any other way. Or consider them as sum of 2 arithmetic progressions (though it would be much better if you see the pairing pattern) I) 10 + 6 + 2 + (-2) ....+(-18) AP with first term = 10 and common diff = -4 Sum = (8/2)(2*10 + 7*(-4)) = -32 II) -8 -4 - 0 - (-4) +..- (-20) AP with first term = -8 and common diff = 4 Sum = (8/2)(2*(-8) + 7*(4)) = 48 Sum of the series = -32 + 48 = 16 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199
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Re: Brute Force or Some Pattern [#permalink]
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01 Apr 2012, 23:34
Yep - I was gonna post the same reply below. there are 2 APs here, you can just sum them
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]
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09 Jun 2012, 12:27
please list the whole series and how a common difference of -4 is obtained .
Sorry my limited wisdom is unable to grasp the process
as far as I can see the terms are decreasing by 2 with alternating + and - sign
so the series should continue as 10 -8 +6 - 4 + 2 - 0 + (-2) - ( -4 ) + ( -6) - (-8 ) + ( -10) -( -12) +( -14 )
- (-16) +(-18)- (-20)
10 - 8 + 6 - 4 + 2 - 0 -2 + 4 - 6 + 8 - 10 + 12 - 14 + 16 - 18 + 20
some one please explain how common difference is - 4
please include the complete series so that we can see how this works
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]
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09 Jun 2012, 12:56
3
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Expert's post
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stne wrote:
please list the whole series and how a common difference of -4 is obtained .
Sorry my limited wisdom is unable to grasp the process
as far as I can see the terms are decreasing by 2 with alternating + and - sign
so the series should continue as 10 -8 +6 - 4 + 2 - 0 + (-2) - ( -4 ) + ( -6) - (-8 ) + ( -10) -( -12) +( -14 )
- (-16) +(-18)- (-20)
10 - 8 + 6 - 4 + 2 - 0 -2 + 4 - 6 + 8 - 10 + 12 - 14 + 16 - 18 + 20
some one please explain how common difference is - 4
please include the complete series so that we can see how this works
Here you go:
The sequence is $$10-8+6-4+2-0+(-2)-(-4)+(-6)-(-8)+(-10)-(-12)+(-14)-(-16)+(-18)-(-20)$$.
Notice that the odd numbered terms (1st, 3rd, 5th...) form arithmetic progression with common difference of -4 and the even numbered terms (2nd, 4th...) form arithmetic progression with common difference of 4:
The sum of the odd numbered terms is $$10+6+2+(-2)+(-6)+(-10)+(-14)+(-18)=10+6+2-2-6-10-14-18=-32$$;
The sum of the even numbered terms is $$-8-4-0-(-4)-(-8)-(-12)-(-16)-(-20)=-8-4-0+4+8+12+16+20=48$$;
Their sum is $$-32+48=16$$.
Though I wouldn't recommend to solve this question this way. It's better if you notice that we have 8 pairs:
10-8=2;
6-4=2;
2-0=2;
(-2)-(-4)=2;
(-6)-(-8)=2;
(-10)-(-12)=2;
(-14)-(-16)=2;
(-18)-(-20)=2;
So, the sum of each pair is 2, which makes the whole sum equal to 8*2=16.
Hope it's clear.
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]
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09 Jun 2012, 13:30
Bunuel wrote:
stne wrote:
please list the whole series and how a common difference of -4 is obtained .
Sorry my limited wisdom is unable to grasp the process
as far as I can see the terms are decreasing by 2 with alternating + and - sign
so the series should continue as 10 -8 +6 - 4 + 2 - 0 + (-2) - ( -4 ) + ( -6) - (-8 ) + ( -10) -( -12) +( -14 )
- (-16) +(-18)- (-20)
10 - 8 + 6 - 4 + 2 - 0 -2 + 4 - 6 + 8 - 10 + 12 - 14 + 16 - 18 + 20
some one please explain how common difference is - 4
please include the complete series so that we can see how this works
Here you go:
The sequence is $$10-8+6-4+2-0+(-2)-(-4)+(-6)-(-8)+(-10)-(-12)+(-14)-(-16)+(-18)-(-20)$$.
Notice that the odd numbered terms (1st, 3rd, 5th...) form arithmetic progression with common difference of -4 and the even numbered terms (2nd, 4th...) form arithmetic progression with common difference of 4:
The sum of the odd numbered terms is $$10+6+2+(-2)+(-6)+(-10)+(-14)+(-18)=10+6+2-2-6-10-14-18=16$$;
The sum of the even numbered terms is $$-8-4-0-(-4)-(-8)-(-12)-(-16)-(-20)=-8-4-0+4+8+12+16+20=48$$;
Their sum is $$-32+48=16$$.
Though I wouldn't recommend to solve this question this way. It's better if you notice that we have 8 pairs:
10-8=2;
6-4=2;
2-0=2;
(-2)-(-4)=2;
(-6)-(-8)=2;
(-10)-(-12)=2;
(-14)-(-16)=2;
(-18)-(-20)=2;
So, the sum of each pair is 2, which makes the whole sum equal to 8*2=16.
Hope it's clear.
Thank you , now the previous explanations make sense
Just a small typo in your answer , I think it should be - 32 instead of 16 ( addition of odd terms ) , please do edit , to prevent confusion.
I was not able to see that even and odd terms are making an AP .
as Kudos is a better way of saying thank you , so you have been awarded , will be needing more of your assistance
in the future
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]
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09 Jun 2012, 13:38
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stne wrote:
please list the whole series and how a common difference of -4 is obtained .
Sorry my limited wisdom is unable to grasp the process
as far as I can see the terms are decreasing by 2 with alternating + and - sign
so the series should continue as 10 -8 +6 - 4 + 2 - 0 + (-2) - ( -4 ) + ( -6) - (-8 ) + ( -10) -( -12) +( -14 )
- (-16) +(-18)- (-20)
10 - 8 + 6 - 4 + 2 - 0 -2 + 4 - 6 + 8 - 10 + 12 - 14 + 16 - 18 + 20
some one please explain how common difference is - 4
please include the complete series so that we can see how this works
just rearrange the terms you have written with putting all the terms subtracted together and the ones added together.
10 -(8) +6 -( 4) + 2 - (0) + (-2) - ( -4 ) + ( -6) - (-8 ) + ( -10) -( -12) +( -14 ) - (-16) +(-18)- (-20)
=> 10 +6 + 2 +(-2) +( -6) +(-10)+( -14 ) +(-18) -(8) -( 4) - (0) -( -4 )- (-8 )-( -12) - (-16)- (-20)
Hope that helps.
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]
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17 Jun 2012, 12:52
The quickest strategy for me was to pair them up and add the 2s.
10-8=2;
6-4=2;
2-0=2;
(-2)-(-4)=2;
(-6)-(-8)=2;
(-10)-(-12)=2;
(-14)-(-16)=2;
(-18)-(-20)=2;
2+2+2+2+2+2+2+2= 2*8 = 16
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]
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21 Dec 2012, 07:48
GMATPASSION wrote:
What is 10 - 8 + 6 - 4 + ... - (-20) ?
A. 8
B. 10
C. 12
D. 14
E. 16
I wrote them down and started cancelling pairs (+) against (-) then I was left with 16.
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]
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25 Nov 2014, 08:13
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GMATPASSION wrote:
What is 10 - 8 + 6 - 4 + ... - (-20) ?
A. 8
B. 10
C. 12
D. 14
E. 16
last term-first term/(difference) +1
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]
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12 Jan 2015, 13:06
I hadn't even realised that this was a series. I thougt this was just an addition, like this:
10 - 8 + 6 - 4 + ... - (-20)
10 - 8 + 6 - 4 + x - (-20)
So, of course, I was waiting to end up with sth like 24+x and to only find one value larger that 24 in the answer options.
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]
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20 May 2016, 23:38
If you write down all the numbers, the numbers from +10-8+6-4+2-0+(-2)-(-4)+(-6)-(-8)+(-10) is a palindrome and its sum is zero... So just focus on 12-14+16-18+20 = 20-4 = 16
Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink] 20 May 2016, 23:38
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Display posts from previous: Sort by | 2016-08-27 06:57:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4642260670661926, "perplexity": 2239.096477244196}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982298551.3/warc/CC-MAIN-20160823195818-00056-ip-10-153-172-175.ec2.internal.warc.gz"} |
https://takeawildguess.net/blog/mdlsel/mdlsel8/ | ## 1. Introduction
After two introductory post-series (linear and logistic regression), we dive into a crucial topic that every machine-learning practitioner should be at least aware of: model selection.
Basically, we do not want our models to learn our data by heart and then to struggle to handle new unseen data samples. We want them to be great at generalizing.
We have introduced the bias and variance concepts in Part1 and the bias-variance dilemma, the model capacity, the training/testing split practice and learning curves analysis in Part2. We moved to the cross-validation and regularization techniques in Part3, implemented the Ridge regression in Python in Part4.
We apply the same workflow of the mini-series about model selection for a linear binary classification problem (first and second posts) to a non-linear case, where the model needs to separate two circular clouds with a circle.
Let’s inspect the model accuracy variability, the application of learning and validation curves with Scikit-learn, selection of the best model capacity with cross-validation with different regularization loss definitions.
## 2. Training and testing accuracy variability
As we have explained in this post, one key point in the machine-learning field regards how the accuracy of the model might change for varying datasets.
We assess the accuracy variability by applying the pipeline (sampling from the dataset distribution, training the model and predicting the outcome for training and test sets) Nsim times. We repeat this process for five different polynomial degrees ranging from 1 to 5.
Nsim = 150
accTrainss, accTestss = [], []
degrees = np.arange(1, 6)
for dgr in degrees:
accTrains, accTests = [], []
for kk in range(Nsim):
XX, YY = genCircles()
Xtrain, Xtest, Ytrain, Ytest = train_test_split(XX, YY, test_size=0.2, random_state=42)
scl = StandardScaler()
pf = PolynomialFeatures(dgr, include_bias=False)
Xtrain = scl.fit_transform(pf.fit_transform(Xtrain))
Xtest = scl.transform(pf.fit_transform(Xtest))
# fit new training data with logistic regression
lgr = LogisticRegression(C=1e5)
lgr.fit(Xtrain, Ytrain)
YpredTR = lgr.predict(Xtrain)
YpredTS = lgr.predict(Xtest)
accTrains.append(metrics.accuracy_score(Ytrain, YpredTR))
accTests.append(metrics.accuracy_score(Ytest, YpredTS))
accTrainss.append(accTrains)
accTestss.append(accTests)
accuraciesTrain = np.array(accTrainss)
accuraciesTest = np.array(accTestss)
We visualize the accuracy variability of each model complexity (degree) with a boxplot.
This chart is very useful to inspect the actual statistical behaviour of the model. In this case, we can see how the median accuracy drastically increases from first to second degree and keeps slightly increasing until the 5-degree case over the training set. However, the second-degree case, which gives the highest values from 25th to 75th percentiles (see the box limits for degree 2), would be the best option.
plt.figure(figsize=(10, 5))
plt.subplot(121)
plt.boxplot(accuraciesTrain.T)
plt.xlabel("X")
plt.ylabel("Y")
plt.ylim([0, 1.025])
plt.subplot(122)
plt.boxplot(accuraciesTest.T)
plt.xlabel("X")
plt.ylabel("Y")
plt.ylim([0, 1.025])
plt.show()
## 3. Learning curves
We apply the learning-curve analysis to this case to a piped model with the learning_curve function.
We use a first-degree input and the logistic model without regularization. We define the learning curve for different sizes of the training set ranging from 10% to 100% of the whole training set. It is fed as a 1D array to the learning_curve function via the train_sizes attribute.
XX, YY = genCircles(250)
model = make_pipeline(PolynomialFeatures(degree=1), StandardScaler(), LogisticRegression(C=1e5))
trainSizes, trainScores, valScores = learning_curve(model, XX, YY, train_sizes=np.logspace(-1, 0, 20))
The figure shows the accuracy trend for training and validation sets. We see both training and validation accuracies do not improve. This is due to the limit of the model, no matter what training set size is being used.
plt.figure()
plt.plot(trainSizes, trainScores.mean(axis=1), label='training')
plt.plot(trainSizes, valScores.mean(axis=1), label='cross-validation')
plt.ylim([0.4, 1])
plt.legend();
We extend this methodology to a 2-degree polynomial function. The figure clearly highlights in this case how the training set size helps to narrow down the training/validation accuracy gap, at the expense of a training accuracy drop of 15%.
model = make_pipeline(PolynomialFeatures(degree=2), StandardScaler(), LogisticRegression(C=1e5))
trainSizes, trainScores, valScores = learning_curve(model, XX, YY, train_sizes=np.logspace(-1, 0, 20))
plt.figure()
plt.plot(trainSizes, trainScores.mean(axis=1), label='training')
plt.plot(trainSizes, valScores.mean(axis=1), label='cross-validation')
plt.ylim([0.4, 1])
plt.legend();
## 4. Validation curves
Let’s use the validation curves to select the most suitable model degree, as the sole hyper-parameter. To this end, we use the validation_curve method that runs the piped model for a set of different parameter values, degrees.
The plot suggests that the second-degree polynomial function gives a huge boost to the model accuracy of both training and validation sets. A more complex model does not show any improvements.
degrees = np.arange(1, 6)
model = make_pipeline(PolynomialFeatures(), StandardScaler(), LogisticRegression(C=1e5))
# Vary the "degrees" on the pipeline step "polynomialfeatures"
trainScores, valScores = validation_curve(model, XX, YY, param_name='polynomialfeatures__degree', param_range=degrees)
# Plot the mean train score and validation score across folds
plt.figure()
plt.plot(degrees, trainScores.mean(axis=1), label='training')
plt.plot(degrees, valScores.mean(axis=1), label='cross-validation')
plt.legend(loc='best');
## 5. Regularization with cross-validation
Rather than finding the best model complexity degree with the validation curves, we could set a very high-dimensional model (degree=6) and seek for the optimal regularization parameter in the logistic regression, C. For every value in alphas ranging from 1e-5 to 1e6, we create the piped model with the inverse regularization factor C=alpha and estimate the accuracy with a 3-fold (cv=3) cross-validation strategy.
The plot suggests that the best alpha value lies between 1e-1=0.1 and 1e0=1. A too high regularization factor (low alpha) reduces the accuracy more severely (5%) than a too low factor (2%).
alphas = np.logspace(-5, 6, 30)
scores = []
for alpha in alphas:
model = make_pipeline(PolynomialFeatures(degree=6), StandardScaler(), LogisticRegression(C=alpha))
scores.append(cross_val_score(model, XX, YY, cv=3).mean())
plt.figure()
plt.plot(np.log10(alphas), scores)
[<matplotlib.lines.Line2D at 0x1c41c7f7c88>]
## 6. Regularization with nested cross-validation
We now extend this approach to a nested cross-validation analysis that combines the regularization factor and the parameters’ loss function, with lasso as l1 and ridge as l2. We change the logistic regression solver to liblinear to handle the l1 loss function as well.
The plot suggests that the best alpha value lies again between 1e-1=0.1 and 1e0=1 for the lasso loss and between 1e-1=0.1 and 1e1=10 for the ridge loss. A very high regularization factor affects the overall accuracy a lot more if combined with the lasso loss definition, which drops down to 50%.
penalties = ['l1', 'l2']
alphas = np.logspace(-5, 5, 30)
scores = []
for penalty in penalties:
scores_ = []
for alpha in alphas:
model = make_pipeline(PolynomialFeatures(degree=6), StandardScaler(),\
LogisticRegression(C=alpha, penalty=penalty, solver='liblinear'))
scores_.append(cross_val_score(model, XX, YY, cv=3).mean())
scores.append(scores_)
scores = np.array(scores).T
plt.figure()
plt.plot(np.log10(alphas), scores)
plt.legend(['Lasso', 'Ridge']);
<matplotlib.legend.Legend at 0x1c41cb3bd30>
## 7. Visualize the best model behaviour
We select the best hyper-parameters from the previous step, wrt the accuracy values stored in scores. Since it is a 2D array, we need the row and column indexes of the minimum value. Numpy provides the unravel_index function to transform the index of a given element of the flatten array scores into a (row, col) index.
idxs = np.unravel_index(scores.argmax(), scores.shape)
alphaOpt = alphas[idxs[0]]
penOpt = penalties[idxs[1]]
We can once again create a model instance for the two best hyper-parameters and outcome the model prediction for the 2D grid.
mdlOpt = make_pipeline(PolynomialFeatures(degree=6), StandardScaler(),\
LogisticRegression(C=alphaOpt, penalty=penOpt, solver='liblinear'))
mdlOpt.fit(XX, YY);
Npnt = 50 # number of points of the mesh
mrg = .5
x1, x2 = XX[:, 0], XX[:, 1]
x1min, x1max = x1.min() - mrg, x1.max() + mrg
x2min, x2max = x2.min() - mrg, x2.max() + mrg
x1grd, x2grd = np.meshgrid(np.linspace(x1min, x1max, Npnt), np.linspace(x2min, x2max, Npnt))
XXgrd = np.vstack((x1grd.ravel(), x2grd.ravel())).T
ygrd = mdlOpt.predict(XXgrd)
ygrd = ygrd.reshape(x1grd.shape)
The final model is able to discriminate the two clouds with a quasi-circular shape as a decision boundary (red line). The model loss is simply due to the noise, which is the only term the model cannot get rid of. A proper regularization process can help to select the best model capacity and complexity wrt the bias and variance on the drawn data.
plt.figure(figsize=(10, 5))
# contour
plt.contourf(x1grd, x2grd, ygrd, cmap=plt.cm.Paired, alpha=0.4)
plt.title("Decision surface of Multinomial classification with Logistic Regression")
plt.axis('tight')
# dataset
plt.scatter(XX[:,0], XX[:,1], c=YY, cmap='viridis')
plt.xlabel("X1")
plt.ylabel("X2")
# decision boundary
cs = plt.contour(x1grd, x2grd, ygrd, levels = [0.5], colors=('r',), linestyles=('-',),linewidths=(3,)); | 2020-10-21 03:54:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4929294288158417, "perplexity": 3940.4108366012156}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107875980.5/warc/CC-MAIN-20201021035155-20201021065155-00646.warc.gz"} |
https://socratic.org/questions/how-do-you-solve-4-5x-7-3x-3-4x-9 | # How do you solve 4 (5x + 7) - 3x= 3(4x - 9)?
Mar 5, 2017
See the entire solution process below:
#### Explanation:
First, expand the terms in parenthesis on each side of the equation by multiplying each term within the parenthesis by the term outside of the parenthesis:
$\textcolor{red}{4} \left(5 x + 7\right) - 3 x = \textcolor{b l u e}{3} \left(4 x - 9\right)$
$\left(\textcolor{red}{4} \times 5 x\right) + \left(\textcolor{red}{4} \times 7\right) - 3 x = \left(\textcolor{b l u e}{3} \times 4 x\right) - \left(\textcolor{b l u e}{3} \times 9\right)$
$20 x + 28 - 3 x = 12 x - 27$
$20 x - 3 x + 28 = 12 x - 27$
$17 x + 28 = 12 x - 27$
Next, subtract $\textcolor{red}{28}$ and $\textcolor{b l u e}{12 x}$ from each side of the equation to isolate the $x$ terms while keeping the equation balanced:
$17 x + 28 - \textcolor{red}{28} - \textcolor{b l u e}{12 x} = 12 x - 27 - \textcolor{red}{28} - \textcolor{b l u e}{12 x}$
$17 x - \textcolor{b l u e}{12 x} + 28 - \textcolor{red}{28} = 12 x - \textcolor{b l u e}{12 x} - 27 - \textcolor{red}{28}$
$5 x + 0 = 0 - 55$
$5 x = - 55$
Now, divide each side of the equation by $\textcolor{red}{5}$ to solve for $x$ while keeping the equation balanced:
$\frac{5 x}{\textcolor{red}{5}} = - \frac{55}{\textcolor{red}{5}}$
$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{red}{5}}} = - 11$
$x = - 11$ | 2019-12-07 06:21:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 17, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6274935007095337, "perplexity": 330.34902749064764}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540496492.8/warc/CC-MAIN-20191207055244-20191207083244-00537.warc.gz"} |
http://www.physicsforums.com/showthread.php?t=316937 | # euler's polynomial proof
by khotsofalang
Tags: euler, polynomial, proof
P: 20 without using a counter example, show a proof that Euler's polynomial equation P(n)=n^2+n+41 can not be used to generate all the primes.can a general proof be made to show that all primes cannot be generated by a specific polynomial?
Math Emeritus Sci Advisor Thanks PF Gold P: 38,886 Well, what, exactly, is "Euler's polynomial equation"? Don't you think that is important?
P: 20 thats the proposition made by Euler that P(n)=n^2+n+41 can generate all primes and it was suddenly proven false by using a counter example, isnt there any way he can be proven to be false?
P: 891
## euler's polynomial proof
Quote by khotsofalang thats the proposition made by Euler that P(n)=n^2+n+41 can generate all primes and it was suddenly proven false by using a counter example, isnt there any way he can be proven to be false?
I believe you mean that P(n) would be prime for positive integers n, but there is now a general proof out there that no polynominal equation can generate only primes for all positive integers. I am sure that someone can cive you a link to a proof.
P: 891 See also http://en.wikipedia.org/wiki/Formula_for_primes Euler's formula for primes as posted in this thread was once widely thought to generate primes for any integer n, but as shown by this link that was false. The proof is simple an noted in the link. Assume that P(x) is a polynominal in x that gives a prime $$p$$ for the value $$n$$. But then $$p|P(n+kp)$$ for all integer $$k$$ so these numbers must be composite for every k so the polynominal is a constant, p, rather than a polynominal. P.S. Euler never said that the polynominal generated "all primes", but then that is obviously not what you meant is it?
P: 2,159
It is possible with polynomials in more variables, as the same wiki article points out:
...is a polynomial inequality in 26 variables, and the set of prime numbers is identical to the set of positive values taken on by this polynomial inequality as the variables a, b, …, z range over the nonnegative integers. A general theorem of Matiyasevich says that if a set is defined by a system of Diophantine equations, it can also be defined by a system of Diophantine equations in only 9 variables. Hence, there is a prime-generating polynomial as above with only 10 variables. However, its degree is large (in the order of 10^45). On the other hand, there also exists such a set of equations of degree only 4, but in 58 variables (Jones 1982).
Sci Advisor HW Helper P: 9,398 That doesn't count - look at the restriction placed on both the input and output variables.
P: 891
Quote by Count Iblis It is possible with polynomials in more variables, as the same wiki article points out:
but the same polynominal would generate composites also with large enough variables. Think how easy it would be to exceed the largest prime otherwise
P: 97 P(n) = n^2 + n + 41 => P(40) = 40^2 + 40 + 41 = 40 * 40 + 40 + 41 = 40 * 41 + 41 = 41 * 41 = composite.
HW Helper
P: 3,680
Quote by ramsey2879 See also http://en.wikipedia.org/wiki/Formula_for_primes Euler's formula for primes as posted in this thread was once widely thought to generate primes for any integer n
Really?
PF Gold P: 1,059 That no polynominal can generate all primes is easily shown using the reference given already http://en.wikipedia.org/wiki/Formula_for_primes Let P(1) = a prime S. $$Then P(1+kS) \equiv P(1) \equiv 0 Mod S.$$
P: 2,159
Quote by ramsey2879 but the same polynominal would generate composites also with large enough variables. Think how easy it would be to exceed the largest prime otherwise
The positive values of the Jones polynomial for positive values of the variables are always primes and all primes can be obtained this way. The problem is just that the probability that a random choice of the input vaiables will yield a positive value is astronomically small. If finally, after billions of years of trying, some positive value is obtained, it will likely be a prime number like 23.
Quote by robert Ihnot That no polynominal can generate all primes is easily shown using the reference given already http://en.wikipedia.org/wiki/Formula_for_primes Let P(1) = a prime S. $$Then P(1+kS) \equiv P(1) \equiv 0 Mod S.$$ | 2014-04-20 23:44:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8048014044761658, "perplexity": 546.1568144908974}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609539337.22/warc/CC-MAIN-20140416005219-00537-ip-10-147-4-33.ec2.internal.warc.gz"} |
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AsciiDoc
AsciiDoc is a text document format for writing short documents, articles, books and UNIX man pages. AsciiDoc files can be translated to HTML and DocBook markups using the asciidoc(1) command. AsciiDoc is highly configurable: both the AsciiDoc source file syntax and the backend output markups (which can be almost any type of SGML/XML markup) can be customized and extended by the user.
AsmRef
'AsmRef' includes a menu system and search function to display data on the Linux kernel and most topics associated with x86 assembler development on GNU/Linux systems.
Aspell
GNU Aspell is a spell checker that can be used either as a library or as an independent spell checker. It does a much better job of coming up with possible suggestions than other English language spell checkers. Other technical enhancements over Ispell include shared memory for dictionaries and intelligent handling of personal dictionaries when more than one Aspell process is open.
Aspell-gu
This package contains the required files to add support for the Gujarati (gu) language to the GNU Aspell spell checker.
Atom
Antifeature: Tracking comment
Atom will by default send “anonymous” usage data to Google Analytics (operating system, Atom version, screen resolution, …). To change this, go to Preferences, and "Core" settings. Change "Send Telemetry data to the Atom Team" to No (Do not send any telemetry data).
Atom is a text and source code editor based on Web technologies, specifically the Chromium project. Atom has a modular design that is integrated around a minimal core, which makes it very flexible and extensible. Atom is based on Electron (formerly known as Atom Shell), a framework that enables cross-platform desktop applications using Chromium and Node.js.
Auctex
AUCTeX is an integrated environment for producing TeX documents in Emacs. It allows many different standard TeX macros to be inserted with simple keystrokes or menu selection. It offers an interface to external programs, enabling you to compile or view your documents from within Emacs. AUCTeX also features the ability to place inline previews of complex TeX statements such as mathematical formulae. AUCTeX provides by far the most wide-spread and sophisticated environment for editing LaTeX, TeX, ConTeXt and Texinfo documents with Emacs or XEmacs. Combined with packages like RefTeX, Flyspell and others it is pretty much without peer as a comprehensive authoring solution for a large variety of operating system platforms and TeX distributions.
AutoConvert
AutoConvert is an intelligent Chinese Encoding converter. It uses built-in functions to judge the type of the input file's Chinese Encoding (such as GB/Big5/HZ), then converts the input file to any type of Chinese Encoding you want. You can use autoconvert to automatically convert incoming e-mail messages. It can also optionally handle the UNI/UTF7/UTF8 encoding.
Bhl
BHL is an Emacs mode that lets you convert plain TXT files into HTML, LaTeX, and SGML (Linuxdoc) files. The BHL mode handles common font-styles, three levels of sections, footnotes, and any kind of lists, tables, URLs and horizontal rules. It also handles a table of contents: you can browse the toc, insert the toc where you want, and update the sections' numbers with one keystroke.
Bib2xhtml
'bib2xhtml' is a program that converts BibTeX files into HTML (specifically, XHTML 1.0). The conversion is mostly done by specialized BibTeX style files, derived from a converted bibliography style template. This ensures that the original BibTeX styles are faithfully reproduced. Some post-processing is performed by Perl code. This is an update of the bib2html program written by David Hull in 1996 and maintained by him until 1998.
BibTeXConv
BibTeXConv is a BibTeX file converter which allows to export BibTeX entries to other formats, including customly defined text output. Furthermore, it provides the possibility to check URLs (including MD5, size and MIME type computations) and to verify ISBN and ISSN numbers.
BigText
The 'BigText' command prints big text using X11 fonts. It is similar to many other banner(1) commands, except that it can draw with all of the X11 fonts.
BirdFont
BirdFont is a font editor which can generate fonts in SVG, EOT and TTF format.
Birdfont
Birdfont is a font editor which lets you create vector graphics and export TTF, EOT and SVG fonts.
Blockly
Blockly is a web-based, graphical programming editor. Users can drag blocks together to build an application. No typing required.
BlueSpice
BlueSpice extends MediaWiki and enhances it with useful features, in particular in the areas of quality management, process support, administration, editing and security. There are two editions available: BlueSpice free and BlueSpice pro. BlueSpice free is a free of charge wiki version. BlueSpice pro is the business-critical solution with comprehensive functionalities and a subscription for support and software maintenance.
Bluefish
Bluefish is a powerful editor targeted towards programmers and webdevelopers, with many options to write websites, scripts and programming code. Bluefish supports many programming and markup languages.
Booktype
Booktype is a free, open source platform that produces beautiful, engaging books formatted for print, iBooks and almost any ereader within minutes. It makes it easier for people and organisations to collate, organise, edit and publish books.
Brackets
Brackets is a code editor, written using Web technologies like HTML, CSS and JavaScript.
C2html
'C2html' is a program which converts C source files to highlighted html files. The produced file can be used for creating technical manuals. A highlighted source code listing is usually much easier to read.
CE
CE is a simple, easy to use unix text editor. It allows full cursor control (you must have cursor keys to use it). It will also support Function keys if your terminal has them. It lets *nix new-comers, those who aren't technically minded, or those who don't want to learn one of the larger, less user friendly *nix editors. The design goal was to have just about any computerphobic person using CE in the shortest amount of time possible (ideally, under 20 minutes), with the smallest amount of documentation possible. It has enough features for text editing for rather good editing for just about anything. CE has been written entirely within CE since version 1.1e.
CHEAT
Minimal unit testing framework for the C programming language.
CVAssistant
Whether you're looking for a job or trying to help a friend to find one, CVAssistant is the number one tool for you. It helps you by preparing resumes and cover letters and organizing your job application process. It: Stores all your skills and experiences. Creates resumes tailored for each job you apply. Creates cover letters summarized to match each job advertisement. Keeps a history of job applications so you are ready when you receive a phone call. Write resumes in your language. All languages are supported! It's a free and open source software which you can easily download to your computer and start using it out of the box. CV Assistant helps you create specialized resumes in Word .docx format fast and easy. The idea is to have a master resume with all skills and experiences in it. Then based on skills mentioned in the job advertisement, export a clean but well formatted word .docx file as a summarized resume with only relevant skills in it. This increases your chance of getting a job interview as most companies are using Applicant Tracking Software (ATS) or at best hiring managers which may be unaware of similarity between phrases like skilled in MS Word, familiar with Microsoft Word and Fully experienced with office suites. So job seekers need to create specialized resumes for each and every job position with the same wordings used in the advertisement. Add all your skills to CV Assistant, pick only relevant ones. It also creates cover letters! Again, write all possible sentences, and select those relevant ones per job post. CVAssistant helps you free of charge and this software remains for free!
Catdoc
The program extracts text from Word files while preserving as many special characters as possible. It does not try to preserve Word formatting, but does extract readable text. A Tcl/Tk graphical viewer is included as well, and versions 0.91.2 and above include an Excel file converter.
Change
'Change' is a non-interactive text editor that is similar to 'sed' but easier to use. It substitutes a specified target pattern in the source text with another specified text pattern. It can operate on multiple files specified on the command line, or on stdin/stdout in filter mode.
CheapskateFonts 2
This is a collection of thirteen free software fonts. Styles include handwritten, sci-fi, basic sans serif and Roman, and others.
Chgrep
'chgrep' searches the input files (or standard input if no files are named) for oldpattern and changes them to newpattern (grep doesn't support this). You can use .lock files (or another extend). It is useful in (but not limited to) mail servers.
ChkTeX
ChkTeX checks for various syntactic, semantic and typographical errors in LaTeX documents, and helps the writer stay focused on the content rather than presentation or syntax of commands.
Cko
'cko' (Colored Kernel Output) is a Linux 2.4 and 2.6 kernel patch that colors kernel messages in the BSD style. If you don't like the default color (brown), you can change the value of the "color" variable and set it to whatever color you like.
ClientTable
ClientTable is a Python module for generic HTML table parsing. It is most useful when used in conjunction with other parsers (htmllib or HTMLParser, regular expressions, etc.), to divide up the parsing work between your own code and ClientTable.
Cobertura
Cobertura is a Java tool that calculates the percentage of code accessed by tests. It can be used to identify which parts of your Java program are lacking test coverage. It is based on jcoverage.
CodeBrowser
Code Browser is a folding and outlining editor for structuring and browsing source code using folders and links. It is somewhere between a traditional text editor, a smalltalk class browser and a web browser. It displays a structured text file (marker-based folding) hierarchically using multiple panes. It is especially designed to keep a good overview of the code of a large project.
CodeLite
CodeLite is a cross platform IDE for the C/C++ programming languages. Particular features are its excellent code-completion and refactoring. It has generic support for compilers, with built-in support for GCC and Clang. It supports debugging with both GDB and LLDB. It comes with many plugins, including ones for Git and Subversion, qmake, CMake, cscope and Cppcheck. Since version 13.0 it also includes the RAD plugin wxCrafter.
Collab
Multiplatform raster graphical editor enabling simultaneous drawing between users. Project including several sub projects as server, painting framework, network library, desktop application and protocol design and documentation.
Compare
'Compare' is similar to cmp (in the 'diffutils' package) but faster and with better readable output. It examines one file and standard in (or two files on a byte by byte basis) and prints the file position of the first difference it finds, first in decimal and then in hexadecimal, followed by the differing byte content in hexadecimal and a quoted character.
Condict
Condict is a program for creating dictionaries. It is written in Python, and uses the wxPython GUI framework, as well as the PyXML library.
Cooledit
Cooledit is a full featured multiple window text editor with interactive graphical debugger for C/C++ programs, anti-aliased fonts, compiler interface, the ability to be used as programmer's IDE with syntax highlighting for a wide variety of programming languages, UTF-8/UCS/Unicode support, and a built-in Python interpreter for macro programming.
Cp-tools
Classpath tools is a collection of tools for GNU Classpath including a documentation generation system for java source files (gjdoc) and a "doclet" for converting comments into GNU Texinfo source (texidoclet), etc. This project has been integrated into the main GNU Classpath project.
Cpp2latex
'cpp2latex' converts C++ into LaTeX either for including into existing LaTeX documents or as standalone documents. The current version (2.0) supports syntax highlighting.
CrocodileNote
Take simple text notes. You can put them into folders to create your own quick, easy and robust file structure. CrocodileNote supports two modes - plain and encryption. In encryption mode all data is encrypted using password-based encryption (PKCS#5) with AES-256. These are common industry standards and used by, e.g., the famous TrueCrypt disk encryption. In plain mode you can view and copy folders directly via PC from your internal SD card. Further features: - Export to ZIP for backup - Linkify notes in case you store e-mail addresses, Internet addresses/URLs or phone numbers - Auto-logout switch for 30 minutes (encryption mode only)
Cssed
'cssed' is a CSS editor and validator with support for other web and programming languages, that can be extended through plugins. Although full-featured, it's meant to be small, consumes few resources, and can be run on a P100 with 32Mb of RAM.
Csv2latex
'csv2latex' is a file format converter that converts a well formed CSV file (like the ones exported from OpenOffice.org) to the LaTeX document format.
Cxref
'Cxref' produces documentation (in LaTeX, HTML, RTF or SGML) including cross-references from C program source code. It works for ANSI C, including most gcc extensions. The documentation for the program is produced from comments in the code that are appropriately formatted. The cross referencing comes from the code itself and requires no extra work. Documentation is produced for files, functions, variables, #include, #define, and type definitions. Cross referencing is performed for files, #include, variables, and functions.
DHEX
'dhex' is an ncurses-based hex-editor with a diff mode. It makes heavy use of colors, but is also themeable to work on monochrome monitors. It includes the Action Cartridge Search Algorithm to find specific changes.
DataEditXml
Edit data held in the XML format using commands embeddedin Perl.
DataMelt
DataMelt (DMelt) is an environment for numeric computation, statistical analysis, data mining, and graphical data visualization on the Java platform. This Java multiplatform program is integrated with a number of scripting languages: Jython (Python), Groovy, JRuby, BeanShell. DMelt can be used to plot functions and data in 2D and 3D, perform statistical tests, data mining, numeric computations, function minimization, linear algebra, solving systems of linear and differential equations. Linear, non-linear and symbolic regression are also available. Neural networks and various data-manipulation methods are integrated using powerful Java API. Elements of symbolic computations using Octave/Matlab scripting are supported.
Dav
Dav (Dav Ain't Vi) is meant to provide a stable text editor that is efficient in both memory and processor usage. Its user interface is designed to be intuitive and to increase productivity.
DejaVu fonts
The DejaVu fonts are a font family based on the Bitstream Vera Fonts. Its purpose is to provide a wider range of characters while maintaining the original look and feel. The family is available as TrueType fonts and also as third-party packages for various operating systems, including handhelds.
Deplate
'deplate' is a tool for converting documents written in an unobtrusive, wiki-like markup to LaTeX, DocBook, HTML, or "HTML slides". It supports embedded LaTeX code, footnotes, citations, bibliographies, automatic generation of an index, etc. In contrast to many wiki engines, it is intended for "offline" use as a document preparation tool.
Devhelp
Devhelp is an API documentation browser for GTK+ and GNOME. It works natively with GTK-Doc (the API reference system developed for GTK+ and used throughout GNOME for API documentation).
DiaSCE
DiaSCE is a C/C++ code editor for GNOME. It pretends to be a complement to Glade, so it doesn't include an environment for GUI development. It has neither a debugger or other kind of tool to help debugging. The idea is for it to be a light code editor that doesn't need too many resources, and makes use of external tools (gcc, glade, ddd, etc.) for some tasks. This project was formerly known as 'david.'
Diakonos
Diakonos is a customizable, usable, console-based text editor. It features arbitrary language scripting, bookmarking, regular expression searching, parsed ("smart") indentation, macro recording and playback, a multi-element clipboard, multi-level undo, a customizable status line, completely customizable keyboard mapping, and customizable syntax highlighting.
Diction
This program includes both 'diction' and 'style'. 'Diction' identifies wordy and commonly misused phrases; 'style' analyzes surface characteristics of a document, including sentence length and other readability measures. While these programs cannot help you structure a document well, they can help to avoid poor wording and compare the readability of your document with others. Both commands support English and German documents.
Diffstat
Diffstat reads the output of the diff command and displays a histogram of the insertions, deletions, and modifications in each file. Diffstat is commonly used to provide a summary of the changes in large, complex patch files.
Diffutils
A group of utilities that displays difference between and among text files. 'diff' outputs the difference between two files in any of several formats. If the files are identical, it normally produces no ouput; if they are binary (non-text) it normally reports only that they are different. 'cmp' shows the offsets and files numbers where two files differ; it can also show, side by side, all the characters that differ between the two files. 'sdiff' merges two files interactively. 'diff3' shows differences among three files. If two people have made independent changes to a common original, diff3 reports that difference between the original and the two changed versions, and can produce a merged file that contains both persons' changes along with warnings about conflicts.
Ding
Ding is a dictionary lookup program that uses the 'agrep' or 'egrep' tools for searching. It comes with a German-English Dictionary with ca. 120,000 entries. It is a Tk based Front-End to [ae]grep, ispell, or dict. 'Ding' can also search in English dictionaries using 'dict' and check spelling using 'ispell.' Configuration options include search preferences, interface language (English or German), and colors. The package includes history functions, help functions, and comes key and mouse bindings for quick and easy lookups. The package has three different search behaviors: o Search after typing in a new word (standard, as before) o Search for selected text when moving the mouse over the ding window o Search immediately on new text selection in another window
Diqt
Diqt is a WWW-based multilingual dictionary reference tool. That is, dictionaries of many languages can be searched using a web browser. Any language is available if you have its dictionary data. For example, you can search English-Japanese, English-German, English-French, and Japanese-English dictionaries at the same time.
Dismal
Dismal (Dis' Mode Ain't Lotus) is a major mode for GNU Emacs that implements a spreadsheet. It is designed to be keystroke driven rather than mouse/menu driven (although it can be menu driven), and it is extensible. Users can write their own commands and functions, for example, to allow a function cell to write to several nearby cells. A ruler can be put up that reflects the semantics of column names past the ones automatically provided as letters. Dismal has some useful functions that implement the keystroke level model of Card, Moran, and Newell. Dismal is now maintained within ELPA, https://elpa.gnu.org.
DocBook XSL Stylesheets
DocBook is an XML and SGML dialect that lets you author and store document content in a presentation-neutral form that captures the logical structure of the content. Using the modular DocBook stylesheets and related resources, you can transform, format, and publish your DocBook content as HTML pages and PDF files, and in many other formats, including TeX, RTF, JavaHelp, UNIX man pages, and TeXinfo. It is part of the DocBook Open Repository project.
DocFrac
'DocFrac' is a tool that converts documents from RTF to HTML and from HTML to RTF. It is useful for bulk document conversion and dynamic Web pages. It does not require a word processor to work.
Docbook2X
'docbook2X' converts DocBook documents to man pages and Texinfo
Doclifter
'doclifter' is a tool that transcodes {n,t,g}roff documentation to DocBook XML markup. It parses man, mandoc, ms, me, or TkMan page sources, does structural analysis, and recognizes common troff-markup cliches. The result is usable without further hand-hacking about 95% of the time.
Docmenta
Docmenta is a Java Web-application for creating publications that need to be published for the Web and print. Supported output formats are PDF, HTML, Web-Help, EPUB (eBook) and DocBook. Main features are:
• Distributed authoring
• WYSIWYG editing
• Approval workflow
• Release-management
• Translation support
• Image gallery
• Listing support (line numbering, syntax highlighting)
• Applicability filtering and more.
Docutils
Docutils is a text processing system for processing plaintext documentation into useful formats, such as HTML or LaTeX. It includes reStructuredText, the easy to read, easy to use, what-you-see-is-what-you-get plaintext markup language.
Docvert
Docvert takes word processor files (typically .doc) and converts them to OpenDocument and clean HTML. The resulting OpenDocument is then optionally converted to HTML or any XML. This is done with XML Pipelines, an approach that supports XSLT, breaking up content over headings or sections, and saving those results to multiple files (e.g., chapter1.html, chapter2.htmlââ¬Â¦). The result is returned in a .zip file.
Dot-mode
dot-mode is a minor mode for GNU Emacs that emulates the .´ (redo) command in vi. It was written so that vi users no longer have an excuse for not switching to emacs…
Dot2Tex
The purpose of dot2tex is to give graphs generated by the graph layout tool Graphviz, a more LaTeX friendly look and feel. This is accomplished by:
• Using native PSTricks and PGF/TikZ commands for drawing arrows, edges and nodes.
• Typesetting labels with LaTeX, allowing mathematical notation.
• Using backend specific styles to customize the output.
• Dot2tex can also automatically adjust the size of nodes and edge labels to fit the output from LaTeX.
Dox
Dox is an extensible browser for manpages and HTML documentation. You can access documentation via tables of contents, keyword indices, and full text searches. The program has interfaces to pydoc and perldoc, and integration with Debian's docbase, and includes a utility that converts Doxygen-generated tafiles to keyword indices.
Doxia
Doxia is a content generation framework which aims to provide its users with powerful techniques for generating static and dynamic content. Doxia can be used to generate static sites in addition to being incorporated into dynamic content generation systems like blogs, wikis and content management systems. Doxia is used exensively by Maven and it powers the entire documentation system of Maven. It gives Maven the ability to take any document that Doxia supports and output it any format. It became a sub-project of Maven early in 2006.
Doxygen
Doxygen is a cross-platform, JavaDoc-like documentation system for C++, Java, C, and IDL. Doxygen can be used to generate an on-line class browser (in HTML) and/or an off-line reference manual (in LaTeX or RTF) from a set of source files. Doxygen can also be configured to extract the code-structure from undocumented source files. This can be very useful to quickly find your way in large source distributions.
Doxymacs
'doxymacs' is an elisp package designed to make using and creating Doxygen easier for Emacs users. It can look up documentation for classes, functions, members, etc in the browser of your choice, fontify Doxygen keywords, and automagically insert Doxygen comments in JavaDoc, Qt, or C++ style. You can also create your own style via templates.
Dvipng
'dvipng' makes PNG graphics from DVI files as obtained from TeX and its relatives. It is the fastest bitmap-rendering code for DVI files; on a fairly low-end laptop, it takes less than a second to generate 150 one-formula images. Furthermore, it does not read the postamble, so it can be started before TeX finishes. There is a -follow switch that makes dvipng wait at EOF for further output, unless it finds the POST marker that indicates the end of the DVI. It supports PK and VF fonts, color specials, and more.
E3
e3 is a full-screen, user-friendly text editor with an interface similar to that of either WordStar, Emacs, Pico, Nedit, or vi. It's heavily optimized for size and independent of libc or any other libraries, making it useful for mini-Linux distributions and rescue disks. There is also a separately distributed version written in C which supports some other Unix versions and CygWin. It is also possible to use regular expressions by using child processes like sed. e3 has a built in arithmetic calculator. The package now supports the ARM Risc CPU, amking it the first assembler program (on user layer) written for 2 different processors (Cisc vs Risc).
EMacro
EMacro is a .emacs that easily configures Emacs and XEmacs on most platforms, without any elisp programming.
EXtrans
eXtrans translates XML documents into other formats or representations. It can output formats HTML, XML, LateX, pictures, sound, or anything else that the python language can manipulate. Those translations are driven by abstract translators (xtrans scripts) embedding python code. The translators are easy to write, since the underlying system habdles all the complicated details of XML parsing, reference resolving, file management and even python programming in a way transparent to the user. This distribution includes GimpClient, a python module for communicating with Gimp. Through it, xtrans scripts can efficiently access a powerful graphics program.
Earm2ipa
This program translates Armenian in UTF-8 Unicode to the International Phonetic Alphabet assuming that the dialect represented is Eastern Armenian.
Easymacs
'Easymacs' is an easy-to-learn configuration for new users of GNU Emacs. It sets up key bindings that conform to a common denominator of the Gnome/KDE/OS human interface guidelines, and provides function-key bindings for other powerful Emacs features. It is fully documented, and the new user can productively edit text right away, without going through the Emacs tutorial. Users can access many commonly-used functions without learning the "chords" or multiple keystrokes that Emacs uses by default.
Ed
Ed is a line-oriented text editor: rather than offering an overview of a document, ed performs editing one line at a time. It can be executed both interactively and via shell scripts. Its method of command input allows complex tasks to be performed in an automated way. GNU ed offers several extensions over the standard utility. The original editor for Unix was the most widely available text editor of its time. For most purposes, however, it is superseded by full-screen editors such as GNU Emacs or GNU Moe. N.B. This pacakge also contains a restricted version of ed, red, that can only edit files in the current directory and cannot execute shell commands.
Eddi
Eddi is a powerful and easy-to-use text editor for X. Features include syntax highlighting, macros, filtering through commands, an interface to su (to save eg system config files), and search and replace with regular expressions. It is exteremely intuitive and therefore very easy to use.
Edictionary
'edictionary' is a command line interface to online dictionaries
EditorConfig core
This package helps developers define and maintain consistent coding styles between different editors and IDEs. The EditorConfig project consists of a file format for defining coding styles and a collection of text editor plugins that enable editors to read the file format and adhere to defined styles. EditorConfig files are easily readable and they work nicely with version control systems. EditorConfig contains a few core libraries for different languages, e.g. C, Python, Java, JavaScript, and a set of editor/IDE plugins which use these library.
Elpy
Elpy is an Emacs package that brings powerful Python editing to Emacs. It combines a number of other packages that are written in Emacs Lisp and Python. Elpy's features includes:
• Code completion (via Rope or Jedi)
• Indentation highlighting (via Highlight-Indentation)
• Snippet expansion (via Yasnippet)
• Inline documentation (via Rope, Jedi or Pydoc)
• Powerful code refactoring (via Rope)
• On-the-fly checks (via Flymake)
• Virtualenv support (via Pyvenv)
• Test running
Emacs
Extraordinarily powerful text editor with additional features including content sensitive major modes, complete online documentation, highly extensible through Lisp, support for many languages and their scripts through its multilingual extension, and a large number of other extensions available either separately or with the GNU Emacs distribution. Runs on many different operating systems regardless of machine. It offers true Lisp, smoothly integrated into the editor, for writing extensions and provides an interface to the X windows system.
This program creates a madx major for emacs that highlights the cern (Methodical Accelerator Design) MAD-X 5 syntax. This is not a GNU package.
EncNotex
EncNotex is a free multiplatform software, which runs natively on GNU/Linux, Windows and macOS, that is useful to write and to manage a file of strongly encrypted textual notes and tasks. It’s aim is to grant the user an highly secure tool to manage very confidential data. For this reason EncNotex uses the AES 256 bit encryption, cipher mode CBC and SHA 512; the user cannot save unencrypted data on the disk, but only copy it in the clipboard; the required password to encrypt a file is necessarily 10 characters long or more, chosen at least from three of these four groups: small and upper case letters, numbers and other characters (asterisk, brackets, etc.); optionally, the password used to save a file could be forgotten by the software and typed again by the user each time a file is to be saved, so that the same password does not remain in the computer’s memory while the software is being used. A file of EncNotex is a textual encrypted file containing many notes (no database is used). To grant a perfect compatibility of data among the different platforms and to be very fast even with big amount of data, EncNotex has a very simple structure of notes. They cannot have pictures inside nor attachments, but their text can be formatted in bold, italic and underline. Every note has a title, a list of tags (keywords) separated by comma and space, a date and a free-length text, and can be printed. The title and the date of every note is shown in a read only grid on the left of the interface of the software, and a note can be shown selecting its title in this grid. Furthermore, in the same grid the title of a note can be indented or deindented, to make it a subnote of the previous one, or moved up and down, along with its possible subnotes. At the left of the text of the notes there is an outlook of its titles, which can be used to reach easily one of them, and of the possible tasks along with their deadline. The tasks of all the notes of a file can be summarized in a list, sorted, filtered and copied in the clipboard to be pasted in a spreadsheet, or saved in csv or ics format. It's possible to search for a note within the titles, the tags, the dates and the texts. A note or all the notes of a file can be copied in the clipboard in HTML format and then pasted in a word processor maintaining the possible HTML tags. Finally, two independent backup files are automatically created when a file is loaded and when it's saved.
Epix
'ePiX', a collection of batch programs, creates mathematically accurate fgures, plots, and animations containing LaTeX typography. The input syntac is easy to learn. The output -- vector image files or LaTeX picture-like environments -- is expressly designed for use with LaTeX.
Epydoc
Epydoc is a tool for generating API documentation for Python modules, based on their inline documentation strings (docstrings). It produces HTML output (similar to the output produced by javadoc) and PDF output. Epydoc supports four markup languages for documentation strings: Epytext, Javadoc, ReStructuredText, and plaintext.
Essays
Essays 1743 is based on the typeface used in a 1743 English translation of Montaigne's Essays (if you've read any of Neal Stephenson's last three books, you've seen this type of font). It contains 817 characters: all of ASCII, Latin-1, and Latin Extended A; some of Latin Extended B (basically, the ones that are more or less based on Roman letters); and a variety of other characters, such as oddball punctuation, numerals, etc. TrueType and PostScript forms are available.
Etherpad is a real-time collaborative editor. It lets you edit text in your browser, while other contributors see the changes instantly. It features basic formatting as well as an history.
Faq-O-Matic
The Faq-O-Matic is a CGI-based system that automates the process of maintaining a FAQ (or Frequently Asked Questions list). It allows visitors to your FAQ to take part in keeping it up-to-date. A permission system also makes it useful as a help-desk application, bug-tracking database, or documentation system.
Fig2ps
'fig2ps' converts xfig files to PS or PDF, processing text using LaTeX. It is intended to help typeset good quality documents, where the font on the pictures is exactly the same as the font in the text. You compile the picture only once and not every time you compile your LaTeX file (as with other xfig exporters such as eepic); this makes it much faster with complex pictures. It should work with LyX.
File
File attempts to classify files depending on their contents and prints a description if a match is found.
Firestr
Fire★ is a a simple platform for decentralized communication and computation. Provides a simple application platform for developing p2p applications and share these applications with others in a chat like user interface. You don't send a message to someone, you send an program, which can have rich content. All programs are wired up together automatically providing distributed communication, either through text, images, or games. The source code to all applications is available immediately to instantly clone and modify.
Fldiff
'fldiff' is a graphical diff program that shows the differences between two files/directories, or a file/directory and a CVS or Subversion repository. It is inspired by xdiff (Motif-based) and xxdiff (Qt-based), whose choice of GUI toolkit has hampered their portability to many of the systems.
Flowblade Movie Editor is designed to provide a fast, precise and as-simple-as-possible editing experience. Flowblade employs film style editing paradigm in which clips are usually automatically placed tightly after the previous clip - or between two existing clips - when they are inserted on the timeline. Edits are fine-tuned by trimming in and out points of clips, or by cutting and deleting parts of clips. Film style editing is faster for creating programs with mostly straight cuts and audio splits, but may be slower when programs contain complex composites unless correct work flow is followed.
Flpsed
flpsed is a WYSIWYG pseudo PostScript editor. "Pseudo", because you can't remove or modify existing elements of a document. But it does let you add arbitrary text lines to existing PostScript documents. Added lines can later be reedited with flpsed. Using pdftops, one can convert PDF documents to PostScript and also add text to them. flpsed is useful for filling in forms, adding notes etc.
Flyspell
Flyspell is an Emacs minor mode performing on-the-fly spelling checking. This spawns a single Ispell process and checks each word. The default flyspell behavior is to highlight incorrect words. It was hosted for a long time on INRIA Sophia-Antipolis's site in France, but is now maintained as a part of GNU Emacs.
Fntsample
fntsample is a program for making font samples that show Unicode coverage of the font. The samples are similar in appearance to Unicode charts. Samples can be saved as PDF or PostScript files.
FontForge
FontForge is an outline font editor that lets you create your own fonts or edit existing ones. Multiple formats including PostScript, TrueType, OpenType, SVG and bitmap (BDF) are supported. It also lets you convert one format to another. This package was formerly known as pfaedit.
FontTools
FontTools/TTX is a library to manipulate font files from Python. It supports reading and writing of TrueType/OpenType fonts, reading and writing of AFM files, reading (and partially writing) of PS Type 1 fonts. The package also contains a tool called "TTX" which converts TrueType/OpenType fonts to and from an XML-based format.
Fontlinge
Fontlinge searches for font files, sorts them into folders by name and look and with human readable names, stores gathered font information in a database, can generate previews and posters, can find and remove duplicates, and can reunite PostScript font families. It also has a web interface for browsing through your fonts. It shows detail previews and font infos, provides font download as a tarball, and can sort fonts. This package is no longer maintained.
Fontopia
Fontopia is an easy-to-use, text-based, console font editor. It's used to edit the fonts that GNU/Linux uses to display text on text-based terminals. Fontopia works on both PSF 1 & 2, BDF, Code Paged (CP) fonts, and Raw font files. It provides a user-friendly, easy-to-use glyph editor and it can easily change font metrics (e.g. length, width, and height) and convert between different font formats.
Fontutils
The GNU Font Utilities (a.k.a. Fontutils) create fonts for use with Ghostscript or TeX. They also contain general conversion programs and other utilities. Some of the programs in Fontutils include bpltobzr, bzrto, charspace, fontconvert, gsrenderfont, imageto, imgrotate… The main purpose of these programs is to form a tool chain to generate Metafont or PostScript fonts from scanned images.
Form Alchemy
FormAlchemy eliminates boilerplate by autogenerating HTML input fields from a given model. FormAlchemy will try to figure out what kind of HTML code should be returned by introspecting the model's properties and generate ready-to-use HTML code that will fit the developer's application. Of course, FormAlchemy can't figure out everything, i.e, the developer might want to display only a few columns from the given model. Thus, FormAlchemy is also highly customizable.
Free Bangla Fonts
The Free Bangla Fonts project is dedicated to creating free, completely Unicode compliant Open Type Bengali fonts. It also aims to be the central resource for getting and developing Free Bengali fonts. The initial goal is to release a full set of Bengali fonts that supports all the major Bengali Yuktakhars (conjuncts). The Akaash set of fonts aims to be such a set. We also plan to convert the other existing Free Bangla (non Unicode compliant) fonts into Unicode compliant Bengali Open Type fonts. Five sets of fonts are currently under development. The Akaash set will have three OTFs, AkaashNormal.ttf, AkaashWide.ttf and AkaashSlanted.ttf. Development is currently going on in the AkaashNormal.ttf, and we aim to move to AkaashWide and AkaashSlanted as soon as possible. The Ani set has two fonts, Ani.ttf and Mitra.ttf. The Mitra font is a monospaced fonts, which is useful in certain specialised applications. The Mukti set has four fonts, MuktiRegular.ttf, MuktiBold.ttf, MuktiNarrow.ttf, and MuktiNarrowBold.ttf. The Likhan and Sagar sets of fonts are also being developed.
Free Oberon
Free Oberon is a cross-platform IDE for development in Oberon programming language made in the classical FreePascal-like pseudo-graphic style. Compilation of user-written programs is performed using the Vishap Oberon Compiler and then GCC. The compiled console programs can be run in the built-in terminal emulator.
Freedoc
"freedoc.sh" is a short script that, when given a URL for a Google Doc as input, will download that Google Doc in the current working directory in OpenDocument Format without running any of Google's nonfree JavaScript. Uploaded at the request of RMS.
Freefont
The GNU FreeFont project aims to provide a useful set of free scalable (i.e., OpenType) fonts covering as much as possible of the ISO 10646/Unicode UCS (Universal Character Set). It includes:
• Latin, Cyrillic, and Arabic, with supplements for many languages
• Greek, Hebrew, Armenian, Georgian, Thaana, Syriac
• Devanagari, Bengali, Gujarati, Gurmukhi, Oriya, Sinhala, Tamil, Malayalam
• Thai, Tai Le, Kayah Li, Hanunóo, Buginese
• Cherokee, Unified Canadian Aboriginal Syllabics
• Ethiopian, Tifnagh, Vai, Osmanya, Coptic
• Glagolitic, Gothic, Runic, Ugaritic, Old Persian, Phoenician, Old Italic
• Braille, International Phonetic Alphabet (and extensions)
• currency symbols, general punctuation and diacritical marks, dingbats
• mathematical symbols (including much of the TeX repertoire of symbols)
• technical symbols: APL, OCR, arrows,
• geometrical shapes, box drawing
• musical symbols, gaming symbols (chess, checkers, mahjong), miscellaneous symbols
Freetype
The FreeType project is a team of volunteers who develop free, portable and high-quality software solutions for digital typography. They specifically target embedded systems and focus on bringing small, efficient and ubiquitous products. The FreeType 2 library is their new software font engine. It has been designed to provide the following important features: * A universal and simple API to manage font files * Support for several font formats through loadable modules * High-quality anti-aliasing * High portability & performance Supported font formats include: * TrueType files (.ttf) and collections (.ttc) * Type 1 font files both in ASCII (.pfa) or binary (.pfb) format * Type 1 Multiple Master fonts. The FreeType 2 API also provides routines to manage design instances easily * Type 1 CID-keyed fonts * OpenType/CFF (.otf) fonts * CFF/Type 2 fonts * Adobe CEF fonts (.cef), used to embed fonts in SVG documents with the Adobe SVG viewer plugin.
• Windows FNT/FON bitmap fonts
GENIA Tagger
The GENIA tagger analyzes English sentences and outputs the base forms, part-of-speech tags, chunk tags, and named entity tags. The tagger is specifically tuned for biomedical text such as MEDLINE abstracts. If you need to extract information from biomedical documents, this tagger might be a useful preprocessing tool.
GLTT
'GLTT' is a library that allows you to read and draw TrueType fonts in any OpenGL application. It supports bitmapped and anti-aliased font drawing as well as vectorized and polygonized drawing.
GNU Edu
GNU Edu allows you to browse documents written in another language, or in your own language but from another country. GNU Edu stores metadata for educational resources. These metadata are of two kinds:
• common metadata for all kinds of documents
• special metadata for educational resources
• GNU Edu metadata conform to international standards
Galway web weaver 2
This is a candidate for deletion: Links broken. No links to page. Email to maintainer broken. Poppy-one (talk) 14:07, 31 July 2018 (EDT) Galway is an GNOME HTML editor with features like Java Script, VRML 2.0, Script-fu and PHP support in additional to ftp publishing, local html previewing, and full scripting capabilities.
Gawk
Gawk is the GNU implementation of AWK, a programming language that has evolved considerably during the past 30 years. It also adds a large number of features over POSIX awk. This package is well suited for working with text files, when several kinds of tasks occur repeatedly, for extracting certain lines and discard the rest is needed, or for making changes wherever certain patterns appear. It can handle simple data-reformatting jobs with just a few lines of code.
Gcide
GCIDE is a free dictionary based on a combination of sources. The dictionary can be used online and offline.
Gdeditor
This is a candidate for deletion: Links broken. No links to page. Email to maintainer broken. Poppy-one (talk) 13:48, 1 August 2018 (EDT) Multidocument text editor with CORBA and Guile interfaces that dialogs with GnoDarwin. The Web site is currently in Spanish only.
Gdictcn
A simple gtk+ chinese dictionary online.
Gdkxft
'Gdkxft' transparently adds anti-aliased font support to gtk+-1.2. Once it is installed, you can run nearly any existing gtk+ binary and see anti-aliased fonts in the gtk widgets without needing to recompile gtk+ or your applications. The latest version includes some international text support.
Geany
Geany is a lightweight editor and IDE with basic features of an integrated development environment. It features syntax highlighting in dozens of languages, code completion, call tips, many supported filetypes (including C, Java, PHP, HTML, DocBook, Perl, LateX, and Bash), and symbol lists. It can be extended with the help of plugins, to add features like window splitting.
Gedit
gedit is a text editor for the GNOME Desktop. It is designed to be simple, light, and fast, but its plugin system can give you incredible power as well. Complete GNOME integration is featured.
'Geiriadur' combines a dictionary lookup engine and a dictionary editing system. It's developed as a tool to create Welsh-Russian and Russian-Welsh dictionaries, but it can also be used for other languages. It consists of two components: a dictionary CORBA server and the Web interface for it. The system works through "words" and "translations". A "translation" is a pair of words or a word with explanation; a "word" means a string of letters without a space, possessing independent meaning in some language. Words can have transcription, attributes (gender, aspect etc.), and "stems" and irregular forms. Regular forms are produced dynamically during a search from "stems" and "endings". The system understands mutations and different spellings (American English, Middle Welsh etc.) If a direct search (with the first word in translations table) yields no results, the system performs an inverse search or asks the user to try a cross-search through a third language.
Gfe
GNU Font Editor (GFE) is a graphical font editor based on GTK+ the GIMP Toolkit. It is easy to use and will eventually support many font types. Currently it supports BDF (bitmap distribution format) font files, that can be converted to many other formats easily.
Gfontview
gfontview is a Font Viewer for outline fonts (PostScript Type 1 and TrueType). It lets you view uninstalled fonts. It will display all fonts present in the chosen directory in a list, with a preview of the font in the main window. It allows printing samples and font catalogs. 'gfontview' also allows you to display a particular character or string of a font in an own window, thus allowing a comparison between several fonts with a particular string sample. This character or string can be antialiased (smoothed).
Ghex
GHex is a simple binary editor. It lets users view and edit a binary file in both hex and ascii with a multiple level undo/redo mechanism. Features include find and replace functions, conversion between binary, octal, decimal and hexadecimal values, and use of an alternative, user-configurable MDI concept that lets users edit multiple documents with multiple views of each.
Ghostwriter
ghostwriter provides a relaxing, distraction-free writing environment, whether your masterpiece be that next blog post, your school paper, or your NaNoWriMo novel. Here are just a few of its features: Syntax highlighting of Markdown Navigation of document headings Full-screen mode Focus mode that highlights the current sentence, line, three lines, or paragraph Two built-in themes, one light and one dark Theme creator for custom colors and background images Spell checking with Hunspell A Live word count A live HTML preview as you type Use of custom CSS style sheets for HTML preview Image URL insertion via dragging and dropping an image file into the editor Sundown processor built in for preview and export to HTML
Gitenc
Gitenc is a simple shell script that works as a placeholder for git add and will parse filenames for sensitive names from git diff and apply GPG encryption as needed (filenames matching config, connection or sqlbackup) while handing everything off to git.
Glark
'glark' offers grep-like searching of text files, with very powerful, complex regular expressions (e.g., "/foo\w+/ and /bar[^\d]*baz$/ within 4 lines of each other"). It also highlights the matches, displays context (preceding and succeeding lines), does case-insensitive matches, and automatic exclusion of non-text files. It supports most options from GNU grep. Glatex glatex is a small program designed to help you to edit your LaTeX document files (sources, styles, bibliography, figures, postscript images, etc.). It maintains a list of all your editable files in order to allow you to edit them quickly. But you can also launch the compilator, viewer, and print commands, and it allows you to have document templates for creating new projects. It is not intended to manage the files themselves. For example, if you move a file from one directory to another, you'll have to remove it from the list and re-add it from its new location. Glimmer Glimmer is a code editor that can be used with almost any language. It uses the GTK+ widget set adn the GNOME libraries. Current features include drag and drop support, syntax and bracket highlighting, the ability to build from within the editor, the ability to save sessions of different code files open at once. It supports for more than 20 languages, and is completely scriptable with Python. This project was formerly known as 'code commander.' Glossword Glossword is a system to create and publish online multilingual dictionary, glossary, or encyclopedia. It includes multiple language support, themes, a powerful administration interface, built-in search and cache engines, export/import dictionaries in XML and CSV format, and W3C-validated code. It is useful for any kind of dictionary, including sites with game cheat codes, online translators, references, and various CMS solutions. Gman Gman is a user-friendly graphical front end for the man system mostly designed for the new users of GNU/Linux. It can help a newbie find specific information or browse other man pages. It is particularly useful as a replacement for xman. Gman's most basic job is to build a database for all the man pages and display them (or part of them) as a list. When the user decides to read a specific man page, gman will launch a xterm window and call the traditional man system to display the man page in the window. Gnotepad+ A simple HTML and text editor for UNIX-based systems running X11 and using GTK and/or GNOME. It was designed to have as little bloat as possible while retaining the features of a modern GUI-based text editor. It remains small for the number of features it contains, and will remain that way. Features includes multiple windows and multiple documents, a complete preferences system, HTML tag insertions and editing dialogs, unlimited redo and undo, autosave, file locking using fcntl() of flock(), and the ability to drag and drop files between gnotepad+ and other applications. This project was a GNU package. It has since been decommissioned and is no longer developed. Gnudos GnuDOS is a set of programs designed to help new users of the GNU system in growing accustomed to the system, particularly users who might be coming from a DOS background. It consists of a file manager, a text editor and a form designer for the console as well as a core library for building similar utilities: • The core library (corelib) contains four utilities: Kbd (for keyboard handling), Screen (for screen drawing), Dialogs (for dialog boxes/window drawing), and Strings (for strings functions). • The software applications are three: Prime (console file manager), Mino (console text editor), and Fog (console form designer). Gnun GNUnited Nations is a build system for translating the web site at www.gnu.org. It works via template files, which allow changes to be merged into individual translations of a page, from which the final HTML is generated. In effect, this helps to keep all translations of a page up-to-date. See also the GNU Web Translation Coordination organizational project. Gnuzilla SpyBlock Spyblock is an extension for IceCat to block privacy trackers. It was originally based on AdBlock Plus. Gobby Gobby is a collaborative editor based on libobby, a library which provides synced document buffers. It supports multiple documents in one session and a multi-user chat. It uses GTK+ 2.6 as its windowing toolkit and thus integrates nicely into the GNOME desktop environment. It provides users with real time collaberation. Each user has its own colour (changeable) to be identified by others. There are IRC-like Chat for communicating with your partners, syntax highlighting for most programming languages, session password protection, multiple documents in one session and the drag'n'drop of documents Gregorio The Gregorio project offers tools for the typesetting of Gregorian chant. These tools include: • gabc: a brief notation for representing Gregorian chant • GregorioTeX: a TeX style for typesetting scores • GregorioXML: an XML representation of a Gregorian chant score Grep Grep is a tool for finding text inside files. Text is found by matching a pattern provided by the user in one or many files. The pattern may be provided as a basic or extended regular expression, or as fixed strings. By default, the matching text is simply printed to the screen, however the output can be greatly customized to include, for example, line numbers. GNU grep offers many extensions over the standard utility, including, for example, recursive directory searching. Groff Based on a device-independent version of troff,' groff' (GNU Troff) is a document processor which reads plain text and formatting commands, produces formatted output from them, and then outputs it to another device. The package is essential for viewing online manual pages. Output can be produced in a number of formats including plain ASCII and PostScript. All the standard macro packages are supported. Gtkdiff A diff front end program using gtk+, primarily used as a front end to the 'diff' command to compare files. It has diff3 and merge features. Gummi Gummi is a lightweight LaTeX editor written in Python/GTK+. HSpell The Hspell project is a free Hebrew linguistic project. Its first aim is to create a free Hebrew spell-checker, and a fully functional and already useful release 0.2 is now available (see below). However the databases and algorithms developed by the Hspell program could also be used as a morphology engine (for example, for search engines), and in the future (with much more work) for advanced things like Hebrew speech synthesis (for the blind who use a free operating system, but also useful for the general population) HTML GenToc HTML::GenToc lets you specify significant elements that will be hyperlinked to in a Table of Contents (ToC) for a given set of HTML documents. It does not require those documents to be strict HTML, which makes it suitable for using with templates, included files, and meta-languages such as WML or PHP. Hashed Text Utilities This is a candidate for deletion: Links broken. Email to maintainer broken. Poppy-one (talk) 12:50, 3 August 2018 (EDT) Hashed Text Utilities is a small set of programs reimplementing the classic comm, diff, uniq, and cksum programs. The advantage is that for comm and uniq files don't have to be sorted. diff can work with extremely huge files (with some limitations). cksum calculates a checksum of either the whole file or each line separately. Header Browser Header Browser helps you to create documentation from your C/C++ header files. It is similar to JavaDoc, Doc++, or KDoc, but it doesn't just create documentation pages; it allows you to really browse your APIs using a five columns view like NeXT's HeaderViewer. Documentation can be generated in several formats, including TexInfo for PostScript, DVI, PDF, manpages, printable HTML, etc. Health GNU Health is a program designed for hospitals, offering the following functionalities: • Electronic Medical Record (EMR) • Hospital Information System (HIS) • Health Information System It has a strong focus on family medicine and primary care, along with socio-economic circumstances. It uses the following disease and medical procedure standards: (ICD-10 / ICD-10-PCS). There are facilities to aid in choosing medicines; prescription writing; patient, hospital finacial, and lab administration tools; a database of 4,200 disease-related genes; epidemiological reporting; and much more. GNU Health is part of GNU Solidario, an NGO offering health and education to the underpriveledged through free software: http://www.gnusolidario.org Help2man Help2man is a program that converts the output of standard --help and --version command-line arguments into a manual page automatically. It lets developers include a manual page in their distribution without having to maintain that document. Since Texinfo is the official documentation format of the GNU project, this also provides a way to generate a placeholder man page pointing to that resource while still providing some useful information. Highlight Highlight is a universal source code to HTML, XHTML, RTF, TeX, or LaTeX converter. (X)HTML output is formatted by Cascading Style Sheets. It supports Bash, C, C++, C#, COBOL, Java, Perl, PHP, and 40 more programming and markup languages. It is also possible to easily enhance the parsing database. Hitch Hitch allows developers to be properly credited when Pair Programming and using Git. Html2xhtml Html to Xhtml Convertor converts HTML pages into XHTML pages. It can process batches of files, convert line breaks, and deal with attribute minimization, quoting of attribute values, and more. Htmlrecode 'htmlrecode' applies modifications to a HTML file. For example, you can completely change the character set you are using without making any of the characters unreadable. Hyperbole Hyperbole is a programmable information and hypertext system for GNU Emacs. It allows hypertext to be embedded within documents, mail messages and news articles. This permits mouse-based control of the displayed information. GNU Hyperbole may be installed by using the Emacs Package Manager. IceCat/Firebug Firebug integrates with Firefox to put a wealth of web development tools at your fingertips while you browse. You can edit, debug, and monitor CSS, HTML, and JavaScript live in any web page. IceCat/Theme Font and Size Changer Theme Font & Size Changer lets you change the global font size and font family used for the user interface in Firefox. Design your browser with your favorite font. Icedove Icedove is the rebranding of Mozilla Thunderbird by the Debian Project. Icedove supports different mail accounts (POP, IMAP, Gmail), has an integrated learning Spam filter, and offers easy organization of mails with tagging and virtual folders. Also, more features can be added by installing extensions. The goal of Icedove is to produce a cross platform standalone mail application using the XUL user interface language. Icedove has IRC support, and the calendar extension Mozilla Lightning is now installed by default. Ide.php 'Ide.php' is a Web-based editor for quick development of server side code. It has a rapid prototyping environment so you can test and save snippets of code with minimal overhead. You can use it to develop PHP, ASP, JSP, SSI, HTML, or CGI. Imediff2 Imediff2 merges two (slightly different) files interactively with a user-friendly fullscreen interface in text mode. It shows the differences between the two files (in color if the terminal supports them), lets you scroll the file, and toggles changes between the old and new versions one by one. Unlike split screen based merge tools, it shows only one version at a time, making it more WYSIWYG. Indexed PDF Creator Indexed PDF Creator creates indexed PDF documents from text files. It was primarily written as a utility to convert old mainframe print formats to something that can easily be posted on the Web. It allows indexing, customizing page settings, font size, font face, and superimposing text over an image in the case of using pre-printed forms. It supports unlimited levels of indexing bookmarks in documents and system/user configuration files Info to html info_to_html does everything info2html does, and more. Added features include links to other info files, the ability to read compressed files, and a nicer layout. Info2html Info files are text files with embedded link directives. They are usually read with emacs or a special purpose browser. 'info2html' looks for a specific info node in an info file and translates it to HTML syntax. Link directives are translated in URLs pointing back to the server. Some icons are provided for link directives and cross references. infocat is a little front-end that gives an index of the .info files available via the local info2html server. Inkscape Inkscape is an SVG editor. Supported SVG features include basic shapes, paths, text, alpha blending, transforms, gradients, filters, node editing, PNG export, grouping, and more. It is meant to provide the free software community with a fully XML, SVG, and CSS2 compliant SVG drawing tool. Intlfonts This directory contains free X11 fonts (BDF format) for all characters that Emacs 20 can handle. They are classified as follows: European, Asian, Chinese, Japanese, Korean, Ethiopic, and misc, with one sub-directory for each category. TrueType fonts are also included. Isabella This font, called 'Isabella' is based on the calligraphic hand used in the Isabella Breviary, made around 1497, in Holland, for Isabella of Castille, the first queen of united Spain. It has all of ASCII, Latin-1, Latin Extended A, about a third of Latin Extended B, Latin Extended Additional, plus punctuation, and should work for most languages that use the Roman alphabet. Modern characters (@, for example) were drawn as best possible. The primary design goal was to make such characters look like they were done with a calligraphic pen; the secondary goal was to look like the other characters of the font. The copyright sign, for example, is made by shrinking down the letter "c" and placing it inside a circle. It also has a Euro symbol. 'Isabella' is available in TrueType and PosctScript (author notes that the PostScript version acts oddly in on-screen use). Ispell Interactive spell checker that suggests "near misses" to replace unrecognized words. JDynamiTe JDynamiTe is a tool which allows you to dynamically create documents in any format from "template" documents. Some typical usage domains of JDynamiTe are: • dynamic Web pages creation, • text document generation, • source code generation... In fact, it can be useful in any case where pre-defined documents (templates) have to be dynamically populated with data. The main benefit of JDynamiTe is to allow a true separation between data (content), presentation (container) and content generation code (written in Java). JDynamiTe does not include a specific template language, and it is not a complete framework. It is a simple "brick" in your software architecture, a "glue" between your data model and your presentation model. JEdit jEdit is an IDE written in Java. Some of its features include: • Built-in macro language; extensible plugin architecture. Hundreds of macros and plugins available. • Plugins can be downloaded and installed from within jEdit using the "plugin manager" feature. • Auto indent, and syntax highlighting for more than 200 languages. • Supports a large number of character encodings including UTF8 and Unicode. • Folding for selectively hiding regions of text. • Word wrap. • Highly configurable and customizable. • Every other feature, both basic and advanced, you would expect to find in a text editor. JEdit Syntax Package The jEdit Syntax Package is a stand-alone version of the text control from an older version of jEdit. It supports features such as syntax highlighting, bracket matching, rectangular editing, macro recording, and more. The jEdit Syntax Package is lightweight, and meant solely for embedding into Java user interfaces. It does not include some of the nicer features of jEdit, including plugins, and scripting. Jade Editor Jade is an Emacs-like text editor that implements most basic Emacs functionality, but is not intended as a straight clone. The Lisp dialect is intended to be compatible with Emacs Lisp, but the interface to the editor internals is not, due to differing philosophies behind the implementations. As a result, most Lisp code written for GNU Emacs will not work; basic GNU Emacs emulation interfaces may be added in the future. Commands are implemented in Lisp, which allows for comprehensive customisation and extension. Java2html When given a source java file, program produces an HTML source with syntax highlighting. JavaDICT This is a candidate for deletion: Cannot find download. Email to maintainer broken. Poppy-one (talk) 13:23, 6 August 2018 (EDT) JavaDICT is a server for the DICT protocol (RFC 2229), a TCP transaction-based query/response protocol that lets a client access dictionary definitions from a set of natural language dictionary databases. So far it is the only DICT server that lets you access dictionaries stored in a database (currently only PostgreSQL is supported). Jaxml Jaxml is a python module designed to automatically generate human readable documents. Joe JOE (Joe's Own Editor) is a small, terminal-based, lightweight, emacs-like editor originally written in 1991. Termcap/Terminfo support allows JOE to use any terminal or terminal emulator. Much of the look and feel of JOE is determined by its simple configuration file "joerc". This package is maintained again by its original author, after a period of absence in which another team continued development. Jove Jove is a compact, powerful, Emacs-style text-editor. It provides the common emacs keyboard bindings, together with a reasonable assortment of the most popular advanced features (e.g., interactive shell windows, compile-it, language specific modes) while weighing in with CPU, memory, and disk requirements comparable to vi. Jq jq accepts a stream of JSON and then transforms it (selecting, iterating, reducing, etc) through one or more filters and then pretty-prints the results. jq is like sed for JSON data - you can use it to slice and filter and map and transform structured data with the same ease that sed, Gawk, grep and friends let you play with text. Junicode The Junicode font is designed to meet the needs of medieval scholars; however, it has a large enough character set to be useful to the general user. It comes in Regular, Italic, Bold and Bold Italic faces. The Regular face has the fullest character set, and is richest in OpenType features. Jupp Joe, the Joe's Own Editor, has the feel of most PC text editors: the key sequences are reminiscent of WordStar and Turbo C editors, but the feature set is much larger than of those. Joe has all of the features a Unix user should expect: full use of termcap/terminfo, complete VI-style Unix integration, a powerful configuration file, and regular expression search system. It also has nine help reference cards which are always available, and an intuitive, simple, and well thought-out user interface. Joe has a great screen update optimisation algorithm, multiple windows (through/between which you can scroll) and lacks the confusing notion of named buffers. It has command history, TAB expansion in file selection menus, undo and redo functions, (un)indenting and paragraph formatting, filtering highlighted blocks through any external Unix command, editing a pipe into or out of a command, block move, copy, delete or filter, a bracketed paste mode automatically enabled on xterm-xfree86 and decimal and hexadecimal gotos for lines, columns, and file offsets. Through simple QEdit-style configuration files, Joe can be set up to emulate editors such as Pico and Emacs, along with a complete imitation of WordStar in non-document mode, and a restricted mode version (lets you edit only the files specified on the command line). Joe also has a deferred screen update to handle typeahead, and it ensures that deferral is not bypassed by tty buffering. It's usable even at 2400 baud, and it will work on any kind of sane terminal. Furthermore, it supports SELinux context copying on Debian systems with the Linux kernel. Juriscraper Juriscraper is a scraper library that gathers judicial opinions and oral arguments in the American court system. It is currently able to scrape: • opinions from all major appellate Federal courts • opinions from all state courts of last resort (typically their "Supreme Court") • oral arguments from all appellate federal courts that offer them KDiff3 KDiff3 compares two or three text input files or directories, shows the differences line by line and character by character, provides an automatic merge facility and an integrated editor for comfortable solving of merge conflicts, and has an intuitive GUI. KVortaro KVortaro is a tool to translate words from one language into another. The word to translate can be selected by clicking on a word anywhere on the desktop; a small window will then pop-up close to the mouse pointer and show the translation. Enclosed are dictionaries for Esperanto-German and English-German. KWrite 'KWrite' is a simple text editor, with syntax highlighting, codefolding, dynamic word wrap and more, it's the lightweight version of Kate, providing more speed for minor tasks. It ships per default with KDEBASE package. Katoob Katoob is a light-weight, multi lingual, BIDI-aware text editor. It supports opening and saving files in multiple encodings. The main support was for the Arabic language but other languages are also supported. Kile Kile is a LaTeX source editor, TeX shell, and gnuplot frontend for KDE 3. It integrates many tools needed to develop documents with LaTeX. The principal LaTex tags can be inserted directly with the "LaTeX", "Math" and "Greek" menus, and LaTeX-related programs can be launched via the "Tools" menu. Kile includes a "structure view" of a document for easier navigation: by clicking on an item in the "Structure" frame, you can jump directly to the corresponding part of a document. The "Messages/Log File" frame lets users see information about processes and the logfile after a LaTeX compilation; The "Next Latex Error" and "Previous Latex Error" commands let you reach the LaTeX errors detected by Kile in the log file. The program also has a gnuplot front end. KnowIt KnowIt is a simple tool for managing notes. It is similar to TuxCards, but KDE-based. Notes are organized in tree-like hierarchy, texts are in RichText format, so bold, italic and lists are supported. Ktexmaker2 * 'Ktexmaker' renamed to 'texmaker' Ktexmaker2 is a LaTeX source editor and TeX shell for KDE2. The principal LaTeX tags can be inserted directly with menus. LaTeX-related programs can be launched launched automatically with menus or manually via the "TeX Terminal" (a special xterm session). Kunjika This is a web-basd Q&A framework similar to StackOverflow. It uses the Python Flask framework, Couchbase for database, and Memcached functionality. Kupu Kupu is a 'document-centric' client-side cross browser editor. Inspired by Maik Jablonski's Epoz editor, it was written by Paul Everitt, Guido Wesdorp and Philipp von Weitershausen (and several other contributors, for a complete list refer to the CREDITS.txt file) to improve the JavaScript code and architecture, pluggability, standards support, support for other webservers than Zope (which was the original target platform for Epoz), configurability and a lot of other issues. Kwaff Kwaff is a pretty tool to convert Kwaff format document into XML document, and also convert XML into Kwaff. Kwaff format is a friendly format for human to read and write than XML. Kwaff format makes XML as easy as YAML to read and write. Kwalify Kwalify is a parser, schema validator, and data binding tool for YAML and JSON. YAML and JSON are simple and nice format for structured data and easier for human to read and write than XML. But there have been no schema for YAML such as RelaxNG or DTD. Kwalify gets over this situation. From version 0.7, Kwalify supports data binding. If you specify class name in schema file, Kwalify YAML parser creates instance objects of that class instead of Hash objects. It means that you don't have to convert Hash into proper object any more. Data binding makes YAML much easier to handle and manipulate. L2P 'L2P' creates PNG images from LaTeX math expressions. It can work with either a fragment of LaTeX code (such as$\frac{x^2+1}{3-x}\$) or with a full LaTeX document. It is designed to be fast, robust, and to offer the user a high degree of flexibility and control. It includes complete documentation.
LTchinese
ltchinese - A library of utilities for the Chinese language (pinyin, zhuyin, encodings, phonetics, etc.) from http://lost-theory.org.
LaTeX
LaTeX is a document preparation system for high-quality typesetting based on TeX. It is most often used for medium-to-large technical or scientific documents, but it can be used for almost any form of publishing. It is not a word processor; instead, it encourages authors not to worry too much about the appearance of their documents, but to concentrate on getting the right content.
LaTeX CD class
This class allows one to print CD covers using LaTeX. Its main features are easy batch printing with crop marks and track number generation.
Lahelper
LaHelper is a GUI that helps in writing documents using LaTeX markup It lets the user navigate a wide selection of LaTeX structure and formatting tags that are used to write a document in LaTeX. It also has a raw text input box with a LaTeX preview for testing out LaTeX markup. Also, each markup has associated help text and is automatically selected to be ready to paste into the user's text editor. Also, this GUI lets the user choose which text editor and supporting programs are used to create their LaTeX document instead of forcing them into a particular interface of a pre-defined IDE.
LanguageTool
It finds many errors that a simple spell checker cannot detect and several grammar problems. There are a few versions available: standalone desktop client, LibreOffice extension and IceCat add-on. This entry is about the desktop client.
Latex4jed
'latex4jed' is an S-Lang file for the Jed editor which provides a greatly enhanced LaTeX mode designed with both the beginner and the advanced LaTeX user in mind. Its features include menus, shortcuts, templates, syntax highlighting, document outlines, integrated debugging, symbol completion, full integration with external programs, and more.
LatexB
LatexB is a very simple LaTeX building script. It lets you properly build a LaTeX file to either a dvi or pdf in one single command. It can also handle BibTeX.
Lazarus
Lazarus is a cross-platform IDE for developers of Free Pascal.
Le editor
LE has many block operations with stream and rectangular blocks, can edit both unix and dos style files (LF/CRLF), is binary clean, has hex mode, can edit files and mmap'pable devices in mmap shared mode (only replace), has tunable syntax highlighting, tunable color scheme (can use default colors), tunable key map. It is slightly similar to Norton Editor, but has more features.
'Leafpad' is a simple GTK+ based text editor. The user interface is similar to "notepad", and it aims to be lighter than GEdit and KWrite and to be as useful as them. It has no toolbar, which maximizes the text viewing area; a single document interface (SDI), to set out windows to view one at a time; and character coding autodetection, to open a file quickly without multi-codeset problems. 'Leafpad' is best used with a lightweight window manager such as xfce, rox, or Icewm.
Less
Less is a paginator file similar to 'more' or 'pg,' but that allows backward as well as forward movement through the file. In addition, it doesn't have to read the entire input file before starting, so it starts large files faster than text editors like vi. Less uses termcap (or terminfo on some terminals) so it can run on a variety of terminals; there is even limited support for hard copy terminals.
Lesspipe.sh
lesspipe.sh is an input filter for the pager 'less' as described in less's man page. It runs under a ksh-compatible shell (ksh, bash, zsh) and lets you use 'less' to view compressed files, archives, and files contained in archives. Viewing files by accessing a device file has been implemented for DOS filesystems and tar files only. The following formats are currently supported (both as plain and compressed files using compress, gzip, bzip2, or zip): tar, nroff, (sh)ar, executables, directories, RPM and Debian (.deb) Archives, Microsoft Word, files and PDF.
Lhendraw
Chemical drawing program for the cdx/cdxml formats. This one tries to be as close and completely as possible to the proprietary reference implementation without forfeiting the KISS principle. It offers a database-less search function and a headless mode for automated editing
Library to create PostScript files
pslib is a C-library for generating PostScript files with little effort. It offers an easy way of generating PostScript text and graphics. Its text function are very sophisticated and support kerning, ligatures and some basic formatting. Hypertext functions are supported through pdfmarks which makes pslib in combination with ghostscript a viable alternative for libraries creating PDF.
LibreOffice
LibreOffice is the power-packed personal productivity suite that gives you six feature-rich applications for all your document production and data processing needs: Writer, Calc, Impress, Draw, Math and Base. There are also a good and growing number of free software extensions and templates available. LibreOffice is a fork of OpenOffice.org, which is now called Apache OpenOffice. Because Apache OpenOffice hosts and recommends using proprietary extensions, we do not recommend using it.
Libtecla
The Tecla library provides programs with interactive command line editing facilities, similar to those of the unix tcsh shell. It supports recall and editing of previously entered command lines, TAB completion of file names and application specific tokens, and in-line wild-card expansion of filenames. The optionally reentrant modules which perform TAB completion and wild-card expansion are also available separately for general use.
Light Table
Light Table is a next generation code editor written in Clojure and using Web technologies.
Lime Text
Lime Text is a powerful and elegant editor, aiming to be successor to Sublime Text. Lime has a few frontends (QML, command-line interface) that can be selectively used with the pluggable back-end.
Linedit
'Linedit' is a readline-style library that provides customizable line editing features. It uses UFFI for foreign bindings, so it is (theoretically) portable. It supersedes Cl-readline. It functions as both a single line text reader and a nulti-line form reader. It has completion on packages and symbols in the current image, as well as on directories and filenames. It has unlimited undo, kill-ring, and history, as well as paren matching.
The Link Grammar Parser is a syntactic parser of English, based on link grammar, an original theory of English syntax. The system assigns to a sentence a syntactic structure, which consists of a set of labeled links connecting pairs of words. The parser also produces a "constituent" representation of a sentence (showing noun phrases, verb phrases, etc.). The parser has a dictionary of about 60000 word forms. It covers a range of syntactic constructions, including many rare and idiomatic ones. The parser skips over the portions of the sentence that it cannot understand, and assigns some structure to the rest of the sentence. It can handle unknown vocabulary, and makes intelligent guesses from context and spelling about the syntactic categories of unknown words. It understands capitalization, numerical expressions, and various punctuation symbols.
Lout
Lout is a document formatting system similar to LaTeX. The system reads a high-level description of a document similar in style to LaTeX and produces a PostScript file which can be printed on most laser printers and graphic display devices. Plain text and PDF (starting from version 3.12) output are also available. Furthermore, Lout is easily extended with definitions which are easier to write than troff or TeX macros because Lout is a high-level language. Lout offers an unprecedented range of advanced features, including:
• optimal paragraph breaking
• automatic hyphenation
• PostScript EPS file inclusion and generation
• equation formatting
• tables
• diagrams
• rotation and scaling
• sorted indexes
• bibliographic databases
• even pages
• automatic cross referencing
• multilingual documents including hyphenation (most European languages are supported, including Russian)
• formatting of C, C++, Java, Eiffel, and other programs
Lpe
Lpe is a small, fast, visual text editor designed to make editing code easier. It provides simultaneously all the features that may be required in a good code editor while preserving a light and intuitive feel that makes it nice to use. It supports seven different languages.
LyX
LyX is an advanced document processor. It encourages an approach to writing based on the structure of your documents, not their appearance, allowing you to concentrate on writing rather than visual layout. It automates formatting according to predefined rule sets, yielding consistency throughout even the most complex documents.
M4
M4 is an implementation of the M4 macro language, which features some extensions over other implementations, some of which are required by GNU Autoconf. It is used as a macro processor, which means it processes text, expanding macros as it encounters them. It also has some built-in functions, for example to run shell commands or to do arithmetic.
MaarchCourrier
Maarch Courrier is an Electronic Correspondence Manager which allows you to easily manage your correspondences trough a work-flow.
MaarchRM
This application allows to store, find and display digital resources in compliance with international regulation ISO 14641-1.
Mad Builder PDF Assembler is a tool for assembling/merging pdf files, extracting information from PDF files, and updating PDF files metadata. In assembling mode (the default mode), it concatenates only pages, other than the outlines. Users can also add outlines via a definition file of outline. By default, file are sorted in alphabetic order before assembling.
MagicPO
MagicPO is a utility to automatically translate a gettext po-file from one language to another. It is useful for languages that are close to each other such as Norwegian Nynorsk and Norwegian BokmÃÂ¥l, and Norwegian BokmÃÂ¥l and Danish. It is also useful for automatically fixing common mistakes in files.
Majix
'MajiX' transforms RTF files such as Microsoft Word documents into XML. It can convert headings, lists (numbered or not), simple tables, bold, italics, and underline.
Man
The man pager suite (man, apropos, and whatis) contains programs used to read most of the documentation on a GNU/ Linux system. The whatis and apropos programs are used to find documentation related to a particular subject.
Man-db
This package provides the man command. This utility is the primary way of examining the on-line help files (manual pages). Other utilities provided include the whatis and apropos commands for searching the manual page database, the manpath utility for determining the manual page search path, and the maintenance utilities mandb, catman, and zsoelim. This package uses the groff suite of programs to format and display the manual pages.
Man2web
'man2web' converts man pages to HTML via a CGI program or the command line. It also handles keyword (apropos) searches and generates section indexes.
Mandoc
Mandoc is a suite of tools compiling mdoc, the roff macro language of choice for BSD manual pages, and man, the predominant historical language for UNIX manuals. It is small, ISO C, ISC-licensed, and quite fast. The main component of the toolset is the mandoc utility program, based on the libmandoc validating compiler, to format output for UTF-8 and ASCII UNIX terminals, HTML 5, PostScript, and PDF.
Manuskript
Manuscript is an organiser for writers. Split your work in smaller units, reorganise them on the go, keep tracks of characters, places, objects, etc.
A small, simple text editor. Features include the full range of standard editing features, as well as popup Menus for faster access to common commands, direct execution of various programs, and built-in compiling commands for C, C++ and Java Files.
Markdown-mode
Markdown Mode is a major mode for GNU Emacs for editing Markdown-formatted text files. It provides syntax highlighting and editing commands.
Markdown2
Markdown is a text-to-HTML filter; it translates an easy-to-read / easy-to-write structured text format into HTML. Markdown's text format is most similar to that of plain text email, and supports features such as headers, emphasis, code blocks, blockquotes, and links. This is a fast and complete Python implementation of the Markdown spec.
MathEOS
This is a text editor for writing math lessons and providing tools for doing all the exercises from elementary school to junior high. The software is especially designed to fulfil the needs of disabled pupils, and pupils suffering from dyspraxia in particular. The program manages the child's documents like a notebook, organized with chapters, and separating lessons, exercises and evaluations, making it very easy to navigate through the documents.
Mc
Midnight Commander is a command-line file manager laid out in a common two-pane format. In addition to standard file management tasks such as copying and moving, Midnight Commander also supports viewing the contents of RPM package files and other archives and managing files on other computers via FTP or FISH. It also includes a powerful text editor for opening text files. Emacs-like key bindings are used in all widgets.
Md-toc
The table of contents (a.k.a: TOC) generated by this program is designed to work with several markdown parsers such as the ones used by GitHub and GitLab. When used with the in-place option this script will write the TOC at the first occurrency of a marker. The default marker is , which, being an HTML comment, will result invisible after the markdown file has been translated. By default titles up to three indentation levels (in HTML: h1, h2, h3) will be included in the TOC but the user can decide to keep all possible levels. md_toc makes it is possible to generate ordered and unordered TOCs. In both cases each element of the TOC is by default a link to a paragraph in the web page. It is also possible to generate a non-linked version of the TOC. If the user wants it, there is the possibility to ignore space indentations within the TOC and to skip an initial number of lines from the markdown file. Rules for generating the TOC are determined by the selected markdown parser. md-toc aimes infact to be as conformant as possible in respect to each one of them. This was possible by studying the available documentations and by reverse engineering the source codes.
Medit
It features:
• Configurable syntax highlighting.
• Configurable keyboard accelerators.
• Multiplatform - works both on unix and windows.
• Plugins: can be written in C or Python.
• Configurable tools available from the main and context menus. They can be written in Python, or it can be a shell script, or in MooScript - simple builtin scripting lanugage.
• Incremental search, regular expression search/replace.
• grep and find frontends, builtin file selector and whatnot.
Metasite extractor
Metasite extractor locates, downloads and packages as much GPL software as possible.
MindForger
Are you drowning in information, but starving for knowledge? Where do you keep your private remarks like ideas, personal plans, gift tips, how-tos, dreams, business vision, finance strategy, auto coaching notes? Loads of documents, sketches and remarks spread around the file system, cloud, web and Post-it notes? Are you affraid of your knowledge privacy? Are you able to find then once you create them? Do you know how are they mutually related when you read or write them? No? MindForger is open, free, well performing Markdown IDE which respects your privacy and enables security. MindForger is actually more than an editor or IDE - it's human mind inspired personal knowledge management tool.
Minimum Profit
Minimum Profit (mp) is a programmer's text editor. It features small memory and disk requirements, syntax highlighting, context-sensitive help for the source code being edited, multiple simultaneous file editing, ctags support, word wrapping, and more. It can be compiled for Linux / Unix (console), GTK, and MS Windows.
Minimum Profit 2
Minimum Profit (mp) is a programmer's text editor. It features small memory and disk requirements, syntax highlighting, context-sensitive help for the source code being edited, multiple simultaneous file editing, ctags support, word wrapping, and more.
Minised
'minised' is the fast, small sed originally distributed in the GNU toolkit and still distributed with Minix. The GNU Project removed it in favor of a sed built around an enhanced regexp package, but it's better for some uses (in particular, it's faster and less memory-intensive).
Miscfiles
Miscfiles is a collection of data files for airport codes, zip codes, a dictionary, and more. Files include:
• abbrevs.talk, abbrevs.gen — Some common abbreviations used in electronic communication
• airport — List of three letter codes for some major airports
• ascii — A map of the ascii character set
• bcp-index.txt — Best Current Practice indexes. Internet standardization documents
• birthtoken — Traditional stone and flower for each month
• cities.dat — geographic coordinates of many major cities
• connectives — English connectives'; prepositions, pronouns, and the like
• countries — country abbreviations and names and capital cities
• currency — currency abbreviations and names
• fyi-index.txt — For Your Information indexes. Internet standardization documents
• GNU-manifesto — The GNU Manifesto
• inter.phone — International country telephone codes
• languages — two-letter codes for languages, from ISO 639-1
• latin1 — like `ascii'; describing the ISO Latin-1 character set
• mailinglists — Description of all the public Project GNU related mailing lists
• na.phone — North American (+1) telephone area codes
• na.postalcodes — postal codes for US states and Canadian provinces
• operator — Precedence table for operators in the C language
• propernames — Some common proper names
• rfc-index.txt — Request for comments indexes. Internet standardization documents
• std-index.txt — Standard indexes of internet standardization documents
• std-index.txt — Indexes of internet standardization documents
• top-level.domains — Top-level domains, based on IANA
• unicode — The official Unicode character set table
• web2 — Webster's Second International English wordlist
• web2a — Webster's Second Internations appendix english wordlist
MkDoxy
mkDoxy is to makefiles what Doxygen is to source files: it parses a makefile and produces HTML documentation of available targets and macros. It considers only comments starting with ##, so it's easy to control the documentation that's generated.
Mod xslt
mod-xslt is an Apache module that converts XML files into HTML files on the fly using XSLT stylesheets. It was written to overcome most of the limits of similar modules and uses a standard API, which can be used for other applications or to support more servers. It can dynamically parse generated documents, both in POST and GET requests, includes a fully featured language to choose the stylesheet to load from both configuration files and from .xml files, and allows stylesheets to access server variables. It supports redirects, dynamically generated stylesheets, and Apache versions 1 and 2.
Moe
Moe is a powerful-but-simple-to-use text editor. It works in a modeless manner, and features an intuitive set of key-bindings that assign a degree of severity to each key; for example, key combinations with the Alt key are for harmless commands like cursor movements while combinations with the Control key are for commands that will modify the text. Moe features multiple windows, unlimited undo/redo, unlimited line length, global search and replace, and more.
Moleskine
Moleskine is a source code editor for the GNOME desktop. It features include syntax highlighting, GUI configuration, easy to navigate bookmarks, word autocompletion, indentation guides, and matching braces. The program can be configured to support any programming language that Scintilla supports. Users must download and install all the following three modules: Moleskine, PyGtkScintilla and GtkScintilla. As of March 3, 2005, this package has no maintainer.
Monica Personal CRM
Monica is a free software web application to organize the interactions with your loved ones. We call it a PRM, or Personal Relationship Management. Think of it as a CRM (a popular tool used by sales teams in the corporate world) for your friends or family. Monica allows people to keep track of everything that's important about their friends and family. Like the activities done with them. When you last called someone. What you talked about. It will help you remember the name and the age of the kids. It can also remind you to call someone you haven't talked to in a while.
Mopowg
mopowg is an easy to install, cross-platform doc generator which is based on docutils. mopowg could generate full documents with figures, styles, and syntax highlighting blocks. It includes a command line tool and will provide the web front-end.
Msort
Msort sorts files in sophisticated ways. Records may be fixed size, newline-separated blocks, or terminated by any specified character. Key fields may be selected by position, tag, or character range. For each key, distinct exclusions, multigraphs, substitutions, and a sort order may be defined or locale collation rules used. Comparisons may be lexicographic, numeric, numeric string, hybrid, random, by string length, angle, date, time, month name, or ISO8601 timestamp. Keys may be reversed so as to generate reverse dictionaries. Optional keys are supported. Unicode is supported, including full case-folding. Msort itself has a somewhat complex command line interface, but may be driven by an optional GUI.
Mule
Mule stands both for MUlti-Language Extensions, MULtilingual Environment and MULtilingual Enhancement to GNU Emacs. The code was formerly part of NEmacs, a Japanese-only version of Emacs. It was written by a core team of developers of the National Institute of Advanced Industrial Science and Technology (AIST), which is a part of Ministry of Economy, Trade and Industry (METI), of the government of Japan. Mule provided support for a large number of languages, including Chinese, Japanese and Korean, and was integrated into Emacs version 20. Current code includes:
Also included is an utility to convert multilingual text into standalone PS. MULE is maintained as a part of GNU Emacs.
Multi Stream Editor
The multi stream editor (mse) can perform basic text transformations on an input stream. It in some ways is similar to another stream editors (sed, awk) but it can process binary data as well as text. Its creation was inspired by SIL (Summer Institute of Linguistics) CC (Consistent Changes) program. The complete texi-manual is included.
Multitail
'MultiTail' lets you view one or multiple files like the original tail program. The difference is that it creates multiple windows on your console (with ncurses). You can also merge logfiles and use colors while displaying the logfiles (through regular expressions), for faster recognition of what is important and what not. 'MultiTail' can also filter lines (again with regular expressions). It has interactive menus for editing given regular expressions and deleting and adding windows. One can also have windows with the output of shell scripts and other software. When viewing the output of external software, the program mimics the functionality of tools like 'watch'.
MuseScore
Full-featured WYSIWYG editor for sheet music. Large vocabulary of notations (jazz notation, percussion, early music, etc.). It will play your scores and can also import and export many formats, including e.g. import and export of MIDI and export to PDF, WAV, and LilyPond.
MyNotex
Notes are gathered under different subjects and are made by a title, a date, a tags (keywords) list and a free-length text. This may be formatted: it is possible to change the font name, size and color of a selected text and of its background, and also to set bold, italic, underline and strike-through; the text may have pictures within it and hashtags. The software can manage paragraph alignment, bullets, numbered and alphabetic lists with automatic indentation. Each note may have any number of attachments (files of every kind), and has also a spreadsheet-like grid to manage a list of activities which is quite similar to the one used in many software of project management. A single file of MyNotex contains various notes filed in different subjects. Some features of the software:
• a spreadsheet-like grid available for each note, in which it is possible to create and manage list of activities and sub-activities with state, dates, resources and cost specifications;
• possibility to encrypt and decrypt a file of MyNotex, or any other file, with GNU Privacy Guard (GPG), if available in the system in use;
• various attachments (files of every kind) for each note, zipped and stored in a directory with the same name and path of the MyNotex file in use and automatically managed by the software; the number of attachments is limited only by the available disk space;
• encryption of the text of the selected notes with AES algorithm;
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NEdit
NEdit is a Unix text editor for programmers and general users. It has a graphical user interface and a macro language with a complete library of editing functions, syntax highlighting for 30 common languages and text processors, and the best mouse-interactivity available in a Unix text editor. It has built-in syntax patterns for CSS, Regex, and XML, and supports wheel mouse scrolling and high/true-color systems.
Nano
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Natural Docs
Natural Docs is an extensible, multi-language, source code documentation generator written in Perl. Its syntax is transparent so the source comments read just as easily as the generated documentation. It also focuses on automation and high-quality HTML output.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the page “GNU Free Documentation License”. | 2019-09-17 00:49:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31177160143852234, "perplexity": 5464.7232175707695}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572980.56/warc/CC-MAIN-20190917000820-20190917022820-00113.warc.gz"} |
http://vealcine.com/quantization-error/quantisation-error-10-bit-adc.php | Home > Quantization Error > Quantisation Error 10 Bit Adc
# Quantisation Error 10 Bit Adc
## Contents
Generally, a smaller number of bits than required are converted using a Flash ADC after the filter. Last edited by BlackMamba; 27th August 2010 at 12:44. 22nd June 2005,17:22 22nd June 2005,18:42 #4 KrisUK Newbie level 4 Join Date May 2005 Posts 7 Helped 0 / The difference between the original signal and the reconstructed signal is the quantization error and, in this simple quantization scheme, is a deterministic function of the input signal. Nicholson, P. http://vealcine.com/quantization-error/quantisation-error-in-10-bit-adc.php
Chou, Tom Lookabaugh, and Robert M. or The RMS signal voltage is then The error, or quantization noise signal is Thus the signal - to - noise ratio in dB. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. If the MSB corresponds to a standard 2 V of output signal, this translates to a noise-limited performance that is less than 20~21 bits, and obviates the need for any dithering.
## Quantization Error Example
The indices produced by an M {\displaystyle M} -level quantizer can be coded using a fixed-length code using R = ⌈ log 2 M ⌉ {\displaystyle R=\lceil \log _{2}M\rceil } John Wiley & Sons. It is a rounding error between the analog input voltage to the ADC and the output digitized value. In the truncation case the error has a non-zero mean of 1 2 L S B {\displaystyle \scriptstyle {\frac {1}{2}}\mathrm {LSB} } and the RMS value is 1 3 L S
• With noise shaping, the improvement is 6L+3dB per octave where L is the order of loop filter used for noise shaping.
• This results in poor linearity.
• At asymptotically high bit rates, cutting the step size in half increases the bit rate by approximately 1 bit per sample (because 1 bit is needed to indicate whether the value
• Many ADC integrated circuits include the sample and hold subsystem internally.
• When the ramp starts, a timer starts counting.
• Mid-riser and mid-tread uniform quantizers Most uniform quantizers for signed input data can be classified as being of one of two types: mid-riser and mid-tread.
For example, an ADC with a resolution of 8 bits can encode an analog input to one in 256 different levels, since 28=256. You have a total 8 of quantizaton steps which would map to [-1 -.75 -.5 -25 0 .25 .5 .75]. Register Remember Me? Quantization Noise Formula For simple rounding to the nearest integer, the step size Δ {\displaystyle \Delta } is equal to 1.
When the spectral distribution is flat, as in this example, the 12 dB difference manifests as a measurable difference in the noise floors. Quantization Error In A/d Converter Granular distortion and overload distortion Often the design of a quantizer involves supporting only a limited range of possible output values and performing clipping to limit the output to this range Examples of fields where this limitation applies include electronics (due to electrons), optics (due to photons), biology (due to DNA), physics (due to Planck limits) and chemistry (due to molecules). This noise floor is depicted in the FFT plot in Figure 9.
Mega-sample converters are required in digital video cameras, video capture cards, and TV tuner cards to convert full-speed analog video to digital video files. Quantization Error In Pcm Figure 10: FFT showing harmonic distortion (Equation 5) The magnitude of harmonic distortion diminishes at high frequencies to the point that its magnitude is less than the noise floor or is Your cache administrator is webmaster. This is done to better illustrate the meaning of the performance specifications.
## Quantization Error In A/d Converter
Lloyd's Method I algorithm, originally described in 1957, can be generalized in a straightforward way for application to vector data. click Figure 8: An FFT of ADC output codes Signal-to-noise ratio The signal-to-noise ratio (SNR) is the ratio of the root mean square (RMS) power of the input signal to the RMS Quantization Error Example A very simple (non-linear) ramp-converter can be implemented with a microcontroller and one resistor and capacitor.[13] Vice versa, a filled capacitor can be taken from an integrator, time-to-amplitude converter, phase detector, Quantization Error Definition Flash ADCs are certainly the fastest type of the three.
doi:10.1109/TIT.2005.846397 ^ Pohlman, Ken C. (1989). http://vealcine.com/quantization-error/quantisation-error-in-adc.php Normally, the number of voltage intervals is given by N = 2 M − 1 , {\displaystyle N=2^{M}-1,\,} where M is the ADC's resolution in bits.[1] That is, one voltage interval The difference between steps is 0.25. Flash ADCs have drifts and uncertainties associated with the comparator levels. Quantization Error Percentage
An important consideration is the number of bits used for each codeword, denoted here by l e n g t h ( c k ) {\displaystyle \mathrm {length} (c_{k})} . Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities. M. http://vealcine.com/quantization-error/quantisation-error.php Dx in this definition seems to be the range of the input signal so we could rewrite this as $$Q = \frac{max(x)-min(x)}{2^{N+1}}$$ Let's look at a quick example.
Quantization error also affects accuracy, but it's inherent in the analog-to-digital conversion process (and so does not vary from one ADC to another of equal resolution). Quantization Error Ppt Therefore, oversampling is usually coupled with noise shaping (see sigma-delta modulators). Its just thrown in my study material without further explanation.
## IT-51, No. 5, pp. 1739–1755, May 2005.
Provided that the input is sampled above the Nyquist rate, defined as twice the highest frequency of interest, then all frequencies in the signal can be reconstructed. In a second step, the difference to the input signal is determined with a digital to analog converter (DAC). Limitations in the materials used in fabrication mean that real-world ADCs won't have this perfect transfer function. Quantization Error In Dsp The result is a sequence of digital values that have been converted from a continuous-time and continuous-amplitude analog signal to a discrete-time and discrete-amplitude digital signal.
Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement Mobile view Introduction Data domains and data conversion Choosing ADC's and DAC's Sampling rate Quantization Error Signal to Noise ratio (SNR) The use of this approximation can allow the entropy coding design problem to be separated from the design of the quantizer itself. Important parameters for linearity are integral non-linearity (INL) and differential non-linearity (DNL). this content However, if the dynamic range of the ADC exceeds that of the input signal, its effects may be neglected resulting in an essentially perfect digital representation of the input signal.
ISBN0-7923-7519-X. ^ a b c Gary J. The presence of quantization error limits the dynamic range of even an ideal ADC. The additive noise model for quantization error A common assumption for the analysis of quantization error is that it affects a signal processing system in a similar manner to that of However, the same concepts actually apply in both use cases.
Quantization error Main article: Quantization error Quantization error is the noise introduced by quantization in an ideal ADC. This includes harmonic distortion, thermal noise, 1/ƒ noise, and quantization noise. (The figure is exaggerated for ease of observation.) Some sources of noise may not derive from the ADC itself. The analysis of quantization involves studying the amount of data (typically measured in digits or bits or bit rate) that is used to represent the output of the quantizer, and studying ISBN0-471-14448-7.
The step size Δ = 2 X m a x M {\displaystyle \Delta ={\frac {2X_{max}}{M}}} and the signal to quantization noise ratio (SQNR) of the quantizer is S Q N R The input frequency (in this case, < 22kHz), not the ADC clock frequency, is the determining factor with respect to jitter performance.[6] Sampling rate Main article: Sampling rate See also: Sampling Comparison of quantizing a sinusoid to 64 levels (6 bits) and 256 levels (8 bits). Most applications use ADCs to measure a relatively static, DC-like signal (for example, a temperature sensor or strain-gauge voltage) or a dynamic signal (such as processing of a voice signal or
How to flood the entire lunar surfaces? For example, quantization error will appear as the noise floor in an FFT plot of a measured signal input to an ADC, which I'll discuss later in the dynamic performance section). In this case, the DC accuracy of a measurement is prevalent so the offset, gain, and nonlinearities will be most important. | 2018-03-23 05:24:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.75824373960495, "perplexity": 1543.0373178560171}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257648178.42/warc/CC-MAIN-20180323044127-20180323064127-00743.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/suppose-a-heat-engine-pulls-389104-j-of-work-from-the-hot-reservoir-and-669103-j-of-that-e-q3382164 | ## Heat Engine 01
Suppose a heat engine pulls 3.89×104 J of work from the hot reservoir and 6.69×103 J of that energy is used to perform work. 1.) How much energy is rejected by the engine? (This energy is "exhausted" to the cold reservoir.) 2.) What is the efficiency of the engine? (enter this as a unitless number between 0 and 1) | 2013-05-23 21:11:58 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8081028461456299, "perplexity": 1180.2853838628419}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703788336/warc/CC-MAIN-20130516112948-00055-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://juliadocs.github.io/Documenter.jl/stable/lib/internals/cross-references/ | # CrossReferences
Documenter.CrossReferences.find_objectMethod
find_object(doc, binding, typesig)
Find the included Object in the doc matching binding and typesig. The matching heuristic isn't too picky about what matches and will only fail when no Bindings matching binding have been included.
source | 2021-09-28 13:37:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41294562816619873, "perplexity": 10241.206578978312}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780060803.2/warc/CC-MAIN-20210928122846-20210928152846-00338.warc.gz"} |
https://math.stackexchange.com/questions/3656169/compute-homology-groups | # Compute homology groups
I'm not confident with this kind of problem, so I post my solution here to ask for checking it. I want to compute the homology groups of the space obtained from two copies of $$\mathbb{R} P^2$$ by gluing them along standard copies of $$\mathbb{R} P^1$$.
First I give it a cell structure: we know that $$\mathbb{R}P^2$$ has the cell structure of one $$0$$-cell $$x$$, one $$1$$-cell $$a$$ and one $$2$$-cell $$A$$ that glues to $$2a$$ (i.e. go around $$a$$ 2 times). So I believe the cell struture of our space is one $$0$$-cell $$x$$, one $$1$$-cell $$a$$ and two $$2$$-cells $$A,B$$ that both glue to $$2a$$. Hence we have the chain complex $$0\to \mathbb{Z}^2 \xrightarrow{d_2} \mathbb{Z} \xrightarrow{d_1}\mathbb{Z} \to 0$$ where $$d_1=0$$ and $$d_2(A)=d_2(B)=2a$$. Hence $$H_0=\mathbb{Z}/0=\mathbb{Z}$$ $$H_1=\langle a\rangle /2\langle a \rangle = \mathbb{Z}_2$$ $$H_2=\langle A-B\rangle / 0 = \mathbb{Z}$$
Is this correct?
• Seems fine. Just be careful with your terminology: you wrote down the chain complex, not an exact sequence. The homology groups of an exact sequence are all zero! – Ethan Dlugie May 3 at 6:08
• edited. Thank you. I am really worried about the cell structure. One move wrong and everything goes wrong. – Marcos G Neil May 3 at 6:13
Let $$A, B, C$$ be CW complexes, and let $$f\colon A \to B$$ and $$g\colon A \to C$$ be cellular maps. Then if $$f'$$ is homotopic to $$f$$ there is a homotopy equivalence $$B\cup_{f, g} C\simeq B\cup_{f',g}C$$.
Now define $$D$$ as the quotient $$\mathbb{RP}^2 \cup_{\iota, \iota} \mathbb{RP}^2$$ where $$\iota\colon \mathbb{RP}^1\to \mathbb{RP}^2$$ is the standard inclusion. This has a cell structure as you've described. We can think about it as starting with a copy of $$\mathbb{RP}^2$$ and attaching a $$2$$-cell via a map $$\varphi\colon\partial D^2 \cong S^1\to \mathbb{RP}^1\cong S^1$$ of degree $$2$$, i.e. $$D$$ is homeomorphic to $$\mathbb{RP}^2\cup_{\varphi} D^2$$.
However, since $$\pi_1(\mathbb{RP}^2)\cong \mathbb{Z}/2$$ this attaching map is null-homotopic so in fact $$D$$ is homotopy-equivalent to $$\mathbb{RP^2}\vee S^2$$ by the above lemma (cf this related question), whose homology groups are easily computable via $$\tilde{H}_k(A\vee B)\cong \tilde{H}_k(A) \oplus \tilde{H}_k(B)$$.
• Yes, I'm writing reduced homology at the end because the additivity statement isn't true in degree $0$. If $r_1=rank (H_0(A))$ and $r_2=rank (H_0(B))$ then $rank (H_0(A\vee B) )= r_1 + r_2 -1$ (since you're wedging together the two components containing the base points). – William May 3 at 16:35 | 2020-08-15 11:04:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 43, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9439008235931396, "perplexity": 126.44904078141411}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439740838.3/warc/CC-MAIN-20200815094903-20200815124903-00061.warc.gz"} |
https://www.physicsforums.com/threads/linear-vector-algebra-kronecker-delta-levi-civita-symbol.116101/ | # Homework Help: Linear & Vector Algebra: Kronecker delta & Levi-Civita symbol
1. Mar 31, 2006
### Dr. Gonzo
Hello all. Happy to have finally found this forum, sorry that it took so long!
I'm working through a Vector Algebra tutorial and I am having much difficulty with the concepts of Kronecker deltas and the Levi-Civita symbol. I can't fully grasp either of them intiutively.
From what I've been able to gather, $$\delta_{ij}= \left\{\begin{array}{cc}1,&\mbox{ if }i=j,\\0, & \mbox{ if } i\neq k\end{array}\right.$$
I'm pretty sure this means that, in the case of two vectors I and J with components $$i_{1},i_{2},i_{3}$$ and $$j_{1},j_{2},j_{3}$$ that $$i_{1}= j_{1},i_{2}= j_{2}, i_{3}= j_{3}$$. In other words, vectors I and J are parallel and equal. Is this correct? Or am I missing something here?
And regarding the Levi-Civita symbol, it's been pointed out to me that another name for this is the anti-symmetric tensor. Unfortunately, this hint has not helped my understanding one iota. So far, my understanding of this symbol states that it takes Kronecker's delta one step further into a third dimension or plane.
I understand that $$\epsilon_{ijk}=\left\{\begin{array}{cc}1,&\mbox{ if }ijk=123, 231, or 312\\-1, & \mbox{ if } ijk= 321, 213, or 132\\0, & \mbox{ if } ijk=anything else\end{array}\right.$$
I am completely confused by these 123 values. What do they represent? Perhaps understanding that will help me complete this puzzle.
I appreciate all and any help on this!
Last edited: Mar 31, 2006
2. Mar 31, 2006
### JasonRox
The best way to see what the Kronecker Delta does is to create a 3x3 matrix where the Kronecker Delta determines each number.
So, for the first slot being 11, you put the number 1 (because 1=1). The slot is 12 (row 1 column 2) and you put the number 0 (because 1=/=2). The slot 13 (row 1 column 3) and you put the number 0.
Keep working that out and see what you find.
Last edited: Mar 31, 2006
3. Mar 31, 2006
### JasonRox
Also, the Kronecker Delta has many more uses. The whole point is just to see how the function works.
The Levi-Cevita symbol is almost the same, but using three variables.
http://mathworld.wolfram.com/PermutationSymbol.html
The site also has some relations with the Kronecker Delta. Maybe proving these statements will lead to a better understanding or simply just play around with them.
4. Mar 31, 2006
### Dr. Gonzo
Thanks for the post. I kind of figured that this delta went something like this, but what confused me is when to use 1 and when to use 0. Let me explain:
Am I to understand that for every matrix of this delta, the outcome will always be the same? If I simply put in a 1 for 1=1, 2=2 and 3=3 (a diagonal from top left to bottom right) and zeros in all other places, I don't see how this has any significance. If vector I = vector I, then there should & would be 1's in all places in the matrix. If vector I does not = vector J, then there would only be one's in some spots in the matrix. But when to use which? That's my dilemma. I don't understand where the values in the matrix come from, and then what to do with them.
5. Apr 1, 2006
### JasonRox
I'm not sure exactly what you are speaking of, but I'll give you another example using vectors.
Let $B=\{v_1, v_2, ...\}$ be an orthonormal set.
So, we have...
$$v_i * v_j = \delta_{ij}$$
* is the dot product or inner product.
Ok, I reread your post. Can you tell what section you are working on that requires these functions? Maybe I can help you much more on where the values come from.
6. Apr 1, 2006
### JasonRox
http://planetmath.org/encyclopedia/LeviCivitaPermutationSymbol3.html [Broken]
There's another website you can look at.
Do you happen to know what an even/odd permutation is?
Last edited by a moderator: May 2, 2017
7. Apr 1, 2006
### Hurkyl
Staff Emeritus
The letters i and j in $\delta_{ij}$ denote indices, not vectors. They are numbers ranging from 1 through the dimension of your vector space. $\delta_{ij}$ is the (i, j)-th component in the matrix representation of the kroneker delta1, according to whatever basis you've chosen.
1: if you're actually using tensor notation, then since they're both subscripts, both indices are selecting columns -- this would actually a 1xn² matrix that's partitioned into n rows of length n. But if you make the appropriate transpositions, you can treat it as an nxn matrix. A notation for the nxn identity matrix would be $\delta_i^j$.
Last edited: Apr 1, 2006
8. Apr 1, 2006
### Dr. Gonzo
OK...things are slowly getting a little bit clearer. I understand that $$v_i\bullet v_j=\delta_{ij}=(v_{ix}*v_{jx})+(v_{iy}*v_{jy})+(v_{ik}*v_{jk})=(1*0)+(0*1)+(0*0)=0$$
I also read planetmath's description of permutations (something I am/was totally unfamiliar with): http://planetmath.org/encyclopedia/Permutation.html [Broken] I'm not entirely sure, but my initial take on even/odd permutations has to do with the number of transpositions...which I do not understand. Is it as simple as seeing a vector with three elements will have 3! permutations?
As for the section I'm working on, it's a tutorial titled Vector Algebra and an Introduction to Matrices. Topics in this tutorial covered prior to this problem include:
1. Euclidean Vectors
1.1 Basic Features and Conventions
2. Vector Manipulations
2.1 Scalar Multiplication
2.3 Scalar Product
2.4 The Vector Product
2.5 Vector Components
3. Subscript Algebra
3.1 Summation Convention
3.2 The Kronecker Delta
3.3 The Levi-Civita Symbol
I am a third-semester physics undergrad with previous math that covers through Calculus III. This is my only experience with Linear Algebra, and my tutorial book is very flimsy in the way of instruction. I've gathered most of my understanding by doing my own research. Unfortunately, I just can't seem to get a handle on this one by myself.
Last edited by a moderator: May 2, 2017
9. Apr 1, 2006
### nrqed
As someone already mentioned, the indices i,j,k usually label the *components* of some vector, with the definition $v_1 = v_x, v_2= v_y, v_3 =v_z$.
You cannot know what value of i,j,k to use unless you have some context in which to use those quantities! The *context* will tell you what value to use. What I am saying is that what you have are the *definitions* of these symbols, but its only when you will use them in some specific problem that you will know what value to use for the indices.
The most famous example of using the Levi-Civita symbol is through the definition of the cross product. One way to write $\vec A \times \vec B = \vec C$ is to give a rule to calculate each component of the vector C by saying
$C_i = \sum_{j,k=1}^3 \epsilon_{ijk} A_j B_k$
(often people do not write the summation explicitly. Not writing explicitly the sums is called ''using Einstein's convention'').
Lets say you want the x component of C using the above formula. That fixes i to be 1. Then you get
$C_1 = \epsilon_{123} A_2 B_3 + \epsilon_{132} A_3 B_2$
(there are many more terms, for example $\epsilon_{112} A_1 B_2$ and so on but they are all zero because the levi civita symbol is zero whenever two indices are equal. So there are really 9 terms corresponding to the 9 values that j and k may take, but of those nine terms, only two are non zero and these are the two given above).
Now plug in the values for the levi-civita symbol for those indices and you get
$C_1 = A_2 B_3 - A_3 B_2$ which translates to $C_x = A_y B_z - A_z B_y$ as expected.
As an exercise, check that you get the correct results for C_y and C_z!!
So you see, when you use the symbols in specific problems you will know what values to take for the indices...
Hope this clarifies things
Patrick
10. Apr 1, 2006
### nrqed
I gave the most famous example of the use of the Levi-Civita symbol. The most famous use of the Kronecker delta is to define the scalar product.
One can write $\vec A \cdot \vec B = \sum_{i,j=1}^3 A_i B_j \delta_{i,j}$. You should verify that this leads to the usual result $A_x B_x + A_y B_y + A_z B_z$.
Patrick
11. Apr 1, 2006
### Hurkyl
Staff Emeritus
I'm going to use superscripts and subscripts... but I suppose you don't need to distingush the two, and can just write everything as a subscript.
Again, to restate what's being said so far, if we're working in 3-space, and we've chosen a basis on our vector space...
When we have a vector, we can write down its coordinates. I'm going to write coordinates as superscripts (in particular, the following are not exponents):
$$\vec{v} = \left[ \begin{array}{c} v^1 \\ v^2 \\ v^3 \end{array} \right]$$
So what is the i-th component of our vector $\vec{v}$? It's $v^i$.
When we have a covector, we do the same, but we use subscripts.
$$\hat{\omega} = [ \omega_1 \, \omega_2 \, \omega_3 ]$$
The i-th component of the covector $\hat{\omega}$ is then $\omega_i$.
When we have a matrix, we do the same:
$$\mathbf{A} = \left[ \begin{array}{ccc} A_1^1 & A_2^1 &A_3^1 \\ A_1^2 & A_2^2 &A_3^2 \\ A_1^3 & A_2^3 &A_3^3 \end{array} \right]$$
What is the (i, j)-th component of our matrix $\mathbf{A}$? It's $A^i_j$.
But the point is that we treat $\vec{v}$, $\hat{\omega}$, and $\mathbf{A}$ as simply being arrays of numbers. The first two were one-dimensional arrays, and the latter was a two-dimensional array. Subscripts and superscripts are how we indicate the actual elements of those arrays.
12. Apr 2, 2006
### Oxymoron
Levi-Civita symbols make long equations of tensors (or vectors if you prefer) short. For example, I assume that you have come across antisymmetric tensors? Well, if you haven't, they are tensors which change sign whenever you interchange any pair of its indices.
$$V(x^1,\dots,x^i,\dots,x^j,\dots,x^n) = -V(x^1,\dots,x^j,\dots,x^i,\dots,x^n)$$
Notice that V is an antisymmetric tensor with n components (or a vector in n dimensions, where each $x^k$ denotes one of its components). Notice that if we then interchange another pair of components (that is, doing it twice) the sign changes again! So we actually have
$$V(x^{\pi(1)},x^{\pi(2)},\dots,x^{\pi(n)}) = (-1)^{\pi}V(x^1,x^2,\dots,x^n)$$
where $\pi[/tex] is some permutation of n indices. Now, youve read mathworld's section on permutations, so you know what an even permutation is, and an odd permutation is? If you have (instead of n indices) say 3 indices, 1,2,3. Then 2,1,3 is an odd permutation because I have swapped a pair of indices 1 times (which is an odd number). What about 2,3,1? Well, I swapped 1,2 and then 1,3 which is two. So this is an even permutation. When it comes to generalizing this for n indices instead of just three, it is important to keep track of your signs. Because we know for an antisymmetric vector we get a negative sign every time we swap the indices an odd number of times! And the negative sign disappears when we do it an even number of times (thus the (-1)^m bit out the front). It gets a little more complicated, but the Levi-Civita symbols make this kind of index swapping very concise. 13. Mar 31, 2010 ### lotm You said what you were looking for was an intuitive picture of the Kroenecker delta and Levi-Civita symbol? Well, sounds like you're pretty damn close with the delta: I don't quite get why you start talking about vectors - you're on the right track when you say you have a matrix which is zero everywhere, except for a diagonal string of 1's from top left to bottom right. This matrix is of pretty massive significance: it's the identity matrix! So, that's one way of understanding the delta (as giving the components of the identity matrix). In linear algebra, doing calculations by writing out full matrices can take ages - by talking about indices instead, things can be done much quicker. Having the Kroenecker delta allows us to talk about the identity matrix in terms of indices, which is good news given the identity matrix's ubiquity. Having a delta pitch up in your calculations is usually good news, since it often allows you to cull some of your summations. A sum over one index (let's say j) of $$\delta_{ij}$$ is basically an assertion that we can scrap the sum over j, get rid of the delta symbol and replace all incidences of j by i. For example: [itex]\sum_{j=1}^3 \sum_{k=1}^3 A_{ij} \delta_{ij} B_{jk} = \sum_{k=1}^3 A_{ii} B_{ik}$
(It's worth checking this out, either by writing out the summation explicitly or rewriting it in matrix notation.)
PS as is probably clear, I'm kind of new and haven't quite got the hang of the latex stuff yet - could someone tell me what I've done wrong? Thanks.
Last edited: Mar 31, 2010
14. Mar 31, 2010
### lotm
The L-C symbol is substantially trickier to get an intuitive handle on - I still don't really have a 'gut feel' for it, even after a few years. The closest thing is probably to understand it as a kind of 'shuffler', which swaps about entries inside matrices in a cyclic sort of way. Hence, it crops up in areas where these shufflings are desired: for example, in taking the determinant of a matrix (think of how each element gets multiplied by the elements which it does not share a row or a column with), or in taking the cross product of two vectors (where a scrambling is needed to ensure that the new vector is perpendicular to both the old ones), or in the curl of a vector field (which you may well not have done yet - roughly, the 'spiraliness' of a field). Of course, all three of these applications are linked - I was taught to find the cross product $\vec u \times \vec v$ by taking the determinant of the following matrix:
$$\left[ \begin{array}{ccc}\mathbf{i} & \mathbf{j} & \mathbf{k} \\u_1 & u_2 & u_3 \\v_1 & v_2 & v_3\end{array} \right]$$
and the curl is found by taking the cross product of the nabla operator.
As to what manner of thing the L-C symbol is - it is indeed an example of a rank-3 tensor, which are (as you mention) extensions of the concept of matrices into three dimensions (if you like, you can imagine a three-dimensional array of numbers - a cube, of 3 numbers to a side - containing the 27 entries, just as a vector can be displayed as a one-dimensional array of the 3 entries, and a linear operator as a two-dimensional array of the 9 entries). However, it's not an extension of the Kroenecker delta specifically - as you can see, the two objects do quite different things to the matrices they act upon. | 2018-08-19 18:05:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8438393473625183, "perplexity": 503.95359165802023}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221215261.83/warc/CC-MAIN-20180819165038-20180819185038-00008.warc.gz"} |
https://math.stackexchange.com/questions/656072/fast-gauss-seidel-convergence-on-low-rank-matrices | # Fast Gauss-Seidel convergence on low rank matrices
I stumbled upon the following remarkable fact when experimenting with the Gauss-Seidel iterative solver: First I construct a low-rank symmetric positive semi-definite matrix $A = M^TM$ with M a random (randn) matrix of size (k x n) with k << n (e.g. k = 100, n = 1000). Secondly I estimate the Gauss-Seidel convergence rate as follows:
• Let $M = D + L$ and $K = U$ ($A = D + L + U$)
• Consider the eigenvalues $\lambda$ of $M^{-1}K$. All will be $<= 1$ in absolute value (Householder-John theorem that proves GS convergence on SPD matrices). The eigenvalues of value $1$ correspond to the kernel of A, and can I ignore these (assuming I am not interested in the minimum norm solution, but any solution. Inspired by https://mathoverflow.net/questions/80793/is-gauss-seidel-guaranteed-to-converge-on-semi-positive-definite-matrices)
• So finally let's call the convergence rate the largest eigenvalue below 1. For large matrices with k near n, this is typically very close to 1, which explains the slow convergence of GS. However, when k << n, I find that the convergence rate is <<1, more like 0.01, thus yielding very fast GS convergence.
Execute the code below in matlab to see for yourself
clear;
n = 1000
k = 100
C = randn(k, n);
A = C'*C;
L = tril(A, -1); U = triu(A, 1); D = diag(diag(A)); %A = D + L + U
M = D + L;
K = U;
R = M\K;
e = abs(eig(R));
rho = max(e( abs(1-e) > 1e-10))
Does anyone have an idea why this occurs?
• Secondly, there seems to be a correlation between the condition number of M and A, and the spectral radius of $-K^{-1}M$. Ill-conditioning means slower convergence. I have found independent empirical evidence on this (http://fedcsis.eucip.pl/proceedings/pliks/65.pdf) but that paper is quite poor. Formal theory I do not know of. I'm going to try to relate the eigenvalues of A to those of $-K^{-1}M$.
• Did you try something more like conjugate gradients or Chebyshev method? Their convergence can be somewhat better be described in terms of the condition number. IMHO the condition number of the low rank matrix is connected to the fact that (although $C^TC$ is a large matrix) the effective condition number is equal to that of $CC^T$ which is a small matrix. It's not surprising if one accepts that small random matrices are better conditioned than the large ones. It is also interesting that although the Gauss-Seidel looks fine, Jacobi fails. – Algebraic Pavel Jan 30 '14 at 18:23 | 2020-01-26 16:08:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9189324975013733, "perplexity": 636.806819216644}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251689924.62/warc/CC-MAIN-20200126135207-20200126165207-00088.warc.gz"} |
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# what is stopwatch in physics
It is commonly used in laboratories, it can measure a time interval up to 0.01 second. I know the uncertainty is the smallest reading you can see divided by 2, but i dont quite get what it would be for this stop watch. For Y, the spacing between the dots increases as time passes. Experimentally, in our physics laboratory we can use any of several methods to measure the velocity of objects. For example, if a stopwatch display shows two digits to the right of the decimal point, it has a resolution of 0.01 s (10 ms, or 1/100 of a second). In the early nineteenth century, a Swiss watchmaker named Louis Berthoud first developed a chronometer for the first time. Physics, 07.01.2021 18:10, diemiten. It starts to indicate the time lapsed as the start/stop button is pressed. Some of the more common clocks and watches can be found in the table below: Equipment: It can be read in hours, minutes and seconds. The stopwatch manual states that the stopwatch has an uncertainty of ±0.05s. It is a kind of watch that stands out for the accuracy and precision with which it can measure the time of an event. It works by pressing a start button and then stopping it. No employee has been able to measure the velocity yet, because […] A stop watch is a device used to measure speed or duration in fractions of a second, typically for sporting or athletic events. Say, for example, that you accept a consulting job from an ammunition manufacturer that wants to measure the muzzle velocity of its new bullets. Raushan9431 Raushan9431 Answer: a stopwatch is a device which show the timing accuratly in second by second ,minute and minute . Runners on the track coach’s team regularly clock 100-m sprints of 11.49 s to 15.01 s. At the school’s last track meet, the first-place sprinter came in at 12.04 s and the second-place sprinter came in at 12.07 s. An usage example is measuring the speed of sound or the duration of a free fall. The stopwatch works by pressing the start button when the event begins. Physics revision site - recommended to teachers as a resource by AQA, OCR and Edexcel examination boards - also recommended by BBC Bytesize - winner of the IOP Web Awards - 2010 - Cyberphysics - a physics revision aide for students at KS3 (SATs), KS4 (GCSE) and KS5 (A and AS level). What is the independent variable and why? There are wristwatches that have a chronometer, but there are also models that can be hung on the neck or carried in the pocket. physics. The digital stopwatch was started at a time t 0 = 0 and then was used to measure ten swings of a simple pendulum to a time of t = 17.26 s. If the time for ten swings of the pendulum is 17.26 s, (a) what is the minimum absolute uncertainty in this measurement? Question 1. 2. As nouns the difference between stopwatch and pendulum is that stopwatch is a timepiece designed to measure the amount of time elapsed from a particular time when activated and when the piece is deactivated while pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity, commonly used to regulate various devices such as clocks. When the race is over, press the stop button. His invention came about because he was able to perfect the string system. You can restart the stopwatch to count another event or event. Jimmy is cooking pasta in a pot of water on the stove. This question appeared on Bangladesh physics Olympiad 2014, Sylhet, Bangladesh for students of class 9 and 10. mark as brainliest " PLEASE " A reset button restores its initial zero settings. (y) So Nice.! Physics. The timers are easy to use, to start the count you must press a start button. Stopwatch types are related to how time is divided and the ability to measure smaller and smaller fractions of time. The stopwatch contains buttons to perform certain functions, such as starting, stopping and split timing. China mechanical stopwatch physics teaching instrument - find detail mechanical stopwatches, analog stopwatch from yuyao xueyou teaching equipment co., ltd. (b) What is the speed when the stopwatch reads 12.0 s? Physics High School Read the elapsed time on the stopwatch and answer the questions. stopwatch to find an average time of fall for 3 trials from the same height and reports the following data: h = 5.25 ± 0.15 m, t = 1.14 ± 0.06 s. a) Use the equation a = 2 h / t 2 to determine the average acceleration and its uncertainty. It can also be used as a start-stop and reset button. IS there any way of downloading ur note’s? Use the equation $$E = IVt$$ to calculate the energy supplied to the metal block. Stopclock- A large digital version of a stopwatch desinged for viewing at a distance , as in a sports stadium, is called a stopclock A car is speeding up and has an instantaneous velocity of 8.0 m/s in the +x-direction when a stopwatch reads 10.0 s. It has a constant acceleration of 3.5 m/s2 in the +x-direction. As nouns the difference between stopwatch and pendulum is that stopwatch is a timepiece designed to measure the amount of time elapsed from a particular time when activated and when the piece is deactivated while pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity, commonly used to regulate various devices such as clocks. please follow me. Hence, Y represent the tape from an object that is accelerating. When you begin working on a task , click the 'stopwatch' icon (located at the bottom of the timesheet) to begin recording your time. What is Difference Between Heat and Temperature? Explanation: please follow me . In which digit is there the least amount of confidence? It is a kind of watch that stands out for the accuracy and precision with which it can measure the time of an event. A stopwatch is used to measure the time interval of an event. Now if this reaction time was always constant the measurement made would still give the correct value. 05 s. Runners on the track coach’s team regularly clock 100-m sprints of 11.49 s to 15.01 s . Your stopwatch could have other functions such as an alarm or calendar function. Some precise stopwatches are connected electronically to the time event and hence, more accurate. Look at the first two digits on a digital stopwatch. Refer to your owner’s manual for a list of all functions of your stopwatch. The procedure to deducing the state of motion from the resulting tape is best explained using an example. ... Record the temperature of the water in the small beaker and start the stopwatch. It is also known as a chronometer and is used to measure fractions of time, usually short and accurately. Switch on the power supply, start a stopwatch and record the readings on the Voltmeter and Ammeter.#Record the time on the stopwatch with every 2°C increase in temperature a minimum of 6 times. For example, if you were timing a race, you would press the start button when the race starts. The dots are made by a ticker tape timer with a time interval of 0.1 seconds. 07 s . 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I feel that human reaction time is self-explanatory. At the end of the event, the stopwatch is stopped and the end time is noted. 1. Let's say that the reaction time is about 0.2 seconds. Explanation: please follow me . The stopwatch is operated manually so due to human reaction time there will be a slight delay when starting and stopping the stopwatch. however it is still the fairest way to go about it for the players. Difference between scientific notation and significant figures, Newton's law of universal gravitation formula, Conservation of mechanical energy: Formula and Examples, Difference Between Electric Potential and Electric Potential Energy. It is also known as a chronometer and is used to measure fractions of time, usually short and accurately. It works by pressing a start button and then stopping it. A stopwatch is used to measure the time interval of an event. Once the event is over, time stops on the stop button. Measure the time between two or more sound events. The reading provides the required time interval. Home O Level Measurement Measurement Of Time. A mechanical stopwatch can measure a time interval of up to 0.1 seconds.It has a knob that is used to wind the spring that powers the watch. Using the same reasoning as above, Z represent the tape from an object that is decelerating. The difference provides the required time interval. We have just done a prac in physics and now im figuring out the errors in the calculations. Raushan9431 Raushan9431 Answer: a stopwatch is a device which show the timing accuratly in second by second ,minute and minute . The time of the race displays on the stopwatch just as the time of day would display on your wristwatch. How many significant figures does this measurement have? In physics, the principle of conservation of momentum comes in handy when you can’t measure velocity with a simple stopwatch. Search for Other Answers. A ticker tape timer is a machine that produce a dot on a tape at a fixed time interval. The students have a force probe, a meterstick, and a stopwatch. Back To Measurement Of Physical Quantities (O Level). The operation of a stopwatch is to accurately count the time of an event. Notify me of follow-up comments by email. Digital stopwatch. So…, Your email address will not be published. The Stopwatch allows you to record the exact number of hours and minutes you worked on a task/activity. The stopwatch is activated by the hand in response to the eye seeing the object meet the marker. I really tried to solve this, but I failed. The time event is then allowed to occur, and at the end of the event, the end time is noted. A stopwatch is used to measure the time interval of an event. a) The x-coordinate of an electron is measured with an uncertainty of 0.20 mm. Help with GCSE Physics, AQA syllabus A AS Level and A2 Level physics. Well these notes are great! A car is speeding up and has an instantaneous speed of 14.0 m/s when a stopwatch reads 9.0 s. It is from the needs of each one that the best choice will emerge. Get an answer to your question “What is the resolution of the stopwatch ...” in Physics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions. These were used by sailors and were developed in the years 1763 to 1761. Learn about and revise energy and how it is transferred from place to place with GCSE Bitesize Physics. Physics, 21.06.2019 23:10 6–55 refrigerant-134a enters the condenser of a residential heat pump at 800 kpa and 358c at a rate of 0.018 kg/s and leaves at 800 kpa as a saturated liquid. I need help quick 2 See answers scrapyharrito scrapyharrito When you are finished working on that task , … Records that show up to 2 decimal places are not appropriate.). The only bad part about stopwatch is it removes potential gameplay and ends a match what can initially seem a bit prematurely and jarring. Some students want to calculate the work done by friction as an object with unknown mass moves along a straight line on a rough horizontal surface. SI unit of time is second (s). Accuracy: ± 0.1 s. (Allowance made to human reaction time limits the accuracy of the stopwatch to 0.1 – 0.4 s for laboratory experiments. In the context of laboratory physics, a stimulus is normally anticipated. mark as brainliest " PLEASE " The initial time is often taken to be zero, as if measured with a stopwatch; the elapsed time is then just t. Average velocity $\bar{v}$ is defined as displacement divided by the travel time. He uses a stopwatch to see how long the pasta takes to cook depending on the temperature of the water in the pot. Those numbers represent the minutes used. As soon as the start/stop button is pressed again, it stops and indicates the time interval recorded by it between the start and stop of an event. How to use: As the time event occurs, the stopwatch is started at the same time. If you spot any errors or want to suggest improvements, please contact us. What do you mean by Thermal conductivity? 04 s and the second-place sprinter came in at 12 . For X, the dots are evenly spaced. In this case to refer to a mechanism with the similar operation of a small portable pendulum clock. Since the dots are made with a fixed time interval, the time in the formula above is fixed. The stopwatch manual states that the stopwatch has an uncertainty of ± 0. Stopwatch and Meterstick: The simplest way to measure velocity is to use a stop watch … You can see a digital stopwatch in the picture to the left. hi i was just wonderin in a physics experiement what is the precision of a stopwatch and would 10 seconds be written as 10.0 or 10.00 seconds? (a) What change in speed occurs between t = 10.0 seconds and t = 12.0 s? The watch starts when the knob is pressed once. Bernoulli equation derivation with examples and applications, Continuity equation derivation in fluid mechanics with applications, Newton’s law of universal gravitation formula, Newton’s First law of Motion Examples in Our Daily Life, Newton’s Second Law Definition and Formula, Newton’s Third Law of Motion Examples in Daily Life, Newton’s three laws of motion with examples and applications, Ampere’s law and its applications in daily life, Formula for ohm’s law with example and problems. We will get an increasing speed as the distance between the dots increases. Required fields are marked *. Physics Primary School What is stopwatch ( very short) 2 See answers babitarajput9820 babitarajput9820 Answer: this is answer. The standard for unit of time, the second (s), is the exact duration of 9,192,631,770 cycles of the radiation associated with the transition between the two hyperfine levels of the ground state of cesium-133 atom. please follow me. It is a kind of watch that stands out for the accuracy and precision with which it can measure the time of an event. Search for Other Answers. The figure above consists of 3 tapes, X, Y and Z, with a length of 1 m from the first dot to the last dot. A brick is thrown vertically upward with an initial speed of 4.30 m/s from … If the stopwatch is setwith a timer of 3.000 s,at what angle relative to the upward vertical direction is the stopwatch traveling at the moment the alarm is heard from the launch location? b) Repeat . Help with Questions in Physics. Get an answer to your question “What is the resolution of the stopwatch ...” in Physics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions. What is the xcomponent of the electron’s velocity, vx, if the minimum percentage uncertainty in a simultaneous measurement of vx is 1.0%. Basically there are two types of stopwatch, Digital stopwatch, and Analog stopwatch. It is a scalar quantity. For Z, the spacing between the dots decreases as time passes. How to use: The tape is attached to an object and the state of motion of the object can be deduced from the dots on the tape. Homepage. Physics. I would be thankful to you if you will add some question to solve because in this way we could also practice. How many Types of Multivibrators Are There? Your email address will not be published. Press the button at the top of the stopwatch to reset the hands to the zero mark. As the distance between the dots decreases as time passes count you must press a start button and then it. 12.0 s to cook depending on the temperature of the event, the end of the in..., similar measuring instruments existed correct value numbers after the : '' mark necessary to mention before! Or more sound events takes to cook depending on the stopwatch reads 12.0 s two digits on a tape a... Is stopped and the ability to measure the time of an event regularly clock 100-m sprints 11.49!, time stops on the stopwatch manual states that the stopwatch contains buttons perform. Split timing suggest improvements, please contact us lapsed as the distance between the dots are made by ticker. Will add some question to solve this, but i failed supplied to the zero mark comes in when. Of laboratory physics, the stopwatch at the end of the water in the formula is! I comment only bad part about stopwatch is started at the first time an object that is.! 10 − 10 seconds is stopped and the end time is noted physics Olympiad 2014,,... Were developed in the formula above is fixed spacing between the dots increases as time passes of momentum comes handy! Time was always constant the measurement made would still give the correct value between =! Race starts divided and the second-place sprinter came in at 12 start/stop is! Water on the stove and deactivation is commonly used in laboratories, it stops the watch while the press! Babitarajput9820 babitarajput9820 Answer: this is Answer Sylhet, Bangladesh for students of class and. Time interval modern history, the end time is about 0.2 seconds his invention came about he! I really tried to solve because in this case to refer to mechanism! Time instead of human error types are related to how time is second ( s.! 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Button and then stopping it of a small portable pendulum clock See answers scrapyharrito... | 2022-09-30 23:25:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37179192900657654, "perplexity": 1135.108993530998}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335504.37/warc/CC-MAIN-20220930212504-20221001002504-00596.warc.gz"} |
https://calcoolator.eu/deltoid-kite-concave-dart-arrowhead-diagonals-area-perimeter-sides- | Choose language
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# Deltoid, kite concave, dart, arrowhead - diagonals, area, perimeter, sides
Calculate the diagonals of a concave deltoid, kite, side lengths, surface area, perimeter and radius of the inscribed circle. Each size can be calculated using many formulas, just indicate what data we have.
## First diagonal of concave deltoid (concave kite, dart, arrowhead)
### First diagonal of concave deltoid on side (a) and angle α
$$e=a\cdot 2\sin\left(\frac{\alpha}{2}\right);$$ $$e=2\cdot\sqrt{a^2-g^2 }$$ where $$g=a\cdot \sin \left(\frac{\alpha}{2}-90^\circ\right)$$
### First diagonal of concave deltoid side (b) and angle β
$$e=b\cdot 2\sin\left(\frac{\beta}{2}\right)$$
### First diagonal of the concave deltoid on the sides, the second diagonal and the angle γ
$$e=\frac{2\cdot a\cdot b\cdot \sin\gamma}{f}$$
### First diagonal of the concave deltoid on the sides, the second diagonal and the angle α
$$e=2\cdot\sqrt{b^2-(f+g)^2}$$ gdzie $$g=a\cdot \sin \left(\frac{\alpha}{2}-90^\circ\right)$$
## Second diagonal of the concave deltoid (concave kite, dart, arrowhead)
### Second diagonal of concave deltoid on sides (a) (b) and angles α & β
$$f=a\cdot cos\left(\frac{\alpha}{2}\right)+ b\cdot cos\left(\frac{\beta}{2}\right)$$
### Second diagonal of the concave deltoid on the sides (a) (b) and the first diagonal
$$f=\sqrt{b^2-\left(\frac{e}{2}\right)^2}-\sqrt{a^2-\left(\frac{e}{2}\right)^2}$$
### Second diagonal of concave deltoid with sides, first diagonal and angle γ
$$f=\frac{2\cdot a\cdot b\cdot \sin\gamma}{e}$$
### Second diagonal of the concave deltoid on the sides and angle γ
$$f=\sqrt{a^2+b^2-2\cdot a \cdot b \cdot \cos\gamma}$$
### Second diagonal of the concave deltoid on the side (a) and the angle β & γ
$$f=\frac{a\cdot \sin\gamma}{\sin\left(\frac{\beta}{2}\right)}$$
### Second diagonal of concave deltoid with sides, first diagonal and angle α
$$f=\sqrt{b^2-\left(\frac{e}{2}\right)^2}-g$$ where $$g=a\cdot \sin \left(\frac{\alpha}{2}-90^\circ\right)$$
## Surface area of the concave deltoid (concave kite, dart, arrowhead)
### Area of the concave deltoid on the sides (a)(b) and angles α & β
$$S=\frac{a^2\cdot \sin\alpha}{2}+\frac{b^2\cdot\sin\beta}{2}$$
### Area of the concave deltoid on the sides (a)(b) and the angle γ
$$S=a\cdot b\cdot \sin\gamma$$
### Area of the concave deltoid from the diagonals
$$S=\frac{e\cdot f}{2}$$
## Concave deltoid circumference (concave kite, dart, arrowhead)
### Concave deltoid circumference from the sides
$$L = 2a + 2b$$
### Concave deltoid circumference from the shorter diagonal and the angle(α) & (β)
$$L = \frac{e}{\sin\left(\frac{\beta}{2}\right)}+\frac{e}{\sin\left(\frac{\alpha}{2}\right)}$$
## Sides of the concave deltoid (concave kite, dart, arrowhead)
### Side (a) of the concave deltoid from the shorter diagonal and angle α
$$a=\frac{e}{2\cdot\sin\left(\cfrac{\alpha}{2}\right)}$$
### Side (b) of the concave deltoid from the shorter diagonal and angle β
$$b=\frac{e}{2\cdot\sin\left(\cfrac{\beta}{2}\right)}$$
### Side (a) of the concave deltoid on the side (b) and angles α & β
$$a=\frac{b\cdot \sin\left(\cfrac{\beta}{2}\right)}{\sin\left(\cfrac{\alpha}{2}\right)}$$
### Side (b) of the concave deltoid on the side (a) and angles α & β
$$b=\frac{a\cdot \sin\left(\cfrac{\alpha}{2}\right)}{\sin\left(\cfrac{\beta}{2}\right)}$$
# Concave deltoid, concave kite, dart, arrowhead
Deltoid - is a quadrilateral whose four sides can be grouped into two pairs of equal length adjacent sides. The sides of the same length have a common vertex.
Deltoid can be convex or concave.
Concave deltoid, also known as an concave kite, dart, arrowhead - is a deltoid in which the internal angle between the shorter sides is greater than 180 °.
Concave deltoid has the following properties:
1. The sum of the measures of all the internal angles of the deltoid is 2Π $$\alpha+\beta+2\cdot\gamma=360^\circ$$
2. Formula for the first diagonal of the concave deltoid on the side (a) and the angle α
3. $$e=a\cdot 2\sin\left(\frac{\alpha}{2}\right);$$ $$e=2\cdot\sqrt{a^2-g^2 }$$ gdzie $$g=a\cdot \sin \left(\frac{\alpha}{2}-90^\circ\right)$$
4. Formula for the first diagonal of the concave deltoid on the side (b) and the angle β
5. $$e=b\cdot 2\sin\left(\frac{\beta}{2}\right)$$
6. Formula for the first diagonal of the concave deltoid on the sides, the second diagonal and the angle γ
7. $$e=\frac{2\cdot a\cdot b\cdot \sin\gamma}{f}$$
8. Formula for the first diagonal of the concave deltoid on the sides, the second diagonal and the angle α
9. $$e=2\cdot\sqrt{b^2-(f+g)^2}$$ gdzie $$g=a\cdot \sin \left(\frac{\alpha}{2}-90^\circ\right)$$
10. Second diagonal of concave deltoid on sides (a) (b) and angles α & β
11. $$f=a\cdot cos\left(\frac{\alpha}{2}\right)+ b\cdot cos\left(\frac{\beta}{2}\right)$$
12. Formula for the second diagonal of the concave deltoid from the sides (a) (b) and the first diagonal
13. $$f=\sqrt{b^2-\left(\frac{e}{2}\right)^2}-\sqrt{a^2-\left(\frac{e}{2}\right)^2}$$
14. Formula for the second diagonal of the concave deltoid from the sides, the first diagonal and the angle γ
15. $$f=\frac{2\cdot a\cdot b\cdot \sin\gamma}{e}$$
16. Formula for the second diagonal of the concave deltoid from the sides and the angle γ
17. $$f=\sqrt{a^2+b^2-2\cdot a \cdot b \cdot \cos\gamma}$$
18. Formula for the second diagonal of the concave deltoid on the side (a) and the angle β & γ
19. $$f=\frac{a\cdot \sin\gamma}{\sin\left(\frac{\beta}{2}\right)}$$
20. Formula for the second diagonal of the concave deltoid from the sides, the first diagonal and the angle α
21. $$f=\sqrt{b^2-\left(\frac{e}{2}\right)^2}-g$$ gdzie $$g=a\cdot \sin \left(\frac{\alpha}{2}-90^\circ\right)$$
22. Formula for Area of the concave deltoid on the sides (a) (b) and angles α & β
23. $$S=\frac{a^2\cdot \sin\alpha}{2}+\frac{b^2\cdot\sin\beta}{2}$$
24. Formula for the Area of the concave deltoid on the sides (a)(b) and the angle γ
25. $$S=a\cdot b\cdot \sin\gamma$$
26. Formula for the Area of the concave deltoid from the diagonals
27. $$S=\frac{e\cdot f}{2}$$
28. Formula for the perimeter of the concave deltoid on the sides
29. $$L = 2a + 2b$$
30. Formula for the circumference of the concave deltoid from the shorter diagonal and the angle(α) & (β)
31. $$L = \frac{e}{\sin\left(\frac{\beta}{2}\right)}+\frac{e}{\sin\left(\frac{\alpha}{2}\right)}$$
32. Formula on the side (a) of the concave deltoid with the shorter diagonal and angle α
33. $$a=\frac{e}{2\cdot\sin\left(\cfrac{\alpha}{2}\right)}$$
34. Formula on the side (b) of the concave deltoid with the shorter diagonal and angle β
35. $$b=\frac{e}{2\cdot\sin\left(\cfrac{\beta}{2}\right)}$$
36. Formula for the Side (a) of the deltoid on the concave side (b) and angles α & β
37. $$a=\frac{b\cdot \sin\left(\cfrac{\beta}{2}\right)}{\sin\left(\cfrac{\alpha}{2}\right)}$$
38. Formula on the side (b) of the concave deltoid on the side (a) and angles α & β
39. $$b=\frac{a\cdot \sin\left(\cfrac{\alpha}{2}\right)}{\sin\left(\cfrac{\beta}{2}\right)}$$ | 2021-09-20 01:21:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8709152340888977, "perplexity": 3303.0433571834496}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056974.30/warc/CC-MAIN-20210920010331-20210920040331-00146.warc.gz"} |
http://mathhelpforum.com/trigonometry/82903-word-problem-trigonometry.html | 1. ## word problem Trigonometry
Hello, me again! and I need ur help!
In summary octupus ride
one revolution=60 seconds
max 4m above ground
min 1 m above ground
h in metres above ground can be modelled by
h=asin (kt) +c where t=time in seconds
question?
what is the desired period of the fxn?
my answer: I just assumed its 60 seconds? am I right
Determin the value of K that results in the period desired
so for amplitude I got 3/2 and vertical translation 5/2
therefore:
h=3/2 sink (60) +5/2
im stuck. I have have no idea how to solve for K, since there is two varialble. any hints is appreciated!
2. Originally Posted by jepal
Hello, me again! and I need ur help!
In summary octupus ride
one revolution=60 seconds
max 4m above ground
min 1 m above ground
h in metres above ground can be modelled by
h=asin (kt) +c where t=time in seconds
question?
what is the desired period of the fxn?
my answer: I just assumed its 60 seconds? am I right
Determin the value of K that results in the period desired
so for amplitude I got 3/2 and vertical translation 5/2
therefore:
h=3/2 sink (60) +5/2
im stuck. I have have no idea how to solve for K, since there is two varialble. any hints is appreciated!
$k = \frac{2\pi}{T}$ , where $T$ is the period | 2017-02-20 13:29:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9775829315185547, "perplexity": 5176.55808730282}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501170562.59/warc/CC-MAIN-20170219104610-00395-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://economics.stackexchange.com/questions/36992/stabilizing-property-of-a-taylor-rule | # Stabilizing Property of a Taylor Rule
Considering the New Keynesian Model we have the Phillips curve and dynamic IS curve in log-linearized form with price shock $$u^{\pi}$$ and demand shock $$u^{IS}$$ :$$\pi_t=\beta E_t\pi_{t+1}+\kappa(y_t-y_t^n)+u_t^{\pi}$$ $$y_t=E_{t+1}-\frac{1}{\sigma}(i_t-E_t\pi_{t+1}-\rho)+u_t^{IS}$$
where $$\kappa>0$$, $$1>\beta>0$$,$$\sigma>0$$. The shocks follow some stochastic process.Furthermore, natural level of output $$y_t^n$$ is determined by a technology shock, also following a stochastic process.
Now, we have the following Taylor rule of the central bank: $$i_t=\rho+\phi_{\pi}E_t\pi_{t+1}+\phi_y E_t(y_{t+1}-y_{t+1}^n).$$
I know that following this Taylor rule, we are not able to stabilize any of these shocks. However, could someone tell me step by step how me come to this conclusion? Also does our conclusion change if we would use t terms rather than expected (t+1) ones?
I came so far:
1. Price shock: inflation increases, central bank reacts (because of higher $$E_t\pi_{t+1}$$?) with higher interest rate.And higher interest rate leads to lower demand and production($$y_t$$). Since in order to decrease inflation an output gap has to be created, divine coincidence does not hold and stabilization is not possible. This is actually a reasoning that my teacher gave. However, if output gap exist because of an attempt to lower inflation, could the inflation gap not close after inflation is stable again? Also, as before, I do not know if we can use expected terms like actual terms. Also, if it is stated that shocks follow a stochastic process, actually all expected terms for the next period, shouldn't they be all 0?
2. In terms of a demand shock, demand increases leading to an increase in actual output, creating a positive output gap, leading to an increase in inflation. If my understanding of the expected terms is right, central bank would expect positive inflation also for the next period? And hence interest rate increases (also with increase of expected output gap)? Then demand decreases and output gap decreases. My teacher stated in the solutions that at some point the interest rate adjusts for the shock, however, not totally. I do not see this though. Could someone explain to me the obvious?
3.In terms of a technology shock, a negative output gap leads to a decrease in inflation. Because of the negative output gap, also a negative output gap should be expected in the future (if we assumed an AR process?), that comes with decrease in inflation, hence, central bank lowers interest rate to adjust demand and output.
I would appreciated it if someone could tell me step by step how the reasoning is done here to come to the conclusion that this Taylor rule cannot stabilize inflation. | 2020-12-01 12:06:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 11, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7811744809150696, "perplexity": 844.1159660019119}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141674082.61/warc/CC-MAIN-20201201104718-20201201134718-00696.warc.gz"} |
https://www.tutorialspoint.com/binomial-distribution-in-data-structures | # Binomial Distribution in Data Structures
The Binomial Distribution is a discrete probability distribution Pp(n | N) of obtaining n successes out of N Bernoulli trails (having two possible outcomes labeled by x = 0 and x = 1. The x = 1 is success, and x = 0 is failure. Success occurs with probability p, and failure occurs with probability q as q = 1 – p.) So the binomial distribution can be written as
$$P_{p}\lgroup n\:\arrowvert\ N\rgroup=\left(\begin{array}{c}N\ n\end{array}\right) p^{n}\lgroup1-p\rgroup^{N-n}$$
## Example
Live Demo
#include <iostream>
#include <random>
using namespace std;
int main(){
const int nrolls = 10000; // number of rolls
const int nstars = 100; // maximum number of stars to distribute
default_random_engine generator;
binomial_distribution<int> distribution(9,0.5);
int p[10]={};
for (int i=0; i<nrolls; ++i) {
int number = distribution(generator);
p[number]++;
}
cout << "binomial_distribution (9,0.5):" << endl;
for (int i=0; i<10; ++i)
cout << i << ": " << string(p[i]*nstars/nrolls,'*') << endl;
}
## Output
0:
1: *
2: ******
3: ***************
4: *************************
5: ************************
6: ****************
7: *******
8: *
9: | 2023-03-28 17:52:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5439785122871399, "perplexity": 7085.590458048045}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948868.90/warc/CC-MAIN-20230328170730-20230328200730-00768.warc.gz"} |
https://math.stackexchange.com/questions/2739925/prove-that-the-chromatic-number-of-a-graph-is-the-same-as-the-maximum-of-the-chr | # Prove that the chromatic number of a graph is the same as the maximum of the chromatic numbers its blocks.
Here's the statement to be proved:
The chromatic number of a graph is the same as the maximum chromatic number of its blocks.
Here's what I think. We consider the graph $G$ with chromatic number $\chi(G)=k$. Let $\chi(B)$ be the maximum chromatic number of a block of $G$. Now, clearly $\chi(B) \leq k,$ since a block is a subgraph of $G.$ This would tell me that every individual block could be colored with at most $k$ colors.
Now, any two blocks share at most one vertex, so intuitively it would make sense that we could find a proper coloration for $G$ with at most $k$ colors, by picking the color of the common vertices in a clever way. But how can I prove this?
Any help is appreciated.
• What is your definition of block? "A subgraph with as many edges as possible and no cut vertex (a vertex whose removal disconnects the subgraph)" ? – Jack D'Aurizio Apr 16 '18 at 15:35
• @JackD'Aurizio My definition of a block is a maximal nonseparable subgraph of a graph $G$. So yes, basically what you just said. – Thomas Bladt Apr 16 '18 at 15:44
• Years ago, I took a course in combinatorial algorithms where the book stated that this was obvious, and I don't think I ever figured out why. Thanks for asking this question. +1 – saulspatz Apr 16 '18 at 16:56
• @saulspatz I'm glad my question has also helped others! – Thomas Bladt Apr 16 '18 at 18:15
## 1 Answer
The block decomposition of a graph leads to a tree. Assume that all the blocks of $G$ have been colored but two blocks $B_1,B_2$ do not agree about the coloring of their common vertex. Then by rotating/replacing the colors in one of the two blocks we may resolve such issue. Due to the tree-structure of the block decomposition, we may pick a block as "root" and resolve all the color-conflicts, proceeding from the root to the leaves and fixing the colors of the children blocks each time.
• +1 Would it also work to just color the blocks top-down in the tree? If I'm not mistaken, no conflicts would arise. – saulspatz Apr 16 '18 at 16:38
• @saulspatz: oh, sure, that is clearly more algorithmically efficient than coloring first and fixing it later. – Jack D'Aurizio Apr 16 '18 at 16:39
• Thank you for you answer. What is still not so clear to me is how we can assure that we will always be able to resolve the possible color conflicts that arise, could you tell me why that is? – Thomas Bladt Apr 16 '18 at 18:14
• @ThomasBladt: color $B_1,B_2,B_3$. Rotate the colors of $B_2$ in such a way that $B_1,B_2$ agree on the common vertex. Then rotate the colors of $B_3$ in such a way that $B_2,B_3$ agree on the common vertex. Top-down. – Jack D'Aurizio Apr 16 '18 at 18:46
• @JackD'Aurizio Oh, now I get it! That's what you meant when you said pick a root block. Thank you very much! – Thomas Bladt Apr 16 '18 at 18:50 | 2019-06-19 09:46:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5578138828277588, "perplexity": 296.503340983678}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998943.53/warc/CC-MAIN-20190619083757-20190619105757-00459.warc.gz"} |
https://www.jkcs.or.kr/journal/view.php?number=6272 | J. Korean Ceram. Soc. > Volume 44(9); 2007 > Article
Journal of the Korean Ceramic Society 2007;44(9): 477. doi: https://doi.org/10.4191/kcers.2007.44.9.477
Statistical Analysis of the Physical Properties in a Slag-OPC-Gypsum System as a Compound Mixing Ratio Kwang-Suk You, Kyung-Hoon Lee1, Gi-Chun Han, Hwan Kim2, Ji-Whan Ahn Minerals & Materials Processing Division, Korea Institute of Geoscience & Mineral Resources1Environment & Energy Department POSCO2Materials Science and Engineering, Seoul National University ABSTRACT The effect of the mixing ratio of compounds in a slag-OPC-Gypsum system on the physical properties of Slag cement is investigated in this study. $Na_2SO_4$ was used as an alkali activator. Blast furnace slag cement was prepared from a mixture of blast furnace slag, ordinary Portland cement and anhydride gypsum. The fluidity and the compressive strength according to the ratio of each mixture were analyzed in statistical analyses in order to discover the parameters influencing the fluidity and compressive strength. The results showed that the hydration of blast furnace slag took place with the addition of $Na_2SO_4$ and that column-crystalline ettringite was created as the main hydration product of the blast furnace slag. In addition, it was found that the compressive strength of blast furnace slag cement tends to increase when the ordinary Portland cement content is higher up to three days. However, it is known that the compressive strength tends to increase as the blast furnace slag content becomes higher with increases in the level of OPC after 28 days. As a result of this analysis, it is believed that the ordinary Portland cement content influences the initial compressive strength of blast furnace slag cement, and that in later days this is highly influenced by the slag content. Key words: Blast furnace slag, Activator, Hydration Activity, Ettringite, Ordinary Portland cement
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1,172 View | 2022-01-23 16:07:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3234109878540039, "perplexity": 5342.950637225881}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304287.0/warc/CC-MAIN-20220123141754-20220123171754-00454.warc.gz"} |
http://openstudy.com/updates/4d88d885012f8b0b2ec0180a | ## anonymous 5 years ago 9x2+7y=6
1. anonymous
y=-12/7
If that is true then $x=\sqrt{2}$, but I think y=30/7 then x=2, wait y could be many values resulting in x having many values. There is no specific solution | 2016-10-25 21:08:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6371614336967468, "perplexity": 2310.0495899490948}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720380.80/warc/CC-MAIN-20161020183840-00156-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://mathhelpforum.com/number-theory/141055-quadratic-residue-proof.html | Let p be a prime such that p is congruent to 3 modulo 4 and let a be a quadratic residue modulo p. Prove that if ab is congruent to p-1 modulo p, then b is a quadratic non-residue modulo p.
2. Originally Posted by Tand
Let p be a prime such that p is congruent to 3 modulo 4 and let a be a quadratic residue modulo p. Prove that if ab is congruent to p-1 modulo p, then b is a quadratic non-residue modulo p.
$ab\equiv p-1\equiv -1\bmod{p}\implies b\equiv-a^{-1}\bmod{p}$
$\left(\frac bp\right) = \left(\frac{-a^{-1}}{p}\right) = \left(\frac{-1}{p}\right)\left(\frac{a^{-1}}{p}\right) = (-1)\cdot(1) = -1$ since $p\equiv3\bmod{4}$.
You may be wondering why $\left(\frac{a^{-1}}{p}\right) = 1$.
Well, $1=\left(\frac1p\right) = \left(\frac{a\cdot a^{-1}}{p}\right) = \left(\frac ap\right)\left(\frac{a^{-1}}{p}\right) = \left(\frac{a^{-1}}{p}\right)$. | 2017-10-21 14:51:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9615471959114075, "perplexity": 93.84286982756873}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824819.92/warc/CC-MAIN-20171021133807-20171021153807-00320.warc.gz"} |
https://clarissewiki.com/5.0/reference/user/MaterialPhysicalHair.html | # Hair#
(MaterialPhysicalHair)
• Category: /Material/Physical
• Default object name: hair
Go to Technical page.
Hair material.
## Attributes#
Name Type Description
Export Aovs bool Compute and write Aovs defined in the shading graph
Arbitrary Output Variables reference (AovStore) Set the list of extra channels to write to the image.
Light Path Expression Label string Set the material label in light path expressions.
Material Sample Count long Material sample count per pixel.
Glossy Reflection Sampling Multiplier double Material glossy reflection sample count multiplier.
Glossy Transmission Sampling Multiplier double Material glossy transmission sample count multiplier.
Russian Roulette double Amount of Russian roulette used on the material samples.
Roughness Noise Optimization double Noise reduction strategy along rough light path.
Glossy Reflection Depth long Maximum glossy reflection depth.
Glossy Transmission Depth long Maximum glossy transmission depth.
Opacity double[3] Opacity of the material.
Normal Mode long Define which geometric normal to use for the shading.
Shadow Casting Mode long Defines the properties of the material when casting shadows: fully opaque (regardless of the actual value of the opacity of the material), artistic (user-defined opacity and coloring), pseudo-caustics (cheaply emulating actual refractive caustics) or physical (intrinsic transparency of the material), where the last three are modulated by the opacity of the material.
Shadow Opacity double Defines how dark the shadows cast by this material are.
Shadow Coloring double Defines how much refraction and absorption colors affect shadowing.
Reflective Caustics long Reflective caustics computation mode.
Refractive Caustics long Refractive caustics computation mode.
Primary Albedo double[3] Albedo of the primary highlight (aka R lobe).
Primary Gain double Gain of the primary highlight (aka R lobe).
Primary Shift double Longitudinal shift of the primary highlight (aka R lobe): a negative value pushes it towards the root, whereas a positive one pushes it towards the tip.
Primary Length double Length, or longitudinal width of the primary highlight (aka R lobe).
Secondary Albedo double[3] Albedo of the secondary highlight (aka TRT-g lobe, or TRT without the glints).
Secondary Gain double Gain of the secondary highlight (aka TRT-g lobe, or TRT without the glints).
Secondary Shift double Longitudinal shift of the secondary highlight (aka TRT-g lobe, or TRT without the glints): a negative value pushes it towards the root, whereas a positive one pushes it towards the tip. When empty, the value is computed from the primary highlight.
Secondary Length double Length, or longitudinal width of the secondary highlight (aka TRT-g lobe, or TRT without the glints). When empty, the value is computed from the primary highlight.
Transmission Albedo double[3] Albedo of the transmission highlight (aka TT lobe).
Transmission Gain double Gain of the transmission highlight (aka TT lobe).
Transmission Shift double Longitudinal shift of the transmission highlight (aka TT lobe): a negative value pushes it towards the root, whereas a positive one pushes it towards the tip. When empty, the value is computed from the primary highlight.
Transmission Length double Length, or longitudinal width of the transmission highlight (aka TT lobe). When empty, the value is computed from the primary highlight.
Transmission Width double Width, or azimuthal width of the transmission highlight (aka TT lobe).
Glints Albedo double[3] Albedo of the glints (aka g lobe, part of the full TRT lobe). Note that it is multiplied by the secondary highlight albedo.
Glints Gain double Gain of the glints (aka g lobe, part of the full TRT lobe). Note that it is multiplied by the secondary highlight albedo.
Glints Spacing double Spacing, or half-angle between the glints (aka g lobe, part of the full TRT lobe).
Glints Width double Width, or azimuthal width of the glints (aka g lobe, part of the full TRT lobe). | 2023-02-03 23:01:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5807837843894958, "perplexity": 13589.36954749154}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500076.87/warc/CC-MAIN-20230203221113-20230204011113-00279.warc.gz"} |
https://www.junhaow.com/lc/problems/graph/133_clone-graph.html | # 133. Clone Graph
Reference: LeetCode
Difficulty: Medium
## Problem
Given a reference of a node in a connected undirected graph, return a deep copy (clone) of the graph. Each node in the graph contains a val (int) and a list (List[Node]) of its neighbors.
Note:
• The number of nodes will be between 1 and 100.
• The undirected graph is a simple graph, which means no repeated edges and no self-loops in the graph.
• Since the graph is undirected, if node p has node q as neighbor, then node q must have node p as neighbor too.
• You must return the copy of the given node as a reference to the cloned graph.
## Analysis
### DFS (recursion)
Optimization: We can combine dfsSetMap and dfsSetNeighbors to get clean code!
Time: $O(V + E)$
Space: $O(V)$
Comment
Junhao Wang
a software engineering cat | 2022-08-20 06:27:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5063683986663818, "perplexity": 2488.774341786319}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573908.30/warc/CC-MAIN-20220820043108-20220820073108-00716.warc.gz"} |
https://www.varsitytutors.com/act_math-help/how-to-find-the-domain-of-a-function?page=2 | # ACT Math : How to find the domain of a function
## Example Questions
2 Next →
### Example Question #11 : How To Find The Domain Of A Function
What is the domain of the following function?
Explanation:
The two potential concerns for domain in a standard function are negative numbers inside even-powered radicals, and dividing by zero. In this case, the radical we have is odd-powered, so having a negative result underneath the radical is fine. All we need to do, then, is avoid dividing by zero, which means avoiding a result which sums to zero under the radical. In this case, only will create this situation, so we must avoid it.
Thus, our domain is
### Example Question #12 : How To Find The Domain Of A Function
Find the domain of the following function: | 2021-12-02 19:01:47 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8163772821426392, "perplexity": 488.19304759444935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362287.26/warc/CC-MAIN-20211202175510-20211202205510-00189.warc.gz"} |
https://math.stackexchange.com/questions/1615002/three-almost-integers-of-the-form-ceh-ah-b-approx-2k-pm1 | # Three almost-integers of the form $ce^{H_a+H_b}\approx 2^k\pm1$
The approximation $$H_n\approx log(2n+1)$$ https://math.stackexchange.com/a/1602945/134791
suggests that the harmonic number for composite odd numbers might be close to the sum of the harmonic numbers for its factors.
When checking for these distances, the following results are obtained:
$$e^{H_1+H_3} \approx 17.002$$ $$2e^{H_1+H_6} \approx 63.00078$$ $$2e^{H_4+H_4} \approx 129.000186$$
although the expected numbers are $$e^{log\left(3\right)+log\left(7\right)} = 21$$ $$2e^{log(3)+log\left(13\right)} = 78$$ $$2e^{log\left(9\right)+log\left(9\right)}= 162$$
The results are far from expected, but the relationship does not seem random. The first observation $$e^{H_1+H_3} =e^{1+\frac{11}{6}}=e^{\frac{17}{6}}\approx 17.002$$ is equivalent to $$\frac{17}{log(17)}\approx6$$ which has the same form as $$\frac{163}{log(163)}\approx32$$ (equation 21 in http://mathworld.wolfram.com/AlmostInteger.html)
Similarly, $$\frac{90}{log(90)}\approx20$$ which is equivalent to $$e^{3H_2}\approx90$$
The third almost-integer appears in an expression very similar to $e^\pi-\pi$: $$2+\frac{e^{2H_4}}{2\left(log(2)+log(3)\right)}\approx 19.99909$$
Q: How can these almost-integers be explained? | 2019-08-24 08:58:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7597262263298035, "perplexity": 424.91969498616874}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027320156.86/warc/CC-MAIN-20190824084149-20190824110149-00183.warc.gz"} |
https://answers.opencv.org/questions/96585/revisions/ | # Revision history [back]
### How to Blur a Rect[] with OpenCV Java
i'm trying to blur the faces detected by the webcam. This is the code to draw the rectangle.
this.faceCascade.detectMultiScale(grayFrame, faces,1.1,2,0 | Objdetect.CASCADE_SCALE_IMAGE,new Size(this.absoluteFaceSize, this.absoluteFaceSize), new Size());
Rect[] facesArray = faces.toArray();
for(int i =0; i<facesArray.length; i++){
Imgproc.rectangle(frame, facesArray[i].tl(), facesArray[i].br(), new Scalar(0,0,255),3); }
This is the code to draw the rectangle. i tried to use this to blur
Imgproc.GaussianBlur(source, destination, new Size(55, 55), 55);
In the field source i put frame ,but in the destination field i don't know how to put the rectangle region. i tried to cast facesArray into a Mat but it doesn't work. Thanks for any help. | 2021-04-23 15:33:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24775411188602448, "perplexity": 6036.062374870034}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039594808.94/warc/CC-MAIN-20210423131042-20210423161042-00166.warc.gz"} |
http://docs.thevirtualbrain.com/_modules/tvb/interfaces/command/demos/importers/h5_import.html | # Source code for tvb.interfaces.command.demos.importers.h5_import
# -*- coding: utf-8 -*-
#
#
# TheVirtualBrain-Framework Package. This package holds all Data Management, and
# Web-UI helpful to run brain-simulations. To use it, you also need do download
# TheVirtualBrain-Scientific Package (for simulators). See content of the
# documentation-folder for more details. See also http://www.thevirtualbrain.org
#
# (c) 2012-2020, Baycrest Centre for Geriatric Care ("Baycrest") and others
#
# This program is free software: you can redistribute it and/or modify it under the
# terms of the GNU General Public License as published by the Free Software Foundation,
# either version 3 of the License, or (at your option) any later version.
# This program is distributed in the hope that it will be useful, but WITHOUT ANY
# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
# PARTICULAR PURPOSE. See the GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along with this
# program. If not, see <http://www.gnu.org/licenses/>.
#
#
# CITATION:
# When using The Virtual Brain for scientific publications, please cite it as follows:
#
# Paula Sanz Leon, Stuart A. Knock, M. Marmaduke Woodman, Lia Domide,
# Jochen Mersmann, Anthony R. McIntosh, Viktor Jirsa (2013)
# The Virtual Brain: a simulator of primate brain network dynamics.
# Frontiers in Neuroinformatics (7:10. doi: 10.3389/fninf.2013.00010)
#
#
"""
Launch an operation from the command line
.. moduleauthor:: Lia Domide <lia.domide@codemart.ro>
"""
if __name__ == "__main__":
from tvb.interfaces.command.lab import *
from tvb.core.entities.storage import dao
from tvb.core.services.operation_service import OperationService
[docs]def import_h5(file_path, project_id):
service = OperationService()
# This ID of a project needs to exists in Db, and it can be taken from the WebInterface:
project = dao.get_project_by_id(project_id) | 2020-12-01 15:38:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38471749424934387, "perplexity": 10609.288985885749}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141674594.59/warc/CC-MAIN-20201201135627-20201201165627-00020.warc.gz"} |
https://mrmackenzie.co.uk/2016/01/diffraction/ | # diffraction
###### red laser beam passing through a diffraction grating. image: en.academic.ru
Diffraction is a test for wave behaviour. When a ray of light passes through a diffraction grating, the energy of the incident beam is split into a series of interference fringes. Constructive interference is occurring at each location where a fringe (or spot) is observed because the rays are in phase when they arrive at these points.
###### image: microscopy uk
Find out about diffraction gratings here.
###### image: laserpointerforums.com
We can measure the relative positions of the fringes in a diffraction pattern to determine the wavelength of the light used. The diffraction grating equation is
$m \lambda = d \sin \theta$
where
• m is the diffracted order – some resources may use n instead of m
• λ is the wavelength
• d is the line spacing.
Here is an infrared diffraction experiment you can try at home to calculate the wavelength of the infrared LED in a remote control.
I’ve attached a set of pdf notes and questions on diffraction. These notes use n rather than m for the diffracted order.
This site uses Akismet to reduce spam. Learn how your comment data is processed. | 2022-05-27 18:32:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5812236666679382, "perplexity": 1448.5716509336542}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662675072.99/warc/CC-MAIN-20220527174336-20220527204336-00599.warc.gz"} |
https://www.vistrails.org/index.php?title=User:Tohline/vtk/ColorLookupTablea&redirect=no | # Color Lookup Tables
| Tiled Menu | Tables of Content | Banner Video | Tohline Home Page |
This presentation is intended to accompany the "Simple Cube" tutorial that we have written as an aid for individuals who are trying to fully utilize the capabilities of VisTrails in their research. It is intended to build upon the information that can be obtained from the VTK User's Guide, authored and published by Kitware, Inc.
In our accompanying discussion, we have explained how VTK's default color table can be relied upon to assign colors to POLYGONS, based on the scalar values with which each POLYGON has been labeled. Then, following an example used in the VTK User's Guide, we have explained how the user can define his/her own color table inside of an input file that adheres to the Simple Legacy Format. By way of illustration, the following short LOOKUP_TABLE has been extracted from Example E in our accompanying discussion:
```LOOKUP_TABLE my_table 8
0.0 0.0 0.0 1.0
1.0 0.0 0.0 1.0
0.0 1.0 0.0 1.0
1.0 1.0 0.0 1.0
0.0 0.0 1.0 1.0
1.0 0.0 1.0 1.0
0.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0
```
## Using VisTrail's vtkLookupTable Module
### Brute Force Definition of Color Table
As is illustrated by the following snapshot of the full VisTrails builder window, the same user-defined color table can be injected into the VisTrails rendering pipeline by using VisTrail's vtkLookupTable module.
• In the left-hand "Modules" segment of the VisTrails builder window, find the vtkLookupTable module and drag it into the pipeline segment of the window.
• Link the standard output from the vtkLookupTable module to the appropriate input channel of the vtkPolyDataMapper module, as shown.
• Click on (i.e., select) the vtkLookupTable module then locate and drag/drop the following Methods into the "Set Methods" segment of right-hand window:
• One instance of the SetNumberOfColors method.
• Eight instances of the SetTableValue method.
• CAUTION: After dropping (approximately) the third instance of SetTableValue into the "Set Methods" window, you will likely discover that the window is completely filled (as illustrated in the screen shot, below) but that VisTrails does not activate scrolling. Hence, it isn't possible to drop the fourth instance of the method below the third instance. What VisTrails expects you to do, instead, is drop all subsequent instances of the SetTableValue method onto the header bar at the top of the window segment that reads, "Set Methods." VisTrails will then insert each additional method into its proper location, at the end of the stack of activated methods.
• In keeping with the above-provided example Lookup Table, type in the following:
• Type the integer "8" into the SetNumberOfColors method window.
• In each instance of the SetTableValue method, (A) use the top "Integer" text window to label, in sequence, each color table value with the appropriate integer number, $~0 - 7$; and (B) use the four "Float" text windows to enter the assigned rgba colors.
VisTrails Screen Snapshot
The new Lookup Table that is now provided by VisTrail's vtkLookupTable module will be treated by the VisTrails pipeline as the default Lookup Table. VTK will use this new color table when rendering the POLYGONS if it is instructed to refer to the default table. This can be accomplished via an explicit instruction inside the user-provided input data file — as in Examples A, B, & C from our accompanying "Simple Cube" tutorial — or by activating the "SetLookupTableName" method in the vtkPolyDataReader module and typing the string "default" into the provided text window. This discussion should be considered a supplement to our related discussion on switching between different color tables.
### Generating a Broad Range of Color Table
Here we will illustrate how to use VisTrail's "vtkLookupTable" module to readily generate a broad range of color tables. For tutorial purposes we will use the "rainbow.vt" vistrail (see …/examples/vtk_examples/Rendering/rainbow.vt) so that immediate parallels can be drawn between our presentation and the explanation of Color Maps that is provided by Schroeder, Martin, & Lorensen (2006) — see their Figure 6-3 and the related code development presented in their §6.6 (especially pp. 196 - 197). A closely related, informative presentation can be found under the subsection labeled "Backing up -- a Colormap" within Matthew Ward's posted computer science class lecture notes at Worcester Polytechnic Institute.
Rainbow Color Maps
Snapshot of a two-by-two VisTrails spreadsheet generated using the "rainbow.vt" vistrail, for comparison with Figure 6-3 of Schroeder, Martin, & Lorensen (2006)
Rainbow image B2:
• When the "rainbow.vt" vistrail is loaded and executed without any alterations, the VisTrails pipeline will render the image that appears in the bottom right-hand corner of the above "Rainbow Color Maps" figure — as displayed, it is image B2 in the VisTrails spreadsheet. Selecting/highlighting the "vtkLookupTable" module in the initial pipeline will reveal that the color table used to generate this image was constructed by brute force, as discussed above; the Methods window contains 256 individually specified colors! (Be patient. After clicking on the "vtkLookupTable" module that exists as part of the default "rainbow" pipeline, VisTrails will spin its wheels and be unresponsive for 10 or more seconds as it loads the extensive set of methods.)
Rainbow image A2:
• The rendering that appears in the bottom left-hand corner of the above "Rainbow Color Maps" figure (i.e., VisTrails spreadsheet image A1) was generated using VTK's default color table.
• Image A2 can be generated by selecting/highlighting the "vtkLookupTable" module, deleting the "SetNumberOfColors" method and all 256 "SetTableValue" methods from the VisTrails Set Methods window, then re-executing the pipeline. (Not recommended, as this is hardly worth the effort!)
• Image A2 can more simply be generated by disconnecting the "vtkLookupTable" module from the "vtkPolyDataMapper" module then re-executing the pipeline.
• Image A2 can also be generated by disconnecting the "vtkLookupTable" module from the "vtkPolyDataMapper" module, creating (by dragging & dropping) a new "vtkLookupTable" module into the pipeline window and connecting it to the "vtkPolyDataMapper" module, then re-executing the pipeline.
Drawing on the design and capabilities of the VTK library, VisTrails' "vtkLookupTable" module most broadly facilitates the creation of color maps using HSVA (i.e., hue, saturation, value, & alpha opacity value) specifications. As Schroeder, Martin, & Lorensen (2006) explain (see p. 196), the procedure for generating lookup table entries is to define pairs of values for HSVA. These pairs define a linear ramp for hue, saturation, value, and opacity and, in turn, these linear ramps are used to generate a table with the number of table entries requested. VTK and, in turn, VisTrails, adopts the following default HSVA specifications: SetHueRange (0,2/3), SetSaturationRange (1,1), SetValueRange (1,1), & SetAlphaRange (1,1); and the default size of the color table is SetNumberOfColors(256).
Rainbow image B1:
• The rendering that appears in the top right-hand corner of the above "Rainbow Color Maps" figure (i.e., VisTrails spreadsheet image B1) was generated by VisTrails after the methods shown in the following table were activated inside the "vtkLookupTable" module.
C++ Code Using VTK Routines Directly [see p. 196 of Schroeder, Martin, & Lorensen (2006)] Equivalent VisTrails Set Methods Window ```vtkLookupTable *lut=vtkLookupTable::New(); lut->SetHueRange(0.66667, 0.0); lut->SetSaturationRange(1.0, 1.0); lut->SetValueRange(1.0, 1.0); lut->SetAlphaRange(1.0, 1.0); lut->SetNumberOfColors(256); lut->Build(); ``` ```vtkLookupTable *lut=vtkLookupTable::New(); lut->SetHueRange(0.66667, 0.0); lut->Build(); ```
Rainbow image A1:
• The rendering that appears in the top left-hand corner of the above "Rainbow Color Maps" figure (i.e., VisTrails spreadsheet image A1) was generated by VisTrails after the methods shown in the following table were activated inside the "vtkLookupTable" module.
C++ Code Using VTK Routines Directly [see p. 196 of Schroeder, Martin, & Lorensen (2006)] Equivalent VisTrails Set Methods Window ```vtkLookupTable *lut=vtkLookupTable::New(); lut->SetHueRange(0.0, 0.0); lut->SetSaturationRange(0.0, 0.0); lut->SetValueRange(0.0, 1.0); ``` | 2021-12-05 20:31:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22917872667312622, "perplexity": 4294.3203076613545}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363216.90/warc/CC-MAIN-20211205191620-20211205221620-00264.warc.gz"} |
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/annales-polonici-mathematici/all/103/2/84632/the-global-existence-of-mild-solutions-for-semilinear-fractional-cauchy-problems-in-the-alpha-norm | Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty
The global existence of mild solutions for semilinear fractional Cauchy problems in the $\alpha$-norm
Tom 103 / 2012
Annales Polonici Mathematici 103 (2012), 161-173 MSC: Primary 34K37; Secondary 26A33, 34A08. DOI: 10.4064/ap103-2-4
Streszczenie
We study the local and global existence of mild solutions to a class of semilinear fractional Cauchy problems in the $\alpha$-norm assuming that the operator in the linear part is the generator of a compact analytic $C_0$-semigroup. A suitable notion of mild solution for this class of problems is also introduced. The results obtained are a generalization and continuation of some recent results on this issue.
Autorzy
• Rong-Nian WangDepartment of Mathematics
NanChang University
NanChang, JiangXi 330031, P.R. China
e-mail
• De-Han ChenDepartment of Mathematics
NanChang University
NanChang, JiangXi 330031, P.R. China
e-mail
• Yan WangDepartment of Mathematics
NanChang University
NanChang, JiangXi 330031, P.R. China
e-mail
Przeszukaj wydawnictwa IMPAN
Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.
Odśwież obrazek | 2020-10-01 12:28:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23621849715709686, "perplexity": 4704.879835420257}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402131412.93/warc/CC-MAIN-20201001112433-20201001142433-00076.warc.gz"} |
http://tex.stackexchange.com/questions/30710/how-can-i-rotate-a-large-part-of-the-page | # How can I rotate a large part of the page?
I'm trying to "hide" and answer by rotating it 180 degrees.
Using \rotatebox works fine if I have a short answer:
\rotatebox{180}{The answer is $\pi$}
However, if I want to put a $$...$$ or maybe rotate a whole paragraph I get errors:
\rotatebox{180}{
$$\sin^2+\cos^2 = 1$$
} gives: ERROR: Missing \$ inserted.
while
\rotatebox{180}{a
b
c
}
gives: ERROR: Paragraph ended before \Grot@box@std was complete.
Is there a better command to be using? or a way to make \rotatebox work for these cases?
PS. I tried using the turn environment of rotating, but while it compiled, it didn't give the desired outcome.
PPS. I tried using the packages listed in this question....to no avail.
-
You could use a \vbox (or a \parbox or a minipage) to box the equation:
\documentclass{article}
\usepackage{graphicx,amsmath}
\begin{document}
\noindent\rotatebox{180}{\vbox{%
$$\sin^2+\cos^2 = 1$$}%
}
\end{document}
-
You can use the adjustbox package for this:
\begin{adjustbox}{minibox=\textwidth,angle=180}
% ... | 2015-11-28 05:54:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 3, "x-ck12": 0, "texerror": 0, "math_score": 0.7806141972541809, "perplexity": 3292.0843834796524}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398451648.66/warc/CC-MAIN-20151124205411-00236-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://artofproblemsolving.com/wiki/index.php?title=2010_AMC_10B_Problems/Problem_18&diff=prev&oldid=91190 | # Difference between revisions of "2010 AMC 10B Problems/Problem 18"
## Problem
Positive integers $a$, $b$, and $c$ are randomly and independently selected with replacement from the set $\{1, 2, 3,\dots, 2010\}$. What is the probability that $abc + ab + a$ is divisible by $3$?
$\textbf{(A)}\ \dfrac{1}{3} \qquad \textbf{(B)}\ \dfrac{29}{81} \qquad \textbf{(C)}\ \dfrac{31}{81} \qquad \textbf{(D)}\ \dfrac{11}{27} \qquad \textbf{(E)}\ \dfrac{13}{27}$
## Solution 1
First we factor $abc + ab + a$ as $a(bc + b + 1)$, so in order for the number to be divisible by 3, either $a$ is divisible by $3$, or $bc + b + 1$ is divisible by $3$.
We see that $a$ is divisible by $3$ with probability $\frac{1}{3}$. We only need to calculate the probability that $bc + b + 1$ is divisible by $3$.
We need $bc + b + 1 \equiv 0\pmod 3$ or $b(c + 1) \equiv 2\pmod 3$. Using some modular arithmetic, $b \equiv 2\pmod 3$ and $c \equiv 0\pmod 3$ or $b \equiv 1\pmod 3$ and $c \equiv 1\pmod 3$. The both cases happen with probability $\frac{1}{3} * \frac{1}{3} = \frac{1}{9}$ so the total probability is $\frac{2}{9}$.
Then the answer is $\frac{1}{3} + \frac{2}{3}\cdot\frac{2}{9} = \frac{13}{27}$ or $\boxed{E}$.
## Solution 2
We see that since $2010$ is divisible by $3$, the probability that any one of $a$, $b$, or $c$ being divisible by $3$ is $\frac{1}{3}$. Because of this, we can shrink the set of possibilities for $a$, $b$, and $c$ to the set $\{1,2,3\}$ without affecting the probability in question.
Listing out all possible combinations for $a$, $b$, and $c$, we see that the answer is $\bold{\boxed{\left( E\right) \frac{13}{27}}}$. | 2022-07-03 08:46:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 43, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8862956762313843, "perplexity": 58.60134541774711}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104215805.66/warc/CC-MAIN-20220703073750-20220703103750-00130.warc.gz"} |
http://openstudy.com/updates/4e698ea70b8b4a2b95d1c756 | ## m.schueyy Group Title Snooker is a kind of pool or billiards played on a 6-foot-by-12-foot table. the side pockets are halfway down the rails (longside) |------| | |12 | | | | |------| 6 Find the distance, to the nearest tenth of an inch, diagonally across from the corner pocket to side pocket 2 years ago 2 years ago
1. Owlfred Group Title
is someone coming?
2. m.schueyy Group Title
|dw:1315540787959:dw|
3. m.schueyy Group Title
huh
4. iamtheos Group Title
you know the "long side" is 12 ft long so half way must be 6ft long or 72 inches. the "short side" is 6ft long also so it is 72 inches as well. so using a^2 + b^2 = c^2 you can solve for the missing side "c" in inches. so 72^2 + 72^2 = C^2 or the square root of 10368 inches.
5. robtobey Group Title
$\sqrt{2*6^2}=6 \sqrt{2}= 8.49 \text{ ft} = 101.88 \text{ inches}$
6. iamtheos Group Title
i don't think he knows the properties of a 45, 45, 90 triangle yet... :/ | 2014-08-27 23:03:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49886518716812134, "perplexity": 3204.7693234840813}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500829916.85/warc/CC-MAIN-20140820021349-00149-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://koreascience.kr/article/JAKO201321963619673.page | # 이중열원을 이용한 전기자동차용 히트펌프 시스템의 난방 성능 특성에 관한 연구
• Woo, Hyoung Suk (Graduate School of Mechanical Engineering, Korea University) ;
• Ahn, Jae Hwan (Graduate School of Mechanical Engineering, Korea University) ;
• Oh, Myoung Su (Graduate School of Mechanical Engineering, Korea University) ;
• Kang, Hoon (Division of Mechanical Engineering, Korea University) ;
• Kim, Yongchan (Division of Mechanical Engineering, Korea University)
• 우형석 (고려대학교 기계공학부 대학원) ;
• 안재환 (고려대학교 기계공학부 대학원) ;
• 오명수 (고려대학교 기계공학부 대학원) ;
• 강훈 (고려대학교 기계공학부) ;
• 김용찬 (고려대학교 기계공학부)
• Published : 2013.04.10
#### Abstract
An electric vehicle is an environment-friendly automobile which does not emit any tailpipe pollutant. In a conventional vehicle with an internal combustion engine, the internal cabin of the vehicle is usually heated using waste heat from the engine. However, for an electric vehicle, an alternative solution for heating is required because it does not have a combustion engine. Recently, a heat pump system which is widely used for residential heating due to its higher efficiency has been studied for its use as a heating system in electric vehicles. In this study, a heat pump system utilizing air source and waste heat source from electric devices was investigated experimentally. The performance of the heat pump system was measured by varying the mass flow rate ratio. The experimental results show that the heating capacity and COP in the dual heat source heat pump were increased by 20.9% and 8.6%, respectively, from those of the air-source heat pump.
#### Acknowledgement
Supported by : 한국산업기술평가관리원, 한국에너지기술평가원
#### References
1. Antonijevic, D. and Heckt, R., 2004, Heat pump supplemental heating system for motor vehicles, Proc. the Institution of Mechanical Engineers, pp. 1111-1115.
2. Hosoz, M. and Direk, M., 2006, Performance evaluation of an integrated automotive air conditioning and heat pump system, Energy conversion and management, Vol. 47, pp. 545-559. https://doi.org/10.1016/j.enconman.2005.05.004
3. Cho, Y. D., Si, J. M., Lee, K. C., and Han, C. S., 2004, Study of heat pump system for automotive, Proceedings of the SAREK, pp. 536-541.
4. Lee, H. S., Won, J. P., Cho, C. W., Kim, Y. C., and Lee, M. Y., 2012, Heating performance characteristics of stack coolant source heat pump using R744 for fuel cell electric vehicles, Journal of Mechanical Science and Technology, Vol. 26, pp. 2065-2071. https://doi.org/10.1007/s12206-012-0516-2
5. Kim, S. C., Kim, M. S., Hwang, I. C., and Lim, T. W., 2007, Heating performance enhancement of a $CO_2$ heat pump system recovering stack exhaust thermal energy in fuel cell vehicles, International Journal of Refrigeration, Vol. 30, pp. 1215-1226. https://doi.org/10.1016/j.ijrefrig.2007.02.002
6. Cho, C. W., Lee, H. S., Won, J. P., and Lee, M. Y., 2012, Measurement and evaluation of heating performance of heat pump system using wasted heat of electric devices for an electric bus, Energies 5, pp. 658-669. https://doi.org/10.3390/en5030658
7. ASHRAE Standard 37-78, 1978, Methods of testing for rating unitary air conditioning and heat pump equipment.
8. ASHRAE Standard 51-75, 1975, Laboratory methods of testing fans for rating.
9. Korean Standards Association, 2003, KS air-conditioner: KS C 9306.
#### Cited by
1. An Experimental Study on the Heating Performance Characteristics of a Vapor Injection Heat Pump for Electric Vehicles vol.26, pp.7, 2014, https://doi.org/10.6110/KJACR.2014.26.7.308
2. Experimental study on the heat pump system using R134a refrigerant for zero-emission vehicles vol.16, pp.6, 2015, https://doi.org/10.1007/s12239-015-0094-2
3. Progress in Heat Pump Air Conditioning Systems for Electric Vehicles—A Review vol.9, pp.4, 2016, https://doi.org/10.3390/en9040240 | 2022-08-18 11:01:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5920539498329163, "perplexity": 11343.278334975223}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573193.35/warc/CC-MAIN-20220818094131-20220818124131-00330.warc.gz"} |
https://puzzling.stackexchange.com/questions/42994/what-is-a-single-word | # What is a Single Word™?
This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles.
If a word conforms to a special rule, I call it a Single Word™.
Use the following examples below to find the rule.
And, if you want to analyze, here is a CSV version:
Single Words™, Non Single Words™
water, food
bear, grizzly
beeswax, honey
zebra, horse
deer, buck
rat, mouse
cat, feline
mom, mother
you, me
• Can you confirm that mouse is Non single??? – greenturtle3141 Sep 22 '16 at 22:16
• @greenturtle3141 yes mouse is non single – Alex Sep 23 '16 at 16:16
• Aw... I really thought that single words were words containing a letter with a different height from the others. – greenturtle3141 Sep 23 '16 at 17:38
• @greenturtle3141 i didn't realize i was so close to fit with another rule! – Alex Sep 23 '16 at 22:32
A Single Words™ looks like one which
Is typed using just one hand with a standard keyboard touch typing method
Left hand letters are Q, W, E, R, T , A, S, D, F, G , Z, X, C, V, B
Right hand letters are Y, U, I, O, P , H, J, K, L , N, M
And the Non Single Words™ need both hands to touch type.
• Nicely Done! This is the answer – Alex Sep 23 '16 at 16:17
I'm not at all sure that I understand the rationale, but, a Non Single word is
one that contains at least one of the letters f, g, h, i, j, k, l and/or n,
and/or contains both letters m and e.
A Single word, obviously, is one that does not conform to the above rule.
My best guess is that it has something to do with the first-person singular pronouns, "I" and "me" — something like
it's not single if I'm there with it
?
The letters f, g, h, i, j, k, l and n are the letters between e and o, which are the last vowel before i and the first vowel after i.
Yes, I know there are no words in the table that contain j. Or p, q, or v. I assume that's just to avoid making it too easy.
• My experience is that answers like this are (usually) frowned upon. – Matsmath Sep 23 '16 at 7:19 | 2020-10-21 10:37:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6028436422348022, "perplexity": 1792.2297587270473}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107876307.21/warc/CC-MAIN-20201021093214-20201021123214-00122.warc.gz"} |
http://lambda-the-ultimate.org/node/4996 | ## Slots as reifications of OOP method names
I've sketched some ideas about slot-based interfaces as a way to turn method names into first-class citizens of the language, with an example of the resulting framework as applied to C++:
"Objects, slots, functors, duality "
The key idea is to treat objects as polymorphic functors and regard a method call like
x.foo(arg1,...,argn)
as an invocation of x where the first parameter (the slot) is an entity indicating the particular method called upon:
x(foo,arg1,...,argn)
If we now define a slot as a generalized functor accepting objects as their first parameter and with the following semantics:
foo(x,arg1,...,argn) --> x(foo,arg1,...,argn)
then objects and slots become dual notions, and many interesting patterns arise around method decoration, smart references, etc.
I wonder if these ideas have been already explored in a more general setting than the toy framework described here.
## Comment viewing options
### multi methods
Why treat the 'first' argument as special? This limitation is one of the annoying limitations in OO programming, could this be extended to treat all arguments equally?
### message passing
I'm a fan of multiple dispatch, but there is motivation for the first argument to be special when dealing with OOP.
In short, OOP is a highly constrained emulation of independent collaborating stateful machines. When that is appropriate, so is single-dispatch, since you're "sending a message" to a particular machine. You may even want to forward the message to another machine on your behalf. In that case, you can really think of a method call as having two arguments: a recipient and a message body.
Of course, you can encode this mechanism using multi-dispatch. Here, it seems like JoaquÃn is talking about encoding this mechanism via the equivalence of objects and closures. There are many examples of encoding objects as closures which take a quoted symbol as a method name, but one could easily strip the quote and define such a symbol to resolve to a reified "method" object. The closure (or object) and the method identifier would both implement a "Callable" interface.
### Nested Visitors
I keep having to implement nested visitors for binary operators that can have arguments of different types. Implementing unification is a classic example, but any binary operation on abstract syntax trees has the same problem. I always dislike the idea that one of the objects is special, should a purchase order object be passed to an account, or vice-versa.
### Agree, but...
I agree: Proper multiple dispatch is much nicer than single-dispatch. I even said I was a fan, but that wasn't my point: My point was that single-dispatch makes sense when emulating sending messages to collaborating machines. I don't dislike "objects", but I dislike programming in a style *oriented* by objects. When you do want to couple state and behavior to emulate communicating processes, single dispatch makes sense. For most everything else, multiple-dispatch functions unassociated with classes or instances makes much more sense.
### The power of the dot
Well, code completion is quite biased to single dispatch, and as a UX problem, no one has really figured out what completion over multiple arguments would even look like.
### dispatch & syntax are independent
You can have noun.verb(args...), or any other noun-before-verb syntax without requiring any particular dispatch mechanism. Look no further than Visual Studio's Intellisense support for F#'s pipeline operator (|>). The offered completion list is derived from a search for functions (not methods!) with a matching first parameter type.
Unrelated: I'm all about better tools, but I find pervasive code completion to be very distracting.
### targeting computers vs. "the force"
My point was that no one has figured out how to do code completion on multiple parameter types yet. It is more a challenge of syntax rather than tooling; i.e. how can we specify parameters we wish to dispatch on before the function doing the dispatching. It doesn't really work just to put the parameters first, as that would mess up normal programming flow (see using a stack-oriented language like Forth).
Also F#'s solution is nice, but only works well for OO-styled functions where the first parameter is special as a receiver. Of course, I'm a firm believer that OO-style is pervasive even in most FP languages, but given a language like Haskell where that isn't really true, all bets are off. (And Haskell is a very strange instance of a sophisticated typed language with poor tooling)
Unrelated: I'm all about better tools, but I find pervasive code completion to be very distracting.
I bet you probably don't like using GPS in your car either :) Many people buy into the "use the force, turn off your targeting computer" thing, I don't.
### Clarifying "pervasive"
What I really mean is that I dislike how autocomplete pops up every time you type "." in an appropriate place. For similar reasons, I dislike the red-squiggly underlining in word processors. I also prefer muted color schemes.
I find anything the computer is doing while I'm typing to be distracting. It's like trying to talk to somebody, only to have them interrupt mid sentence and be like "I know what you were going to say!" They might be right, but they might also prevent me from ever saying what I was actually going to say.
As for things like squiggly underlines and gutter markings: I wish they were only available on demand. I don't care if I spelled anything right until I get the idea out. I don't care if my code will compile, until I have the general structure or algorithm jotted down.
When I've used Visual Studio (and IntelliJ) in the past for C# (and Java), I tend to also use Vim for most of my work, only switching over to the IDE for refactoring, code analysis, specialized searches, etc. I tend to use the IDE in a manner similar to a linter. Funny enough, I only started doing this because I was not only *using* Visual Studio, but working on Xbox integration for it while at Microsoft. Running two instances at once was a pain, so I started using Vim, and found that I felt more focused in that context.
If it were up to me, I'd live in my distraction-free editor and have my bells-and-whistles code analyzer tools be one keystroke away.
Also, I realize your GPS comment was a joke, but I want to point out the distinction: Driving and navigating are largely non-creative tasks. There's no deep thought process to interrupt, other than maybe some road hypnosis.
### Autocomplete HCI
There are a number of ways to do autocompletion. I personally like using the tab key for this purpose: when I press tab, give me my autocomplete options.
This is really quite orthogonal to Sean's belief that noun-verb order is somehow better for autocompletion.
### have vs want
One other comment about the noun-verb order:
Completion for verbs in noun.verb is based on what you "have" and offers you choices of what you can get from that.
However, completion for verbs in verb(noun) form could be based on return type. That is, you "want" something and are offered ways to get that thing.
The thing is that the former has a non-meta key to listen for, namely the "." where as the latter would have to listen for an explicit "return" keyword or something like that.
### You can't really complete on
You can't really complete on an expected type given the way most of us think. For that to work, you have to think from order of "what you want" to "how you can get it," but people often think from "what they have" to "what they can get!"
Thinking order is where functional and OO styles really diverge, especially in syntax. The OO programmer works left to right, starting with something to get or do something else. So they have x and can get P from x via "x.P." The functional style instead focuses on P and how you get it with x via "P(x)." Fascinating actually.
### You can't really complete on
You can't really complete on an expected type given the way most of us think. For that to work, you have to think from order of "what you want" to "how you can get it," but people often think from "what they have" to "what they can get!"
Thinking order is where functional and OO styles really diverge, especially in syntax. The OO programmer works left to right, starting with something to get or do something else. So they have x and can get P from x via "x.P." The functional style instead focuses on P and how you get it with x via "P(x)." Fascinating actually.
### Huh?
You can't really complete on an expected type given the way most of us think.
IntelliJ supports completion based on type-context:
Smart Type Code Completion
Seems like that works just fine... Frankly, that better matches the way I think...
For that to work, you have to think from order of "what you want" to "how you can get it," but people often think from "what they have" to "what they can get!"
The point I was making was that there are two different thought patterns with two different completion mechanisms. There's no reason that you couldn't have a common shortcut which presents the intersection of both methods. You should have multiple ways to think about a problem in order to figure out the best solution, but you shouldn't have two different ways to invoke completion.
Thinking order is where functional and OO styles really diverge, especially in syntax. The OO programmer works left to right, starting with something to get or do something else. So they have x and can get P from x via "x.P." The functional style instead focuses on P and how you get it with x via "P(x)." Fascinating actually.
Which is why this entire first-class method thing is interesting to begin with. You don't have to choose noun.verb() over verb(noun) because you can view "." as an application operator.
In Clojure, which is what I work in most of the time lately, keywords (self-evaluating symbols) are functions of associative structures, and associative structures are functions of their keys. This way you can (person :first-name) or (:first-name person). And the -> macros let you choose the most appropriate noun/verb order for your problem. So you can (-> db (get-person 5) :first-name) or (:first-name (:get-person db 5)) or whatever combination works for you. The ->> macro lets you do the same with the *last* argument.
The more interesting distinction isn't noun then verb or verb then noun. It's what vs how. In a stack language, for example, instructions are executed linearly from left to right. Here's "how" to get a result in a sequence of steps. In a functional language (with applicative order) arguments are evaluated inside out. Here's "what" I want from these inputs. The arrow macros in Clojure (or the pipeline operator in F#, etc) let me choose, on a per-expression basis, if I want to emphasize evaluation order or results. The language and the tools should (and can!) support both styles seamlessly.
### I don't think having two
I don't think having two ways to express the same thing is really the answer. Multi-identifier auto completion is a good answer, but it skips a lot of steps and might not be always viable for anything but static member access.
Also, does Clojure even support auto completion? Its not exactly a language with a friendly syntax to grock.
### does Clojure even support
does Clojure even support auto completion?
As a language, it doesn't do anything special to encourage completion (such as manifest types), but it sure avoids a lot of things it might do to discourage it (eg. dynamic meta-programming).
As for the current state of Clojure tools: Completion of top-levels is trivial and common in Clojure tools. Completion of locals is less common, but readily available from the analyzer API. Completion based on type information or similar isn't available yet as far as I know, but the type hint system (or the more sophisticated Typed Clojure) could conceivably enable it with some effort.
However, if I were to attempt auto-completion for Clojure, I'd also invest in abstract interpretation. That's how JavaScript completion generally works (in combination with type inference), and Clojure is much more amenable to static analysis than JavaScript.
Its not exactly a language with a friendly syntax to grock.
Not going to take the Lisp syntax flame bait... It suffices to say that I quite enjoy Clojure's syntax.
### Abstract interpretation
Abstract interpretation hasn't worked so well for Javascript, which is why we are getting Dart and Typescript, which is probably more analogous to typed clojure.
Not going to take the Lisp syntax flame bait... It suffices to say that I quite enjoy Clojure's syntax.
It is difficult to grock Clojure syntax without knowing Clojure, fair enough? Great if you are insider, bad if you are an outsider.
### Dart & TypeScript
TypeScript et al are motivated by much more than just editor support.
Not saying that TypeScript doesn't facilitate better editor functionality more easily (it does). Just that abstract interpretation has in fact worked just fine for JavaScript to the caliber expected of contemporary IDEs. In fact, IntelliJ's JavaScript support is richer than Visual Studio's TypeScript support, from what I can tell... For now.
### Typescript and Dart are all
Typescript and Dart are all about tooling and not really just about type checking...it's the new upcoming view that type systems are not just about detecting type errors anymore; if anything code completion is more important and soundness be damned.
We had abstract interpretation also, it just isn't good enough to satisfy most developers. You get into an intractable global analysis very quickly and your type feedback still isn't that great.
### I for one like the "clack"
I for one like the "clack" of my model M, it doesn't bother me because I expect it, if I don't here it, then I would be worried. For identifiers in progress, I expect them to "not found," and I expect completions to be there. There is stuff on the screen that I totally expect, its not annoying, it is already part of my rhythm in writing code. It does take some getting used to, just like driving with a GPS does, but done right you can eventually get used to it.
I find Visual Studio's 500 millisecond delay for feedback to be extremely annoying. I want my clack "now" not later. Bad feedback is not with you, but behind you. If the computer only recognizes mis-spelled word after 500 ms, that screws up my rhythm and is annoying; no feedback is better than late feedback! Visual Studio is an example of feedback done wrong. Most IDEs follow that given some misguided user research (don't feedback right away, it will bother the user who isn't used to it!). Victor shows us that feedback can be magical if done right.
To quote Hancock, on demand feedback is like shooting with bow and arrow, continuous timely feedback is like shooting with a water hose. Some people are more comfortable with bow and arrows, but you'll hit the target faster with a water hose.
word.
### Stack based languages with
Stack based languages with well defined types, such as Cat or Joy, should enable a lot of type-driven autocompletion based on the types known to be in the tacit environment, along with automatic visualization of the tacit environment. Sadly, this hasn't really been explored.
I'm not sure what you mean by "normal programming flow".
Stack based languages don't feel any more or less natural to me at this point, though they were unfamiliar to start. Stack based programming does emphasize bottom-up rather than top-down, but this seems natural in its own way.
### The problem with stack
The problem with stack languages is that you have to keep track of the stack in your head; making arguments implicit in some stack state is quite difficult to deal with. Perhaps you could make that easier via the IDE, but I haven't seen any decent proposals yet, nor is anyone really seriously looking at stack based languages beyond Chuck Moore.
### stack mentality
The problem with stack languages is that you have to keep track of the stack in your head;
Traditionally they say that if you have a real problem like that your definitions are too complicated and you ought to break them up.
Tradition aside: is that problem more than an aesthetic one? How do we know?
### You can leave things on the
You can leave things on the stack for multiple instructions, duplicate, and so on. You have to understand multiple lines of code to understand one line of code, whereas at least in a normal language you have the names of local variables to help in reading.
### in a normal language you
in a normal language you have the names of local variables to help in reading
In a concatenative language, you tend to refactor complicated functions into a few sub-functions. Then function names help you in reading. This works pretty well, though automatic visualization of the stack would also be nice.
### Keeping track of the stack
Keeping track of the stack should be easy to automate and render to screen, not much different than the sort of continuous feedback you expect from any good IDE for a typeful language.
Re: "I haven't seen any decent proposals yet" - How hard have you looked for decent proposals? As is, simply printing the stack at each step in a REPL isn't bad, and we could do a lot better for continuous feedback at edit time just by running code (and printing stacks) against a set of examples or tests. This seems very similar to more conventional language adaptations of REPLs to live programming.
Re: "nor is anyone really seriously looking at stack based languages" - I am. And I know of others. Granted, it isn't a very popular area. But I seriously consider tacit concatenative languages the most promising basis for both streaming code and generative programming, and a good fit for a code-as-material metaphor and component based programming. My own language isn't quite stack-based, but it's close in nature.
### I do look you know...and I
I do look you know...and I haven't seen much...especially in the area of IDE support for stack-based languages (well, there is color forth). There just isn't very much work on concatenative languages being done, less that is published in a way that I can really soak it in. If I could see some advantage to be had, I would be all over it, but I don't see it right now.
### DCI
I always dislike the idea that one of the objects is special, should a purchase order object be passed to an account, or vice-versa.
False dichotomy. Another choice is to model a purchase as an interaction or process independent of the documents and accounts that participate. Look into DCI (data context interaction).
I used to model visitors a lot, but at some point I changed how I approached problems and the visitors just disappeared. I think it's when I started favoring object capability model patterns, which in general don't use class information and operate only at the interface level.
### DCI
I guess in many languages like Python with no real data-hiding, objects behave like a plain old 'C' structs, and with duck-typing you can operate on objects of different types, so DCI makes some sense. You will end up using conditional statements to specialise behaviour which is slower than virtual method dispatch, so multi-methods offer a better performance guarantee (note 'guarantee', I am sure a sufficiently clever compiler could optimise the conditionals to a vm-table dispatch if you get the incantation just right, but I prefer a hard guarantee).
If I want strong data-hiding, and strong typing (with parametric polymorphism) I need modules to replace objects for data hiding, otherwise every object gets getter/setters for every property; and I need multi-methods to replace duck-typing.
In the case of the visitor, this is because I am writing many processes that descend abstract-syntax-trees, where nodes are different subclasses. I can't see how DCI helps here (although keeping each process state in the visitor is quite DCI like). This is particularly ugly when doing binary operations on ASTs (nested visitors). Multi-methods seem necessary for doing this neatly.
### Well, the intention is not
Well, the intention is not to cover multimethods here, but explore the arising patterns around, as Brandon puts it very succintly, treating both objects and method names as closures or callable entities. For instance, within this framework it is very simple to decorate an object x to, say, log each method invocation on x, and, given the duality between objects and method names, the same logging decorator can be used with a particular method name foo to register calls of the form y(foo,...).
That said, a potential approach to covering multimethods could be to treat sets of multidispatched objects as closures themselves. For instance, restricting ourselves to binary methods we can define a binary slot as a slot dealing with product type values and presenting the following semantics:
foo(x*y,arg1,...argn) --> (x*y)(foo,arg1,...,argn)
where the default product of objects can dispatch to its first component:
(x*y)(foo,arg1,...argn) --> x(foo,y,arg1,...arg)
or something else that users can later override. Just thinking out loud here.
### Sure
Craig Chambers' Cecil and Diesel treat all arguments as equal. Personally, I don't think the added complexity of multiple dispatch is worth the headaches.
Hi guys,
Interesting as the discussions on IDE autocompletion are, they're not really related to the OT, which deals with reification of method names as callable entities... I'd appreciate if I can get some feedback on that front :-) Thank you!
### Signals and Slots
Is this in any way related to signals and slots in the Qt or GTK gui libraries?
### Nothing to do with slots
Is this in any way related to signals and slots in the Qt or GTK gui libraries?
I don't think so. The name "slot" means here "reified method name", nothing to do with slots in signal frameworks...
Let me elaborate a bit: in the statement
x.foo(1);
x and 1 are run-time entities of the program (an object variable and a constant), but foo is merely a source-code-level identifier for a particular method x has. If we replace the statement with the "slotified"
x(foo,1);
we're treating foo as a first-class citizen (i.e. an entity of the program); moreover, if we define it to be a functor with some duality properties we can write this in an equivalent manner:
foo(x,1); // --> x(foo,1) ~ x.foo(1)
which opens up possibilities around method decoration and others explained at the article referred to in my original post.
### Passing Slots
So the purpose is not to be able to pass a 'slot' to another method so it can use it generically? Because it would seem to enable that kind of thing if the functor 'foo' were first class it could passed as an argument and be used as a signal from some process, with a list of objects that have that slot as the receivers.
### So the purpose is not to be
So the purpose is not to be able to pass a 'slot' to another method so it can use it generically?
The framework explores ideas of decoration among which, well, we can consider too composition of objects or methods. For instance, a sort of (compile-time) signals setup can be built if we create sets of receivers {x1,...,xm} with the following semantics:
{x1,...,xm}(foo, argn1,...,argn) --> {foo(x1,arg1,...,argn),...,foo(xm,arg1,...,argn)}
which further reduces (from the properties of foo as a slot) to
{x1(foo,arg1,...,argn),...,xm(foo,arg1,...,argn)}
At the end of the day, this is merely mapping foo(_,arg1,...,argn) over {x1,...,xm}. But, as I was saying, this is just one application of this "method names as functors" approach, not the only one. | 2018-10-19 15:13:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.36346787214279175, "perplexity": 1939.9777720179345}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512411.13/warc/CC-MAIN-20181019145850-20181019171350-00504.warc.gz"} |
https://learn.careers360.com/ncert/question-an-isosceles-triangle-has-perimeter-30-cm-and-each-of-the-equal-sides-is-12-cm-find-the-area-of-the-triangle/ | # Q6. An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
R Ritika Kankaria
The perimeter of an isosceles triangle is 30 cm (Given).
The length of the sides which are equal is12 cm.
Let the third side length be 'a cm'.
Then, $Perimeter = a+b+c$
$\Rightarrow 30= a+12+12$
$\Rightarrow a = 6cm$
So, the semi-perimeter of the triangle is given by,
$s= \frac{1}{2}Perimeter =\frac{1}{2}\times30cm = 15cm$
Therefore, using Herons' Formula, calculating the area of the triangle
$A = \sqrt{s(s-a)(s-b)(s-c)}$
$= \sqrt{15(15-6)(15-12)(15-12)}$
$= \sqrt{15(9)(3)(3)}$
$= 9\sqrt{15}\ cm^2$
Hence, the area of the triangle is $9\sqrt{15}cm^2.$
Exams
Articles
Questions | 2020-04-06 02:22:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8444309830665588, "perplexity": 759.5103917280037}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371612531.68/warc/CC-MAIN-20200406004220-20200406034720-00273.warc.gz"} |
http://googology.wikia.com/wiki/User_blog:Googleaarex/A_new,_really_strong_OCF_definition%3F | 10,828 Pages
Definition
$$D[0]$$ is least cardinality and $$D[\alpha+1]$$ is greater cardinality than $$D[\alpha]$$. Also, $$D[\alpha[D_0]]$$ is similar to weakly inaccessible cardinals in OCFs, which:
• $$\psi_{D[\alpha[D_0]]}(0)[1]$$ = $$D[\alpha[1]]$$
• $$\psi_{D[\alpha[D_0]]}(0)[n]$$ = $$D[\alpha[\psi_{D[\alpha[D_0]]}(0)[n-1]]]$$
• $$\psi_{D[\alpha[D_0]]}(\beta+1)[1]$$ = $$D[\alpha[\psi_{D[\alpha[D_0]]}(\beta)+1]]$$
• $$\psi_{D[\alpha[D_0]]}(\beta+1)[n]$$ = $$D[\alpha[\psi_{D[\alpha[D_0]]}(\beta)+\psi_{D[\alpha[D_0]]}(\beta+1)[n-1]]]$$
Then a new definition happen to prove it WAY stronger:
• $$D[\alpha[\beta[D[\alpha[D_{\gamma+1}]]]]]$$ can be reduced to $$D[\alpha[\beta[D_{\gamma}]]]$$, where $$\beta$$ must be less than $$D_{\gamma+1}$$ and $$\gamma$$ > 0.
• Do not follow the rule if $$\beta$$ is a cardinal that does not have the fundamental sequence.
I named the notation $$D[\alpha]$$ as Dropper Ordinal Notation and named $$D_n$$ as (1+n)th dropper cardinal.
Rules
Now here is OCF expansion rules:
• $$\psi_{D[0]}(0)[1]$$ = $$\omega$$
• $$\psi_{D[0]}(0)[n]$$ = $$\omega^{\psi_{D[\alpha]}(0)[n-1]}$$
• $$\psi_{D[0]}(\alpha+1)[1]$$ = $$\psi_{D[0]}(\alpha)$$
• $$\psi_{D[0]}(\alpha+1)[n]$$ = $$\psi_{D[0]}(\alpha)^{\psi_{D[0]}(\alpha+1)[n-1]}$$
• $$\psi_{D[0]}(\alpha)[\beta]$$ = $$\psi_{D[0]}(\alpha[\beta])$$
• $$\psi_{D[\alpha+1]}(0)[1]$$ = $$D[\alpha]$$
• $$\psi_{D[\alpha+1]}(0)[n]$$ = $$D[\alpha]^{\psi_{D[\alpha+1]}(0)[n-1]}$$
• $$\psi_{D[\alpha+1]}(\beta+1)[1]$$ = $$\psi_{D[\alpha+1]}(\beta)$$
• $$\psi_{D[\alpha+1]}(\beta+1)[n]$$ = $$\psi_{D[\alpha+1]}(\beta)^{\psi_{D[\alpha+1]}(\beta+1)[n-1]}$$
• $$\psi_{D[\alpha+1]}(\beta)[\gamma]$$ = $$\psi_{D[\alpha+1]}(\beta[\gamma])$$
• $$\psi_{D[\alpha[D_0]]}(0)[1]$$ = $$D[\alpha[1]]$$
• $$\psi_{D[\alpha[D_0]]}(0)[n]$$ = $$D[\alpha[\psi_{D[\alpha[D_0]]}(0)[n-1]]]$$
• $$\psi_{D[\alpha[D_0]]}(\beta+1)[1]$$ = $$D[\alpha[\psi_{D[\alpha[D_0]]}(\beta)+1]]$$
• $$\psi_{D[\alpha[D_0]]}(\beta+1)[n]$$ = $$D[\alpha[\psi_{D[\alpha[D_0]]}(\beta)+\psi_{D[\alpha[D_0]]}(\beta+1)[n-1]]]$$
• $$\psi_{D[\alpha[D_0]]}(\beta)[\gamma]$$ = $$\psi_{D[\alpha[D_0]]}(\beta[\gamma])$$
• $$\psi_{\alpha}(\beta[\alpha])[1]$$ = $$\psi_{\alpha}(\beta[1])$$
• $$\alpha$$ must be an element of $$D[\beta]$$.
• $$\psi_{\alpha}(\beta[\alpha])[n]$$ = $$\psi_{\alpha}(\beta[\psi_{\alpha}(\beta[\alpha])[n-1]])$$
• $$\alpha$$ must be an element of $$D[\beta]$$.
• $$D[\alpha[\beta[D[\alpha[D_{\gamma+1}]]]]]$$ can be reduced to $$D[\alpha[\beta[D_{\gamma}]]]$$, where $$\beta$$ must be less than $$D_{\gamma+1}$$ and $$\gamma$$ > 0.
• Do not follow the rule if $$\beta$$ is a cardinal that does not have the fundamental sequence.
Fundamental sequences
This is real one to define Dropper Ordinal Notation with fundamental sequences.
• $$\psi_{D[0]}(0)$$ = $$sup\{\omega,\omega^{\omega},\omega^{\omega^{\omega}},...\}$$
• $$\psi_{D[\alpha+1]}(0)$$ = $$sup\{\psi_{D[\alpha]}(0)+1,\omega^{\psi_{D[\alpha]}(0)+1},\omega^{\omega^{\psi_{D[\alpha]}(0)+1}},...\}$$
• $$\psi_{D[A]}(\beta+1)$$ = $$sup\{\psi_{D[A]}(\beta)+1,\omega^{\psi_{D[A]}(\beta)+1},\omega^{\omega^{\psi_{D[A]}(\beta)+1}},...\}$$, only if $$A$$ = 0 or $$\alpha+1$$
More coming soon!
Reduced rules
Now here is the rules using logic:
• $$A_0(\alpha,\beta)$$ = $$\{0\}\cup_{\gamma<\beta}D[\gamma]$$
• $$A_n(\alpha,\beta)$$ = $$\{\gamma+\delta:\gamma,\delta\in A_{n-1}(\alpha,\beta)\}\cup\{\omega^{\gamma}:\gamma\in A_{n-1}(\alpha,\beta)\}$$
• $$A(\alpha,\beta)$$ = $$\cup_{\gamma<\omega}A_{\gamma}(\alpha,\beta)$$
Analysis
You can find an analysis of this OCF vs other OCFs here. | 2017-08-20 03:59:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9418109655380249, "perplexity": 1100.294526323694}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105970.61/warc/CC-MAIN-20170820034343-20170820054343-00287.warc.gz"} |
https://www.transtutors.com/questions/9-the-difference-between-the-balance-of-a-plant-asset-account-and-the-related-contra-1358275.htm | # 9. The difference between the balance of a plant asset account and the related contra-asset...
9. The difference between the balance of a plant asset account and the related contra-asset account is termed: (a) expired cost, (b) accrual, (c) book value, (d) depreciation, (e) none of the above.
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you just need to work on Assignment 1 Question part 1 and part 2 files others files are only just sample solutions for tutore helpHow much?deadline 8 hours | 2018-07-23 11:17:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24534285068511963, "perplexity": 4625.023488677149}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676596336.96/warc/CC-MAIN-20180723110342-20180723130342-00277.warc.gz"} |
https://gateoverflow.in/463/gate2008-51 | 2.4k views
Match the following:
E. Checking that identifiers are declared before their use P. $L \: = \: \left\{a^nb^mc^nd^m \mid n\: \geq1, m \geq 1\right\}$ F. Number of formal parameters in the declaration of a function agrees with the number of actual parameters in a use of that function Q. $X\: \rightarrow XbX \mid XcX \mid dXf \mid g$ G. Arithmetic expressions with matched pairs of parentheses R. $L\: = \left\{wcw\mid w \: \in \left(a\mid b\right)^* \right\}$ H. Palindromes S. $X \: \rightarrow \: bXb \mid \:cXc \: \mid \epsilon$
1. $\text{E-P, F-R, G-Q, H-S}$
2. $\text{E-R, F-P, G-S, H-Q}$
3. $\text{E-R, F-P, G-Q, H-S}$
4. $\text{E-P, F-R, G-S, H-Q}$
edited | 2.4k views
+1
H-S is true coz strings generated by this grammar satisfies the definition of an even length palindrome string. this rules out B and D options.
G-Q is confirmed as both options A and C has it as true.
E-R is true coz R is the only grammar that checks: what$(w)$ has occurred earlier is present afterwards This equals the definition of E
Hence, option C is true.
edited by
+1
Sir, Can you explain why G - Q ??
+6
I have no clue there. Guess the reason given in answer is the best :)
0
What's wrong with F-R? Formal parameter declaration must be in exaclty same fashion as actual parameter called! F-R also makes absolute sense. Why (A) is not the answer?
+31
$X\: \rightarrow XbX \mid XcX \mid dXf \mid g$
Here,
$X$ is $expr$
$b$ and $c$ are operators
$d$ is opening paranthesis "$\big($"
$f$ is closing paranthesis "$\big)$"
$g$ is a variable.
Now it says,
$expr\: \rightarrow expr \text{ operator1 } expr \mid expr \text{ operator2 } expr \mid \big(expr\big) \mid var$
+1
Why not is E matched with P?
as given in the previous question:- https://gateoverflow.in/2461/gate1994_1-18 CSL checks whether a variable has been declared before its use and I think P is CSL whereas R is DCFL?
So why not E with p?
Plz explain..
0
here F-R is not valid always because formal parameter name may differ with actual parameter and R is L={wcw/..} which means corresponding parameters name should be same .
calling function can be like fun(int p,int q,int r) and called function can be like fun(int x,int y,int z).
So in this case string will be something like pqrcxyz which doesn,t belong to L.
0
Abhishek Rai 2 I think the datatype of the formal arguments are matched with that of the actual arguments. What you are doing appears like you are trying to match the variable names which is not required. Here in your calling functions no. of 'int' type parameters is 3 and the same is for the case of called function where no. of 'int' type parameters is also 3. So it is like {a3b0c3d0} where (a and c) stand for no. of int type arguments and (b and d) for some other data type like char.
Example:
calling function --> Fun(int m,int n, char o) // a2b1
called function --> Fun(int x,int y, char s) // c2d1
In that way the matching is done. Feel free to correct me if you find it wrong.
We can match H-S just by checking the grammar we can generate all the even lenght palindromes
So we left with option A and C(only in these options H-S matched)
In both the cases G-Q so we left with matching for E and F
For E the grammar should check the identifiers are declared before their use So R is more accurate since the grammar is
L={wcw ∣ w∈ (a∣b) } where w is occured earlier and then it is used which matches with checking declaratation of identifiers
and also E-P makes no sense
Therefore we can conclude C. E-R, F-P, G-Q, H-S
edited
–1 vote
0 | 2018-07-19 08:44:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5817614793777466, "perplexity": 2799.574841799238}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590711.36/warc/CC-MAIN-20180719070814-20180719090814-00321.warc.gz"} |
https://www.hpmuseum.org/forum/thread-16557-post-145413.html | New Sum of Powers Log Function
03-29-2021, 04:53 PM
Post: #1
Namir Senior Member Posts: 813 Joined: Dec 2013
New Sum of Powers Log Function
Hi All,
I just published a new function on my web site. The function is SopLog which is short for “Sum of Powers Logarithm”. The function is defined as SolLogN(S) = x where N is an integer base (number of integers to add), S is the sum of terms, and x is the power to which is integer is raised. This means that:
S = sum i^x for i=1 to N
The power x is calculated as the root of the following function:
S – sum i^x for i=1 to N
You can download the article here. The article contains listings for SopLog in Excel VBA, Matlab, Python, C++, HP-71B BASIC, Generic legacy Pocket Computer BASIC, HP-41C, HP-41CX (with and without the Advantage module), HP-67/97, and HP-15C.
The article also shows an empirical relationship between x, S, and N.
The SopLog function is good for bench-marking. I leave it to other math-oriented folks to find other uses for SopLog.
Enjoy!
Namir
03-29-2021, 08:39 PM (This post was last modified: 03-29-2021 08:46 PM by C.Ret.)
Post: #2
C.Ret Member Posts: 143 Joined: Dec 2013
RE: New Sum of Powers Log Function
Nice article Namir ! Thanks for sharing.
I don't know what will be a practical application of this new function, but meanwhile, here is my contribution for the SHARP PC-1211 inspired from the generic program you give for BASIC pocket machines.
Since, it is a venerable and aged pocket, I add a way to get an estimation, for any user in a hurry, who may not have time or patience to wait for the several minutes needed to compute the exact x value by (numerus) iterations.
Code:
1:Y=1:FOR I=2 TO N:Y=Y+I^Z:NEXT I:Y=S-Y:RETURN 2:INPUT "N.TERMS N=";N,"TOT SUM S=";S:RETURN 3:PAUSE "NEW SOPLOG.N.(S) = X ":PAUSE "S=SUM I^X FOR I=1 TO N":GOTO 2 4:L=LOG N,X=10^(-.314706469-.965654959*LOG L)*LN S-1.1689028*(1-EXP -1.6467435L:GOTO 6 5:H=€-3*(1+ABS X,Z=X:GOSUB 1:F=Y,Z=X+H:GOSUB 1:D=HF/(Y-F,X=X-D,R=R-1:IF RIF ABS D>TGOTO 5 6:BEEP 1:PRINT "SOPLOG";N;"(";S;E$;X:PRINT E$;X:RETURN 8:"Z"GOSUB 3:X=1,T=€-7,R=€3,E$=")=":GOSUB 5:GOTO 8 9:"A"GOSUB 3:E$=")¥":GOSUB 4:GOTO 9
In DEF-mode, press shift+Z for the exact value obtained by the iterative process or press shift-A for an immediate estimation.
Code:
> [mode] DEF > [shift][ Z ] NEW SOPLOG.N.(S) = X S= SUM I^X FOR I=1 TO N N.TERM N=_ 10 [enter] TOT SUM S=_ 250 [enter] <... 2'38" ...> SOPLOG10.(250.)=1.784518 [enter] )=1.784518859
Code:
[shift][ A ] NEW SOPLOG.N.(S) = X S= SUM I^X FOR I=1 TO N N.TERM N=_ 1€3 [enter] TOT SUM S=_ 7500 [enter] SOPLOG1000.(7500.)¥3.356 [enter] )¥3.358863814€-01
P.S.:
¥ is shift-Y (Yen) character that I use to indicate approximative egality.
€ is the standard bold |Exp key that indicates ten's exponentiation on this pocket.
03-29-2021, 10:47 PM
Post: #3
Albert Chan Senior Member Posts: 1,676 Joined: Jul 2018
RE: New Sum of Powers Log Function
(03-29-2021 04:53 PM)Namir Wrote: S = sum i^x for i=1 to N
We can solve for x, without actually summing N terms.
As a rough approximation, s ≈ ∫(t^x, t=1/2 .. n+1/2)
Since sum(k, k=1..n) = (n²+n)/2, a guess for x is log(s)/log(n) - 1
To get more accurate x, we can use Euler–Maclaurin formula, for f(t) = t^x:
Operator shorthand, we have s = Σf = (D^-1 - 1/2 + D/12 - D^3/720 + D^5/30240 - ...) f
Drop higher-order derivatives, we have:
Code:
RHS = lambda p,n: ((n+1)**(p+1)-1)/(p+1) - ((n+1)**p-1)/2 + p*((n+1)**(p-1)-1)/12 solvex = lambda n,s: findroot(lambda p: RHS(p,n)/s-1, log(s,n)-1) roughx = lambda n,s: findroot(lambda X: ((n+.5)**X-0.5**X)/(s*X)-1, log(s,n)) - 1
Note: we solve RHS/LHS-1 = 0, because findroot like numbers in the "normal" range.
For comparision, I copied SopLog.pdf Table 1, for solved (s,x)
>>> from mpmath import *
>>> n=100
>>> SX = (100,0),(150,0.110121),(250,0.245589),(500,0.424944),(750,0.527995)
>>> SX += (1000,0.600423),(1100,0.624305),(1200,0.646061),(1300,0.666037)
>>>
>>> for s,x in SX: print '%g\t%f\t%f\t%f' % (s,x, solvex(n,s), roughx(n,s))
...
100 0.000000 0.000000 0.000000
150 0.110121 0.110121 0.110134
250 0.245589 0.245589 0.245605
500 0.424944 0.424944 0.424956
750 0.527995 0.527995 0.528004
1000 0.600423 0.600423 0.600430
1100 0.624305 0.624305 0.624311
1200 0.646061 0.646061 0.646067
1300 0.666037 0.666037 0.666042
03-30-2021, 01:44 AM
Post: #4
Albert Chan Senior Member Posts: 1,676 Joined: Jul 2018
RE: New Sum of Powers Log Function
(03-29-2021 10:47 PM)Albert Chan Wrote: Since sum(k, k=1..n) = (n²+n)/2, a guess for x is log(s)/log(n) - 1
If we have LambertW, we can get a much better guess, without solver.
s ≈ ∫(t^x, t=1/2 .. n+1/2) = (n+1/2)^(x+1)/(x+1) - (1/2)^(x+1)/(x+1)
If we drop the last term, and let N=n+1/2, X=x+1, we have
s = N^X / X
ln(s) = X*ln(N) - ln(X)
We wanted to match W(a) = z → a = z * e^z → ln(a) = z + ln(z)
ln(1/s) = X*ln(1/N) + ln(X)
ln(1/s*ln(1/N)) = X*ln(1/N) + ln(X*ln(1/N))
→ X = W(ln(1/N)/s) / ln(1/N) = -W(-ln(N)/s) / ln(N)
Turns out, LambertW -1 branch is the one we need.
Lets' try this out, for s = Σ(k, k=1 .. n)
>>> guessx = lambda n,s: -lambertw(-ln(n+.5)/s,-1) / log(n+.5) - 1
>>> for n in range(1000,5001,1000):
... s = n*(n+1)/2
... print n, log(s)/log(n)-1, guessx(n,s)
...
1000 0.899801360605113 0.999999961026799
2000 0.908873017486397 0.99999999120301
3000 0.913467137635656 0.999999996300753
4000 0.916458516421875 0.999999997995799
5000 0.918641366353455 0.999999998752945
03-30-2021, 11:05 AM (This post was last modified: 03-30-2021 11:06 AM by Namir.)
Post: #5
Namir Senior Member Posts: 813 Joined: Dec 2013
RE: New Sum of Powers Log Function
Thanks Albert!
Any implementation for the Lambertw function (the version with two parameters) on vintage calculators like the HP-41C, HP-67, and HP-15C?
Namir
03-30-2021, 11:41 AM
Post: #6
Paul Dale Senior Member Posts: 1,733 Joined: Dec 2013
RE: New Sum of Powers Log Function
The WP 34S has an implementation of Lambert's W function -- it's in XROM so it's a keystroke program that ought to convert to other devices without too many issues.
Pauli
03-30-2021, 01:43 PM
Post: #7
Gene Moderator Posts: 1,201 Joined: Dec 2013
RE: New Sum of Powers Log Function
Angel's Sandmath has Lambert mcoded.
03-30-2021, 04:01 PM (This post was last modified: 03-30-2021 04:41 PM by C.Ret.)
Post: #8
C.Ret Member Posts: 143 Joined: Dec 2013
RE: New Sum of Powers Log Function
The french Silicium Forum have various implementations of Lambert W function for HP-Prime, SHARP PC-1211 and HP-15C
For example:
Code:
001- LBL A CF 8 STO 0 1 + LN 1 ENTER e^x + LN ÷ GTO 0 014- LBL B CF 8 STO 0 1 e^x × 2 ENTER CHS ENTER RCL 0 x² LN - √x × - GTO 0 032- LBL C STO 0 re↔im STO 1 re↔im LN ENTER ENTER LN - x↔y LSTx ÷ 1/x + 047- LBL 0 048- CF 0 PSE ENTER ENTER e^x ENTER R↑ × + LSTx FS? 8 GSB 1 060- RCL-0 ENTER ABS RND x>0? SF 0 075- R↓ x↔y ÷ - LSTx ABS RND x=0? CF 0 075- R↓ FS? 0 GTO 0 078- RTN 079- LBL 1 re↔im RCL-1 re↔im RTN
Set desired precision with FIX 1~9.
Enter argument x (or complex z) in first stack level X: and press:
f- A for real value of $$W_0(x)$$ in main positive branch
f- B for real value of $$W_{-1}(x)$$ in negative branch
f- C for complex value of $$W(z)$$
03-30-2021, 04:35 PM
Post: #9
Albert Chan Senior Member Posts: 1,676 Joined: Jul 2018
RE: New Sum of Powers Log Function
Hi, Namir
The algorithm for LambertW -1 branch is the same as W0, just different guess, see here
y = W-1(a) is real only for a = [-1/e, 0]
A simple way is just iterate for it: y = log(-a), then iterate y = log(a/y) ...
If converged, y=log(a/y) ⇒ e^y = a/y ⇒ y*e^y = a
>>> a = mpf(-0.005) # example
>>> y = log(-a)
>>> for i in range(5): y = log(a/y); print y
...
-6.9657066586895
-7.23931642716726
-7.27784415235106
-7.28315205198181
-7.28388110922369
We could speed up convergence with Newton's method
f(y) = y - log(a/y)
f'(y) = 1 + 1/y
y = y - (y-log(a/y))/(1+1/y) = y * (1+log(a/y))/(1+y)
>>> y = log(-a) # same guess
>>> for i in range(5): y *= (1+log(a/y))/(1+y); print y
...
-7.3536234060935
-7.28404934413218
-7.28399713512886
-7.28399713509908
-7.28399713509908
>>> y*exp(y) # confirm y = W-1(a)
-0.005
03-30-2021, 05:56 PM
Post: #10
Namir Senior Member Posts: 813 Joined: Dec 2013
RE: New Sum of Powers Log Function
Thank you all for your feedback.
My preliminary testing using lambertw in Matlab and Python shows some interesting features. The decimal part is close to the results of SopLog but one has to manipulate the integer part. I will share more details after I look at the newer messages.
Namir
03-30-2021, 08:35 PM
Post: #11
Albert Chan Senior Member Posts: 1,676 Joined: Jul 2018
RE: New Sum of Powers Log Function
(03-30-2021 01:44 AM)Albert Chan Wrote: If we have LambertW, we can get a much better guess, without solver.
s ≈ ∫(t^x, t=1/2 .. n+1/2) = (n+1/2)^(x+1)/(x+1) - (1/2)^(x+1)/(x+1)
If we drop the last term, and let N=n+1/2, X=x+1, we have ...
We could estimate the dropped term, and add it back.
Code:
def guess2(n,s): t = -log(n+.5) p = lambertw(t/s,-1) / t s += 0.5**p/p return lambertw(t/s,-1) / t - 1
Above estimated x has similar error as roughx(n,s), but twice as fast. (on my machine)
(03-30-2021 01:44 AM)Albert Chan Wrote: Turns out, LambertW -1 branch is the one we need.
Illustrate the reason, by example:
>>> n, s = 100, 1000
>>> t = -log(n+.5)
>>> p = lambertw(t/s,-1) / t # W1 resulted p
>>> p, (n+.5)**p/p, .5**p/p
(1.60037803179321, 1000.0, 0.2060704060225)
>>>
>>> p = lambertw(t/s, 0) / t # W0 resulted p
>>> p, (n+.5)**p/p, .5**p/p
(0.00100464230172027, 1000.0, 994.686243766351)
Both solved p, for s = (n+.5)**p/p.
But, the assumption that last term can be dropped is false for W0
03-30-2021, 10:26 PM (This post was last modified: 04-01-2021 11:59 AM by Albert Chan.)
Post: #12
Albert Chan Senior Member Posts: 1,676 Joined: Jul 2018
RE: New Sum of Powers Log Function
Even faster version, eliminated second LambertW, by taylor series approximation.
W(x+h) ≈ W(x) + W'(x) * h
w*e^w = x
(w+1)*e^w dw = dx
dw/dx = e^-w / (w+1) = w/(w*x+x)
Code:
def guess3(n,s): t = -log(n+.5) x = t/s w = lambertw(x,-1) p = w/t h = t/(s+0.5**p/p) - x return p-1 + p/(w*x+x) * h
To speed up search, solvex use log scale.
With secants method, and tolerance of 1e-5, we expected 5*1.6 = 8 "correct" decimals.
("correct" from solving root of formula point of view, not actual x)
Code:
RHS = lambda p,n: ((n+1)**(p+1)-1)/(p+1) - ((n+1)**p-1)/2 + p*((n+1)**(p-1)-1)/12 solvex = lambda n,s: findroot(lambda p: log(RHS(p,n)/s), log(s,n)-1, tol=1e-5)
03-31-2021, 01:27 PM (This post was last modified: 03-31-2021 01:31 PM by Namir.)
Post: #13
Namir Senior Member Posts: 813 Joined: Dec 2013
RE: New Sum of Powers Log Function
Albert,
Your guess3() function provides good approximation to the SopLog function.
Here is the SopLog implementation in Matlab:
Code:
function x = soplog(N, S) %SOPLOG implements the SopLog function. toler=1e-8; % default tolerance x = 1; % initial guess for x maxiter = 1000; for iter =1:maxiter h = 0.001 * (1 + abs(x)); f0 = sumFx(N, S, x); fp = sumFx(N, S, x + h); fm = sumFx(N, S, x - h); diff = 2 * h * f0 / (fp - fm); x = x - diff; if abs(diff) < toler, break; end end end function y =sumFx(N,S,x) sumx = 1; for i=2:N sumx = sumx + i^x; end y = S - sumx; end
Here is my copy of your Python guiess3() + some test calls:
Code:
from mpmath import * import numpy as np def guess3(n,s): t = -np.log(n+.5) x = t/s w = lambertw(x,-1) p = w/t h = t/(s+0.5**p/p) - x return p-1 + p/(w*x+x) * h print(guess3(100,1500)) print(guess3(1000,5000)) print(guess3(1000,500))
Here is my Matlab version of your guess3() function which I call soplogw3:
Code:
function x = soplogw3(n,s) %SOPLOGW Summary of this function goes here t = -log(n+.5); x = t/s; w = lambertw(-1,x); p = w/t; h = t/(s+0.5^p/p) - x; x = real(p-1 + p/(w*x+x) * h); end
I do beleive we must use the solution path of -1 with the Lambert function. The W0(x) does not give the same answers.
Here are three test values:
Code:
soplog(100,1500) -> 0.701661431056288 print(guess3(100,1500)) -> 0.70166598312237 soplogw3(200,2500) -> 0.701665983122370 soplog(1000,5000) -> 0.267187615565215 print(guess3(1000,5000)) -> 0.267188163707435 soplogw3(1000,5000) -> 0.267188163707435 soplog(1000,500) -> -0.118482712209941 soplogw3(1000,500) -> -0.118485900562627 print(guess3(1000,500)) -> -0.118485900562627
The soplog() is my original Matlab implementation. The guess3() is you latest implementation, and the soplogw3() is the Matlab equivalent of your guess3(). The results show that using the Lambert W function yields results that match to 5 or 6 decimals. Pretty good!
03-31-2021, 02:19 PM
Post: #14
Namir Senior Member Posts: 813 Joined: Dec 2013
RE: New Sum of Powers Log Function
Albert,
Going back to an earlier post in this thread. Here is my Python copy of your code that uses the findroot() function:
Code:
from mpmath import * import numpy as np def roughx(n,s): return findroot(lambda X: ((n + .5) ** X - 0.5 ** X) / (s * X) - 1, np.log(s)/np.log(n)) - 1 def RHS(p,n): return ((n+1)**(p+1)-1)/(p+1) - ((n+1)**p-1)/2 + p*((n+1)**(p-1)-1)/12 def solvex(n,s): return findroot(lambda p: RHS(p,n)/s-1, np.log(s)/np.log(n)-1) n=100 SX = (100,0),(150,0.110121),(250,0.245589),(500,0.424944),(750,0.527995) SX += (1000,0.600423),(1100,0.624305),(1200,0.646061),(1300,0.666037) for s,x in SX: print('%g\t%f\t%f\t%f' % (s,x, solvex(n,s), roughx(n,s)))
The output is:
Code:
100 0.000000 0.000000 0.000000 150 0.110121 0.110121 0.110134 250 0.245589 0.245589 0.245605 500 0.424944 0.424944 0.424956 750 0.527995 0.527995 0.528004 1000 0.600423 0.600423 0.600430 1100 0.624305 0.624305 0.624311 1200 0.646061 0.646061 0.646067 1300 0.666037 0.666037 0.666042
Here is a Matlab script that implements the Matlab version of the above three Python functions:
Code:
clc close clear n=100; s=1500; fprintf("SopLog(%i,%i) = %f12\n", n, s, soplog(n,s)); fprintf("Solvex(%i,%i) = %f12\n", n, s, solvex(n,s)); fprintf("Roughx(%i,%i) = %f12\n", n, s, roughx(n,s)); n=100; s=5000; fprintf("SopLog(%i,%i) = %f12\n", n, s, soplog(n,s)); fprintf("Solvex(%i,%i) = %f12\n", n, s, solvex(n,s)); fprintf("Roughx(%i,%i) = %f12\n", n, s, roughx(n,s)); n=1000; s=5000; fprintf("SopLog(%i,%i) = %f12\n", n, s, soplog(n,s)); fprintf("Solvex(%i,%i) = %f12\n", n, s, solvex(n,s)); fprintf("Roughx(%i,%i) = %f12\n", n, s, roughx(n,s)); function x = roughx(n,s) x = fsolve(@(x) ((n + .5)^x - 0.5^x) / (s * x) - 1, log(s)/log(n)) - 1; end function x =RHS(p,n) x= ((n+1)^(p+1)-1)/(p+1) - ((n+1)^p-1)/2 + p*((n+1)^(p-1)-1)/12; end function x = solvex(n,s) x = fsolve(@(p) RHS(p,n)/s-1, log(s)/log(n)-1); end
The output is:
Code:
SopLog(100,1500) = 0.70166112 Solvex(100,1500) = 0.70166112 Roughx(100,1500) = 0.70166612 SopLog(100,5000) = 0.99757912 Solvex(100,5000) = 0.99757912 Roughx(100,5000) = 0.99757912 SopLog(1000,5000) = 0.26718812 Solvex(1000,5000) = 0.26718812 Roughx(1000,5000) = 0.26718812
The arbitrarily selected values of N and S show that the Solvex() and Roughx() give the same digits. While both functions use Matlab's fsolve the do not require loops to perform any summation. Of course the same is true for the Python version.
The end of the study that I posted on my web site I discuss some variants of the SopLog function. These variants deal with scaling up/down the powers of the next integers, so the powers to which the integers are raise vary from term to term.
Another variation of the SopLog function is to specify the number of integers AND the integer-increment for the next term. And of course you can combine this variant with the scaled up/down powers.
Namir
03-31-2021, 04:06 PM
Post: #15
Albert Chan Senior Member Posts: 1,676 Joined: Jul 2018
RE: New Sum of Powers Log Function
(03-31-2021 01:27 PM)Namir Wrote: I do beleive we must use the solution path of -1 with the Lambert function. The W0(x) does not give the same answers.
Although not a proof, I had shown the reason for this here
Here is another way. If x = 0, we have s = Σ(1, k=1..n) = n
This is when both branches of LambertW gives the same value.
p = -W(-ln(N)/s) / ln(N), where N = n+1/2
With s=n ⇒ p=x+1=1, we do not need the +1/2 correction:
s = ∫(1, t=1/2 .. n+1/2) = ∫(1, t=0 .. n)
p = -W(-ln(n)/n) / ln(n) = ln(n) / ln(n) = 1 // W both branches, see identities
For n≠s, we have p≠1, but 2 solutions for p.
Dropped term 0.5**p/p is a decreasing function, so we want the maximum p.
In other words, we pick most negative value of W(-ln(N)/s), i.e. -1 branch.
03-31-2021, 09:25 PM
Post: #16
Albert Chan Senior Member Posts: 1,676 Joined: Jul 2018
RE: New Sum of Powers Log Function
(03-31-2021 01:27 PM)Namir Wrote: Here is the SopLog implementation in Matlab ...
Code:
f0 = sumFx(N, S, x); fp = sumFx(N, S, x + h); fm = sumFx(N, S, x - h); diff = 2 * h * f0 / (fp - fm); x = x - diff; ...
Without function for the derivative, Newton's method is very inefficient.
We should consider secant's method (or, improved secant)
Also, curve is very close to LambertW, we should use log scale.
>>> n, s = 1000, 5000
>>> x = log(s,n)-1
>>> x1, y1 = x, log(fsum(k**x for k in range(1,n+1))/s)
>>> x1, y1
(mpf('0.23299000144533966'), mpf('-0.20890713759105706')
>>> x = guess3(n,s)
>>> x2, y2 = x, log(fsum(k**x for k in range(1,n+1))/s)
>>> x2, y2
(mpf('0.26718816370743487'), mpf('3.3544082779438775e-6'))
>>> x = x2 - y2 * (x2-x1)/(y2-y1)
>>> x3, y3 = x, log(fsum(k**x for k in range(1,n+1))/s)
>>> x3, y3
(mpf('0.26718761459859175'), mpf('-5.9153427886634265e-9'))
>>> x = x3 - y3 * (x3-x2)/(y3-y2)
>>> x4, y4 = x, log(fsum(k**x for k in range(1,n+1))/s)
>>> x4, y4
(mpf('0.26718761556521503'), mpf('-2.2204460492503136e-16'))
---
Turns out mpmath implemented Euler–Maclaurin Asymptotic expansion of sums
Summation will continue, as long as additional term improve the sum, by at least 1 decimal.
>>> x = solvex(n, s) # my version, without higher derivatives
>>> x, fsum(k**x for k in range(1,n+1))
(mpf('0.26718762849802313'), mpf('5000.0003957177305'))
>>> x = findroot(lambda x: log(sumem(lambda k: k**x, [1,n])/s), log(s,n)-1)
>>> x, fsum(k**x for k in range(1,n+1))
(mpf('0.26718761309749891'), mpf('4999.9999244928886'))
04-01-2021, 02:56 PM
Post: #17
Albert Chan Senior Member Posts: 1,676 Joined: Jul 2018
RE: New Sum of Powers Log Function
Revised guess3(n,s), with less code.
Code:
def guess3(n,s): t = -log(n+.5) w = lambertw(t/s,-1) p = w/t return p-1 - p/((w+1)*(s*p*2.**p+1))
Note that guess3 had a weekness, when t/s < -1/e, LambertW returned complex values.
Even if w is real, if n ≫ s > 1, we have p=x+1 ≈ 0. Two terms taylor series estimate is still bad.
Code:
from mpmath import * RHS = lambda p,n: ((n+1)**(p+1)-1)/(p+1) - ((n+1)**p-1)/2 + p*((n+1)**(p-1)-1)/12 solvex = lambda n,s: findroot(lambda p: log(RHS(p,n)/s), log(s,n)-1, tol=1e-5) exactx = lambda n,s: findroot(lambda x: log(fsum(k**x for k in range(1,n+1))/s), log(s,n)-1)
>>> n, s = 100, 13 # t/s ≈ -0.35463, slightly above -1/e ≈ -0.36788
>>> print exactx(n,s), solvex(n,s), guess3(n,s), log(s,n)-1
-0.622429308602986 -0.622506385172213 -0.544275714709962 -0.443028323846582
---
Thus, if we want fully converged x, we should start with solvex.
We can use y = log(fsum(k**x for k in range(1,n+1))/s), to estimate next x.
Note: x correction is opposite the sign of y
>>> n, s = 1000, 5000 # previous post example
>>> x = solvex(n,s)
>>> x1, y1 = x, log(fsum(k**x for k in range(1,n+1))/s)
>>> x1, y1
(mpf('0.26718762849802312'), mpf('7.9143542807225195e-8'))
>>> x = x1 - abs(x1)*y1/2
>>> x2, y2 = x, log(fsum(k**x for k in range(1,n+1))/s)
>>> x2, y2
(mpf('0.26718761792493534'), mpf('1.4440531777112248e-8'))
>>> x = x2 - y2 * (x2-x1)/(y2-y1)
>>> x
mpf('0.26718761556521503')
04-01-2021, 06:05 PM (This post was last modified: 04-01-2021 06:12 PM by Namir.)
Post: #18
Namir Senior Member Posts: 813 Joined: Dec 2013
RE: New Sum of Powers Log Function
Does any of your previous analysis and approximations work on the following variants of the SopLog summations?
Code:
def sdSum(n,s,x,scale): sumx = 1 factor = 1 for i in range(n,2,-1): sumx += i ** (x * factor) factor *= scale return sumx - s def siSum(n,s,x,scale): sumx = 1 factor = 1 for i in range(2,n+1): sumx += i ** (x * factor) factor *= scale return sumx - s def siSum2(n,s,x,incr): sumx = 1 factor = 1 j = 2 for i in range(2,n): sumx += j ** (x * factor) j += incr return sumx - s def siSum3(n,s,x,incr,scale): sumx = 1 factor = 1 j = 2 for i in range(2,n+1): sumx += j ** (x * factor) j += incr factor *= scale return sumx - s
The "scale" can be above or below 1. The "incr" is an integer >= 1.
04-01-2021, 11:05 PM
Post: #19
Albert Chan Senior Member Posts: 1,676 Joined: Jul 2018
RE: New Sum of Powers Log Function
(04-01-2021 06:05 PM)Namir Wrote: Does any of your previous analysis and approximations work on the following variants of the SopLog summations?
It depends on the function, and its argument. Euler–Maclaurin might not work.
Example, on your sdSum (I think you meant range(n,1,-1), or range(2,n+1) in reverse)
Code:
exact = lambda x,n,scale: 1 + fsum(k**(x*scale**(n-k)) for k in xrange(2,n+1)) guess = lambda x,n,scale: 1 + sumem(lambda k: k**(x*scale**(n-k)), [2,n])
>>> x, n, scale = 0.5, 100000, 0.5
>>> exact(x,n,scale), guess(x,n,scale)
(100337.09650943844, 100318.790872778)
Try a big x, guess is so wrong, it "sumed" negative !
>>> x = 1.5
>>> exact(x,n,scale), guess(x,n,scale)
(31728482.871558648, -38398120.2216635)
04-01-2021, 11:55 PM (This post was last modified: 04-02-2021 01:24 AM by Namir.)
Post: #20
Namir Senior Member Posts: 813 Joined: Dec 2013
RE: New Sum of Powers Log Function
(04-01-2021 11:05 PM)Albert Chan Wrote:
(04-01-2021 06:05 PM)Namir Wrote: Does any of your previous analysis and approximations work on the following variants of the SopLog summations?
It depends on the function, and its argument. Euler–Maclaurin might not work.
Example, on your sdSum (I think you meant range(n,1,-1), or range(2,n+1) in reverse)
Code:
exact = lambda x,n,scale: 1 + fsum(k**(x*scale**(n-k)) for k in xrange(2,n+1)) guess = lambda x,n,scale: 1 + sumem(lambda k: k**(x*scale**(n-k)), [2,n])
>>> x, n, scale = 0.5, 100000, 0.5
>>> exact(x,n,scale), guess(x,n,scale)
(100337.09650943844, 100318.790872778)
Try a big x, guess is so wrong, it "sumed" negative !
>>> x = 1.5
>>> exact(x,n,scale), guess(x,n,scale)
(31728482.871558648, -38398120.2216635)
I am looking to solve for x given all other parameters--n, s, scale and leading to a zero value for s - sum_of_series.
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https://www.shaalaa.com/question-bank-solutions/atom-atomic-mass-define-atomic-mass-unit_7376 | # Solution - Atom - Atomic Mass
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ConceptAtom - Atomic Mass
#### Question
Define atomic mass unit.
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Solution for concept: Atom - Atomic Mass. For the course 8th-10th CBSE
S | 2017-10-20 05:18:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29735296964645386, "perplexity": 5326.4900250716055}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823731.36/warc/CC-MAIN-20171020044747-20171020064747-00741.warc.gz"} |
https://codeyarns.com/tech/2012-06-29-inserting-an-algorithm-in-latex.html | # Inserting an algorithm in LaTeX
📅 2012-Jun-29 ⬩ ✍️ Ashwin Nanjappa ⬩ 🏷️ algorithm, latex ⬩ 📚 Archive
One of the simple and beautiful ways to insert algorithms or procedures into a LaTeX document is using the algorithmicx package. The simple example given below generated the above figure. For more control structures and configurations check out the package documentation.
% Add the packages
\usepackage{algorithm}
\usepackage{algpseudocode}
% Insert the algorithm
\begin{algorithm}
\caption{Compute sum of integers in array}
\label{array-sum}
\begin{algorithmic}[1]
\Procedure{ArraySum}{$A$}
\State $sum = 0$
\For {each integer $i$ in $A$}
\State $sum = sum + i$
\EndFor
\State Return $sum$
\EndProcedure
\end{algorithmic}
\end{algorithm}
Tried with: MikTeX 2.9 on Windows 7 64-bit | 2021-04-17 11:45:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9085480570793152, "perplexity": 10830.376506869114}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038119532.50/warc/CC-MAIN-20210417102129-20210417132129-00211.warc.gz"} |
http://mymathforum.com/elementary-math/331951-what-log-function.html | My Math Forum What is log function?
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion
May 22nd, 2016, 11:16 PM #1 Banned Camp Joined: May 2016 From: earth Posts: 703 Thanks: 56 What is log function? Hello, Why we use log function in mathematics?
May 22nd, 2016, 11:22 PM #2 Math Team Joined: Nov 2014 From: Australia Posts: 688 Thanks: 243 The log function was developed to transform multiplication problems into simple addition problems. Suppose that $a$ and $b$ are horrible-looking decimals and we want to work out $ab$. If we take the logarithm of this, we get $\log (ab) = \log a + \log b$ by a simple law of logarithms. There are other reasons, such as the useful fact that $\displaystyle \int\dfrac{1}{x}\,dx = \ln |x| + C$. Thanks from MMath
May 22nd, 2016, 11:47 PM #3 Banned Camp Joined: May 2016 From: earth Posts: 703 Thanks: 56 PLEASE GIVE EXAMPLE MORE: a=5.7895 b=2.2358 a*b=? = 12.9441 log(ab)=log a +log b =0.76264 + 0.34943=0.26649 they are not same?
May 23rd, 2016, 01:54 AM #4 Senior Member Joined: Apr 2014 From: UK Posts: 883 Thanks: 323 a=5.7895 b=2.2358 a*b= 12.9441 log(ab)=log a +log b log(12.94416) = log (5.7895) + log (2.2358 ) 1.112074 = 0.762641 + 0.349433 They are the same. Last edited by weirddave; May 23rd, 2016 at 01:55 AM. Reason: brackets went smiley on me
May 23rd, 2016, 02:11 AM #5
Math Team
Joined: Nov 2014
From: Australia
Posts: 688
Thanks: 243
Quote:
Originally Posted by MMath PLEASE GIVE EXAMPLE MORE: a=5.7895 b=2.2358 a*b=? = 12.9441 log(ab)=log a +log b =0.76264 + 0.34943=0.26649 they are not same?
Remember that $ab = e^{\ln (ab)}$, so it's not quite as simple as that.
May 23rd, 2016, 04:51 AM #6 Banned Camp Joined: May 2016 From: earth Posts: 703 Thanks: 56 I have CASIO fx 82 ms please tell how to do this?
May 23rd, 2016, 04:55 AM #7
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Joined: Dec 2012
From: Hong Kong
Posts: 853
Thanks: 311
Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics
Quote:
Originally Posted by MMath I have CASIO fx 82 ms please tell how to do this?
I have fx-3650P and fx-50H. In both, the ln button is below x^3. Perhaps this is also true of your model...
May 23rd, 2016, 05:05 AM #8 Banned Camp Joined: May 2016 From: earth Posts: 703 Thanks: 56 Nothing is coming i have taken example of a=5 and b=3 also.. log(a*b) = log5 + log 3 = 0.698 + 0.477=1.175 so, e and e^x are coming in my calculator both are not giving 15??
May 23rd, 2016, 05:12 AM #9
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Joined: Dec 2012
From: Hong Kong
Posts: 853
Thanks: 311
Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics
Quote:
Originally Posted by MMath Nothing is coming i have taken example of a=5 and b=3 also.. log(a*b) = log5 + log 3 = 0.698 + 0.477=1.175 so, e and e^x are coming in my calculator both are not giving 15??
Use the ln button. The log button in Casio calculators is the common logarithm, not the natural logarithm.
May 23rd, 2016, 05:23 AM #10 Banned Camp Joined: May 2016 From: earth Posts: 703 Thanks: 56 i am not getting please tell in step.
Tags function, log
### EX2.2 OF ELEMENTMATH 12
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Contact - Home - Forums - Cryptocurrency Forum - Top | 2018-09-22 03:34:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6568988561630249, "perplexity": 12522.622226190899}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267158011.18/warc/CC-MAIN-20180922024918-20180922045318-00290.warc.gz"} |
https://nemeth.aphtech.org/lesson1.2 | - Use 6 Dot Entry Switch to UEB Math Tutorial
# Lesson 1.2: Punctuaion
## The Punctuation Indicator
The punctuation indicator, dots four five six, must be placed between a numeral and a mark of punctuation such as a period or question mark. It indicates that the numeral has ended and that which follows is a mark of punctuation rather than a digit. For example, the period, dots two five six, would represent the digit four if the punctuation indicator did not precede it. Likewise, the question mark, dots two three six, would be interpreted as the digit eight without the presence of the punctuation indicator.
### Example 1
$\text{Problem}\phantom{\rule{.3em}{0ex}}10\text{.}$
⠠⠏⠗⠕⠃⠇⠑⠍⠀⠼⠂⠴⠸⠲
### Example 2
$\text{Are you going to the park at}\phantom{\rule{.3em}{0ex}}3\text{?}$
⠠⠁⠗⠑⠀⠽⠕⠥⠀⠛⠕⠊⠝⠛⠀⠞⠕⠀⠞⠓⠑⠀⠏⠁⠗⠅⠀⠁⠞⠀⠼⠒⠸⠦
The punctuation indicator must come before the following marks of punctuation: period, question mark, colon, semicolon, apostrophe, quotation marks, and exclamation point. There are three marks of punctuation that do not require the punctuation indicator; these are: comma, hyphen, and dash.
### Example 3
$\text{We will be home between}\phantom{\rule{.3em}{0ex}}2:30-2:45\text{.}$
⠠⠺⠑⠀⠺⠊⠇⠇⠀⠃⠑⠀⠓⠕⠍⠑⠀⠃⠑⠞⠺⠑⠑⠝⠀⠼⠆⠸⠒⠼⠒⠴⠤⠆⠸⠒⠼⠲⠢⠸⠲
### Example 4
$\text{Circle all of the}\phantom{\rule{.3em}{0ex}}2\text{'s.}$
⠠⠉⠊⠗⠉⠇⠑⠀⠁⠇⠇⠀⠕⠋⠀⠞⠓⠑⠀⠼⠆⠸⠄⠎⠲
### Example 5
$\text{Do problems}\phantom{\rule{.3em}{0ex}}5-10\text{.}$
⠠⠙⠕⠀⠏⠗⠕⠃⠇⠑⠍⠎⠀⠼⠢⠤⠂⠴⠸⠲
### Example 6
$\text{Read pages}\phantom{\rule{.3em}{0ex}}56-62\text{.}$
⠠⠗⠑⠁⠙⠀⠏⠁⠛⠑⠎⠀⠼⠢⠖⠤⠖⠆⠸⠲
### Example 7
$\text{Do you have a "}5\text{"?}$
⠠⠙⠕⠀⠽⠕⠥⠀⠓⠁⠧⠑⠀⠁⠀⠦⠼⠢⠸⠴⠦
### Example 8
$\text{We won with a score}\phantom{\rule{.3em}{0ex}}3-1\text{!}$
⠠⠺⠑⠀⠺⠕⠝⠀⠺⠊⠞⠓⠀⠁⠀⠎⠉⠕⠗⠑⠀⠼⠒⠤⠂⠸⠖
### Example 9
$\text{We have a car that will seat}\phantom{\rule{.3em}{0ex}}4\text{- maybe}\phantom{\rule{.3em}{0ex}}5\text{.}$
⠠⠺⠑⠀⠓⠁⠧⠑⠀⠁⠀⠉⠁⠗⠀⠞⠓⠁⠞⠀⠺⠊⠇⠇⠀⠎⠑⠁⠞⠀⠼⠲⠤⠤⠍⠁⠽⠃⠑⠀⠼⠢⠸⠲
Rules:
1. The numeric indicator is placed before a numeral when the numeral is at the beginning of a braille line or when the numeral follows a space.
2. The numerals are all in the lower part of a braille cell, using only dots two, three, five, and/or six.
3. When a numeral is followed by a mark of punctuation other than a comma, hyphen, or dash, the punctuation indicator must be used to separate the numeral and the mark of punctuation.
These three rules govern the use of all numerals, except page numbers which are always written in literary code. Thus, dots one, two, four, and/or five in the upper part of the braille cell are used to represent page numbers. Nemeth code numerals, in the lower portion of the braille cell, are not used to number pages. Note that literary code numerals are also preceded by the numeric indicator.
All numbers in a work that is mathematical or scientific are Nemeth Code numbers. Even within the textual portions of the material, all numbers are Nemeth numbers. The only occurrences when literary braille numbers are used are:
• on title pages
• at the corners of pages (page numbering)
• at the ends of page-separation lines
• when the technique of keying is employed
In all other cases, the numerals of the Nemeth Code must be used (NBC, §7b).
The punctuation indicator terminates the effect of the numeric indicator, as well as any other mathematical symbol that may precede the mark of punctuation. It is placed directly after the numeral or other symbol, and preceding the mark of punctuation. | 2023-03-29 22:19:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 9, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6876757740974426, "perplexity": 3759.830080562556}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949035.66/warc/CC-MAIN-20230329213541-20230330003541-00568.warc.gz"} |
http://datasciencehack.com/blog/2020/09/ | ## Illustrative introductions on dimension reduction
“What is your image on dimensions?”
….That might be a cheesy question to ask to reader of Data Science Blog, but most people, with no scientific background, would answer “One dimension is a line, and two dimension is a plain, and we live in three-dimensional world.” After that if you ask “How about the fourth dimension?” many people would answer “Time?”
Terms like “multi dimensional something” is often used in science fictions because it’s a convenient black box when you make a fantasy story, and I’m sure many authors would not have thought that much about what those dimensions are.
In Japanese, if you say “He likes two dimension.” that means he prefers anime characters to real women, as is often the case with Japanese computer science students.
The meanings of “dimensions” depend on the context, but in data science dimension is in short the number of rows of your Excel data.
When you study data science or machine learning, usually you should start with understanding the algorithms with 2 or 3 dimensional data, and you can apply those ideas to any D dimensional data.
But of course you cannot visualize D dimensional data anymore, and that is almost an imaginary world on blackboards.
In this blog series I am going to explain algorithms for dimension reductions, such as PCA, LDA, and t-SNE, with 2 or 3 dimensional visible data. Along with that, I am going to delve into the meaning of calculations so that you can understand them in more like everyday-life sense.
#### This article series is going to be roughly divided into the contents below.
1. Curse of Dimensionality (to be published soon)
2. PCA, LDA (to be published soon)
3. Rethinking eigen vectors (to be published soon)
4. KL expansion and subspace method (to be published soon)
5. Autoencoder as dimension reduction (to be published soon)
6. t-SNE (to be published soon)
I hope you could see that reducing dimension is one of the fundamental approaches in data science or machine learning.
## Spiky cubes, Pac-Man walking, empty M&M’s chocolate: curse of dimensionality
“Curse of dimensionality” means the difficulties of machine learning which arise when the dimension of data is higher. In short if the data have too many features like “weight,” “height,” “width,” “strength,” “temperature”…. that can undermine the performances of machine learning. The fact might be contrary to your image which you get from the terms “big” data or “deep” learning. You might assume that the more hints you have, the better the performances of machine learning are. There are some reasons for curse of dimensionality, and in this article I am going to introduce three major reasons below.
1. High dimensional data usually have rich expressiveness, but usually training data are too poor for that.
2. The behaviors of data points in high dimensional space are totally different from our common sense.
3. More irrelevant featreus lead to confusions in recognition or decision making.
Through these topics, you will see that you always have to think about which features to use considering the number of data points.
### 1, Number of samples and degree of dimension
The most straightforward demerit of adding many features, or increasing dimensions of data, is the growth of computational costs. More importantly, however, you always have to think about the degree of dimensions in relation of the number of data points you have. Let me take a simple example in a book “Pattern Recognition and Machine Learning” by C. M. Bishop (PRML). This is an example of measurements of a pipeline. The figure below shows a comparison plot of 3 classes (red, green and blue), with parameter x7 plotted against parameter x6 out of 12 parameters.
* The meaning of data is not important in this article. If you are interested please refer to the appendix in PRML.
Assume that we are interested in classifying the cross in black into one of the three classes. One of the most naive ideas of this classification is dividing the graph into grids and labeling each grid depending on the number of samples in the classes (which are colored at the right side of the figure). And you can classify the test sample, the cross in black, into the class of the grid where the test sample is in.
As I mentioned the figure above only two features out of 12 features in total. When the the total number of plots is fixed, and you add remaining ten axes one after another, what would happen? Let’s see what “adding axes” mean. If you are talking about 1, 2, or 3 dimensional grids, you can visualize them. And as you can see from the figure below, if you make each grids respectively in 1, 2, 3 dimensional spaces, the number of the small regions in the grids are respectively 10, 100, 1000. Even though you cannot visualize it anymore, you can make grids for more than 3 dimensional data. If you continue increasing the degree of dimension, the number of grids increases exponentially, and that can soon surpass the number of training data points soon. That means there would be a lot of empty spaces in such high dimensional grids. And the classifying method above: coloring each grid and classifying unknown samples depending on the colors of the grids, does not work out anymore because there would be a lot of empty grids.
* If you are still puzzled by the idea of “more than 3 dimensional grids,” you should not think too much about that now. It is enough if you can get some understandings on high dimensional data after reading the whole article of this.
I said the method above is the most naive way, but other classical classification methods , for example k-nearest neighbors algorithm, are more or less base on a similar idea. Many of classical machine learning algorithms are based on the idea smoothness prior, or local constancy prior. In short in classical ways, you do not expect data to change so much in a small region, so you can expect unknown samples to be similar to data in vicinity. But that soon turns out to be problematic when the dimension of data is bigger because you will not have training data in vicinity. Plus, in high dimensional data, you cannot necessarily approximate new samples with the data in vicinity. The ideas of “close,” “nearby,” or “vicinity” get more obscure in high dimensional data. That point is related to the next topic: the intuition have cultivated in normal life is not applicable to higher dimensional data.
### 2, Bizarre characteristics of high dimensional data
We form our sense of recognition in 3-dimensional way in our normal life. Even though we can visualize only 1, 2, 3 dimensional data, we can actually expand the ideas in 2 or 3 dimensional sense to higher dimensions. For example 4 dimensional cubes, 100 dimensional spheres, or orthogonality in 255 dimensional space. Again, you cannot exactly visualize those ideas, and for many people, such high dimensional phenomenon are just imaginary matters on blackboards.
Those high dimensional ideas are designed to retain some conditions in 1, 2, or 3 dimensional space. Let’s take an example of spheres in several dimensional spaces. One general condition of spheres, or to be exact the surfaces of spheres, are they are a set of points, whose distance from the center point are all the same.
For example you can calculate the value of a D-ball, a sphere with radius in dimensional space as below.
Of course when is bigger than 3, you cannot visualize such sphere anymore, but you define such D-ball if you generalize the some features of sphere to higher dimensional space.
Just in case you are not so familiar with linear algebra, geometry, or the idea of high dimensional space, let’s see what D-ball means concretely.
But there is one severe problem: the behaviors of data in high dimensional field is quite different from those in two or three dimensional space. To be concrete, in high dimensional field, cubes are spiky, you have to move like Pac-Man, and M & M’s Chocolate looks empty inside but tastes normal.
2_1: spiky cubes
Let’s look take an elementary-school-level example of geometry first.
In the first section, I wrote about grids in several dimensions. “Grids” in that case are the same as “hypercubes.” Hypercubes mean generalized grids or cubes in high dimensional space.
* You can confirm that the higher the dimension is the more spiky hypercube becomes, by comparing the volume of the hypercube and the volume of the D-ball inscribed inside the hypercube. Thereby it can be proved that the volume of hypercube concentrates on the corners of the hypercube. Plus, as I mentioned the longest diagonal distance of hypercube gets longer as dimension degree increases. That is why hypercube is said to be spiky. For mathematical proof, please check the Exercise 1.19 of PRML.
#### 2_2: Pac-Man walking
Next intriguing phenomenon in high dimensional field is that most of pairs of vectors in high dimensional space are orthogonal. First of all, let’s see a general meaning of orthogonality of vectors in high dimensional space.
#### 2_3: empty M & M’s chocolate
That is why, in high dimensional space, M & M’s chocolate look empty but tastes normal: all the chocolate are concentrated beneath the sugar coating. Of course this is also contrary to our daily sense, and inside M & M’s chocolate is a mysterious world.
This fact is especially problematic because many machine learning algorithms depends on distances between pairs of data points. Even if you van approximate the distance between two points as zero, like you do in ////, there is no guarantee that you can do the same thing in higher dimensional
3, Peeking phenomenon
## Back propagation of LSTM: just get ready for the most tiresome part
In this article I will just give you some tips to get ready for the most tiresome part of understanding LSTM.
### 1, Chain rules
In fact this article is virtually an article on chain rules of differentiation. Even if you have clear understandings on chain rules, I recommend you to take a look at this section. If you have written down all the equations of back propagation of DCL, you would have seen what chain rules are. Even simple chain rules for backprop of normal DCL can be difficult to some people, but when it comes to backprop of LSTM, it is a monster of chain rules. I think using graphical models would help you understand what chain rules are like. Graphical models are basically used to describe the relations of variables and functions in probabilistic models, so to be exact I am going to use “something like graphical models” in this article. Not that this is a common way to explain chain rules.
First, let’s think about the simplest type of chain rule. Assume that you have a function $f=f(x)=f(x(y))$, and relations of the functions are displayed as the graphical model at the left side of the figure below. Variables are a type of function, so you should think that every node in graphical models denotes a function. Arrows in purple in the right side of the chart show how information propagate in differentiation.
Next, if you a function $f$ , which has two variances $x_1$ and $x_2$. And both of the variances also share two variances $y_1$ and $y_2$. When you take partial differentiation of $f$ with respect to $y_1$ or $y_2$, the formula is a little tricky. Let’s think about how to calculate $\frac{\partial f}{\partial y_1}$. The variance $y_1$ propagates to $f$ via $x_1$ and $x_2$. In this case the partial differentiation has two terms as below.
In chain rules, you have to think about all the routes where a variance can propagate through. If you generalize chain rules, that is like below, and you need to understand chain rules in this way to understanding any types of back propagation.
The figure above shows that if you calculate partial differentiation of $f$ with respect to $y_i$, the partial differentiation has $n$ terms in total because $y_i$ propagates to $f$ via $n$ variances.
### 2, Chain rules in LSTM
I would like you to remember the figure I used to show how errors propagate backward during backprop of simple RNNs. The errors at the last time step propagates only at the last time step.
At RNN block level, the flows of errors are the same in LSTM backprop, but the flow of errors in each block is much more complicated in LSTM backprop.
3, How LSTMs tackle exploding/vanishing gradients problems
## How to develop digital products and solutions for industrial environments?
### The Data Science and Engineering Process in PLM.
Huge opportunities for digital products are accompanied by huge risks
Digitalization is about to profoundly change the way we live and work. The increasing availability of data combined with growing storage capacities and computing power make it possible to create data-based products, services, and customer specific solutions to create insight with value for the business. Successful implementation requires systematic procedures for managing and analyzing data, but today such procedures are not covered in the PLM processes.
From our experience in industrial settings, organizations start processing the data that happens to be available. This data often does not fully cover the situation of interest, typically has poor quality, and in turn the results of data analysis are misleading. In industrial environments, the reliability and accuracy of results are crucial. Therefore, an enormous responsibility comes with the development of digital products and solutions. Unless there are systematic procedures in place to guide data management and data analysis in the development lifecycle, many promising digital products will not meet expectations.
Various methodologies exist but no comprehensive framework
Over the last decades, various methodologies focusing on specific aspects of how to deal with data were promoted across industries and academia. Examples are Six Sigma, CRISP-DM, JDM standard, DMM model, and KDD process. These methodologies aim at introducing principles for systematic data management and data analysis. Each methodology makes an important contribution to the overall picture of how to deal with data, but none provides a comprehensive framework covering all the necessary tasks and activities for the development of digital products. We should take these approaches as valuable input and integrate their strengths into a comprehensive Data Science and Engineering framework.
In fact, we believe it is time to establish an independent discipline to address the specific challenges of developing digital products, services and customer specific solutions. We need the same kind of professionalism in dealing with data that has been achieved in the established branches of engineering.
Data Science and Engineering as new discipline
Whereas the implementation of software algorithms is adequately guided by software engineering practices, there is currently no established engineering discipline covering the important tasks that focus on the data and how to develop causal models that capture the real world. We believe the development of industrial grade digital products and services requires an additional process area comprising best practices for data management and data analysis. This process area addresses the specific roles, skills, tasks, methods, tools, and management that are needed to succeed.
More than in other engineering disciplines, the outputs of Data Science and Engineering are created in repetitions of tasks in iterative cycles. The tasks are therefore organized into workflows with distinct objectives that clearly overlap along the phases of the PLM process.
Real business value will be generated only if the prediction model at the core of the digital product reliably and accurately reflects the real world, and the results allow to derive not only correct but also helpful conclusions. Now is the time to embrace the unique chances by establishing professionalism in data science and engineering.
# Authors
Peter Louis
Peter Louis is working at Siemens Advanta Consulting as Senior Key Expert. He has 25 years’ experience in Project Management, Quality Management, Software Engineering, Statistical Process Control, and various process frameworks (Lean, Agile, CMMI). He is an expert on SPC, KPI systems, data analytics, prediction modelling, and Six Sigma Black Belt.
Ralf Russ
Ralf Russ works as a Principal Key Expert at Siemens Advanta Consulting. He has more than two decades experience rolling out frameworks for development of industrial-grade high quality products, services, and solutions. He is Six Sigma Master Black Belt and passionate about process transparency, optimization, anomaly detection, and prediction modelling using statistics and data analytics.4 | 2021-10-27 05:50:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5134114623069763, "perplexity": 745.5316297718357}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588102.27/warc/CC-MAIN-20211027053727-20211027083727-00702.warc.gz"} |
https://computergraphics.stackexchange.com/tags/physics/hot | # Tag Info
30
To start, I highly suggest reading Naty Hoffman's Siggraph presentation covering the physics of rendering. That said, I will try to answer your specific questions, borrowing images from his presentation. Looking at a single light particle hitting a point on the surface of a material, it can do 2 things: reflect, or refract. Reflected light will bounce away ...
23
I was actually wondering about exactly this a few days ago. Not finding any resources within the graphics community, I actually walked over to the Physics department at my university and asked. It turns out that there are a lot of lies we graphics people believe. First, when light hits a surface, the Fresnel equations apply. The proportions of reflected/...
13
The next step up from a pinhole camera model is a thin lens model, where we model the lens as being an infinitely thin disc. This is still an idealization that pretty far from modeling a real camera, but it will give you basic depth of field effects. The image above, from panohelp.com, shows the basic idea. For each point on the image, there are multiple ...
11
Warning: I am not a physicist. As Dan Hulme already explained, light can't travel through metals, so dealing with IOR is a lot more... complex. I will answer why that happens and how to calculate the reflection coefficient. Explanation: Metals are filled with free electrons. Those electrons react to external fields and reposition until electrostatic ...
10
Here's a chromaticity diagram that includes a projection of the sRGB color space: a triangle whose vertices are red (1,0,0), green (0,1,0), and blue (0,0,1). Encoding the reflectance of a surface as the color at F0 and getting a value that is outside of the (somewhat arbitrary chosen) sRGB gamut is totally reasonable. It just means that gold is "more red" ...
9
RGB color is a bit more complicated a subject than readily seems apparent. The reflectance wavelength diagram shows the reason quite well actually. RGB color model has several central problems: What the colors represent: They represent 3 spikes in a continuous spectrum. The R, G and B aren't energetically equivalent let alone evenly spaced. What their ...
8
The concept of a point source is an approximation. Physically, light sources are extended objects and emit light from every point on their surface; but when you're far enough away (i.e. the distance to the source is large compared to its size) it's useful to approximate it as a point source. You can get the $1/r^2$ law out of it as follows. Imagine a ...
7
Few things, but usually this is what it takes to make the difference: 1- the material reflection at his head, he is bald, yet the diffuse texture shows color difference where the hair is, this means he has a shaved head, not a natural bald, this should translate in reflection, take a look at his head, top right (top left for the image), the reflection is ...
6
Look at the refractive index of several metals. They are all complex numbers and the math does work out when you put this into the fresnel equation: you get the expected high reflectivity at all angles. There are also subtle color shifts because the index depends on wavelength. This is actually used in rendering but it is not common. The function is ...
5
PhysX is a C++ API and can thus not directly be integrated with the JavaScript-based WebGL. Depending on your needs, you have the following options: Use a JavaScript-based physics engine, mostly suitable for 2D use cases. Use a Game Engine that can export for the web (e.g. Unity 3D) and build your application in there, using full 3D physics capability. ...
5
It is the inverse square law of light for a pure point light. $E = \frac{I}{r^2}$ Where E is illuminance and I is pointance or power/flux per unit solid angle.
4
I think you identified the problem yourself in your question : it still definitely looks like a 3d model It's obviously hard to tell and subjective, but while many things are off in this picture, the expression and the proportions of the character model are what I find most unrealistic. It is to the appreciation of the art director, but most of the time, ...
4
Hard to say because we can not see the code. Subsurface scattering might be part of that equation. I would just point out that human brains are extremely specialized in facial recognition. It has been postulated that the brain has a inbuilt defence mechanism to detect alien impostors/anomalous people. You are right in middle of what is known as uncanny ...
4
Firstly, I highly suggest reading Eric Heitz's paper "Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs", which covers the full derivation of microfacet-based BRDFs. The $\frac{1}{4(N \cdot V)(N \cdot L)}$ term is a side effect of the derivation of the BRDF for specular microfacets. Specifically, it comes from the Jacobian of the ...
4
I don't have any experience with Gradient Domain Path Tracing, but here are my thoughts: There seems to be a different problem If you look carefully at the little spikes of distortion in the final image, you will see that they are all lit from the same direction - on their top left side at a consistent 45 degrees. The sphere also appears to be lit from ...
4
I'll give an intuitive idea of the reason in this answer. Once this intuitive idea is grasped, it can be easier to absorb the mathematical descriptions. Other people find it easier the other way around, so look at all the answers and see which approach works for you personally. A spherical shell of photons Imagine a point light source. Picture an instant ...
4
See Kolb, et al., A Realistic Camera Model for Computer Graphics, SIGGRAPH 95. However, do bear in mind that camera models which mimic real-world cameras aren't necessarily what you want for the rendering phase. In a visual effects/post-production scenario, the more blur/vignetting/distortion that the camera model introduces, the worse it is for the ...
4
For rendering of gases, I think the usual approach is to simply render each particle as a tiny disc. Gases don't really coalesce into surfaces like liquids do, so this should produce acceptable results. You could perhaps apply a light blur over the gas layer afterwards to soften it and hide the fact that it is made of discrete elements. Liquids, on the ...
4
The shape you’re trying to draw is called a catenary: it’s the shape that a cable/cord of constant density takes when supported at each end. You’ll have to do some research to find a parametric equation for its shape—this page has a start, though it doesn’t let you substitute in the endpoints so you’ll need some additional work there. Once you have an ...
4
Radiance (in terms of flux) has the following definition: $L_o = \frac{\mathrm{d}\Phi}{\mathrm{d}\omega^\perp\mathrm{d}A} = \frac{\mathrm{d}\Phi}{\cos{\theta} \mathrm{d}\omega \mathrm{d}A}$. Thus in order to get the total emitted power we need to integrate over the area of the light and we need to integrate over the projected solid angle of the hemisphere (...
3
For the lightning, I recommend using a midpoint displacement algorithm. You start with a line segment between any 2 points A and B (this works in either 2D or 3D). Calculate the midpoint of the segment AB. Now move that point a random amount in the direction perpendicular to the line segment AB and call it point C. Replace the original segment AB with 2 line ...
3
I can only cite what I have learned in my lecture on Global Illumination techniques which was unfortunately some time ago: Radiant Power : The amount of energy emitted by a light source in unit time. denoted by $\Phi$ and is measured in Watt which equals to Joules per second. (This does not specify any area!) Irradiance: The irradiance denotes the incident ...
3
"the information that $f(l_k,v)$ carries is low-frequency enough": As IneQuation explains, low-frequency was used to refer to the detail of the brdf function. I did actually mean that $f_r$ was low frequency though (which is the case with diffuse lighting), not $L_i$. "with respect to $L_i$": what this means it that, since there aren't any large peaks in $... 2 I see several things that are off in addition to what others have said. He doesn't appear to be breathing. He's in a very cold place (it appears to be snowing), yet there's no breath in front of his nose or mouth. It's snowing, but none of the snow is in front of him. It's all behind him, or on his clothes, but not falling around him. I feel like our brains ... 2 Say the point light is at$P_L$, the shading is happening at$P_S$It's true that the radiance is constant along a shadow ray$P_L \rightarrow P_S$, but that's not the key property for solving the rendering equation at$P_S$. The rendering equation, somewhat simplified, is:$L_o(\omega_o) = L_e(\omega_o) + \int_{\Omega} \, f_r(\omega_i, \omega_o)\, L_i(\...
2
Thanks for your answers. That was helpfull. This is how I understand the 1/r² term for point source (tell me if I'm wrong). Let's take the BRDF definition : $$L_o = \int f(\omega, \omega_o) \, dE$$ Now, we have to answer this question : How is the Irradiance E distributed ? For one point source, we have : $$dE = \delta(\omega_i-\omega)E \, d\omega$$ ...
2
Compare it with someone else's software. Run some standardized test and find out if you get roughly the same answer as others. If you get the same answer, than the probability of having your code right is quite high. Some tests: Flow past cylinder. In 2d take rectangular domain, cylinder in the middle, inflow on the left, outflow on the fight and calculate ...
2
I think the assumption (perhaps stated perhaps not, I dont' have the text handy) is that the radiance is emitted in a cosine-lobe distribution. This means that there's falloff in proportion to the cosine of the angle between the emitter's normal, and the direction of emission. If you look in the global illumination compendium, under Hemispherical Geometry, ...
1
The damping force you mentioned $f=-k \frac{\dot{l} \cdot l}{|l|} \frac{l}{|l|}$ is a special case of $f=-k \dot{C} \frac{\partial C}{\partial \mathbf{x}}$. Let \begin{align} C(\mathbf{x}) &= \lVert\mathbf{l}\rVert-l_0 \\ \mathbf{l} &= \mathbf{x}_1 - \mathbf{x}_2 \\ \mathbf{\dot{l}} &= \mathbf{v}_1 - \mathbf{v}_2 \\ \mathbf{v} &= \dot{\...
1
If we sidestep your typo (the last term has one absolute too much), both formulations are correct. They just express different things. The $k$ in Hooke's law is for a particular spring. $k_s$ is the siffness for a paricular material. Now in the linear portion there is a direct relationship betwen these the material stffness is directly propotional to the ...
Only top voted, non community-wiki answers of a minimum length are eligible | 2019-10-18 04:02:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8321422934532166, "perplexity": 750.3908390909486}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986677884.28/warc/CC-MAIN-20191018032611-20191018060111-00040.warc.gz"} |
https://iidb.org/threads/and-she-called-me-stupid.18513/page-2#post-712206 | And she called me stupid
TSwizzle
Let's Go Brandon!
In a casual arrangement such as this, I would hang on to the $200 until I was asked for it. When asked, I would pay back$100 and explain I am withholding the other $100 as it is being used to pay a long overdue debt of$100. Then I would promise myself never to lend or borrow from that person again.
What does it being casual have to do with anything? It doesn’t give you a moral pass to shrewdly balance the books.
It's a casual arrangement based on a friendship or some kind of relationship, it makes the agreement a bit more flexible as opposed to dealing with a financial institution. Getting payment for what is owed is not "shrewdly balancing the books". It's settling an overdue debt. I have no qualms about it. Lesson learned is not to lend or borrow with this person again.
Actually, the stupid part of it all is borrowing $200 from someone that owes you$100. That makes no sense in the first place.
ronburgundy
Contributor
Depends.
I'd say that it is within your moral rights to only give $100 back, but it isn't "stupid" to give the full$200 back.
After the first week when they didn't pay you, it becomes equivalent to theft on their part. You have a right to get your property back short of causing them direct physical harm to do it. Lying is not inherently immoral, and can even be a moral requirement. So, pretending you'll give it all back but not is not immoral itself. And I would say that if the consequence of lying is that you get back your rightful property, then you've done nothing wrong.
However if it is someone you care about and they might need the full $200 back now and you don't really need the$100 now, then give the $200 back and hopefully they will be able to pay you in the future. IOW, giving the$200 is not morally required but would be a kind and generous act, and it's not stupid to be kind.
fast
Contributor
Angra Mainyu,
I want to take this moment to explicitly express that I have respect for you and value your perspective. Thank you.
In my struggle to reconcile what seems to be differences, it has dawned on me what might be going on. Explaining it, with my atrocious skills at clearly and concisely explaining it might require ibuprofen afterwards, so forgive me as I take a pot shot at explaining it.
You speak of one party having an obligation. I’m sure you recognize people can have a variety of obligations, but when you speak of a particular obligation, it’s singular in nature (which it should be if you’re focused on one), whereas I am so hung ho on compartmentalizing things, I don’t complete what you might call something similar to a cost-benefit analysis.
Your stance is reminiscent of an approach a judge might take when reconciling the fall out from a divorce or dissolution of a business partnership. You look at everything and make an evaluation that’s reflective of all things considered. That is not abnormal. When most people list the pros and cons of something, it culminates in a single overall conclusion after the evaluation.
When the benefits of something or some course of action outweigh the costs, people won’t conclude that the course of action is harmful; indeed, they’ll say it’s beneficial, and they’ll do that even if there are elements (or fragments) of harm within the cons.
What I see is the preanalysis. I see Jack owing $200, and I see Joe owing$300, so I don’t have a conclusion whereby I arrive at a single obligation (Joe owes $100). I see two obligations. If you were a judge (and remember, I admitted there was an air of unfairness in what I’ve been saying), you would evaluate (as would the judge) the individual things I see and arrive at your conclusion. If there is a tradition that is outdated and it’s replaced with a more progressive appeal, I see harm (the destruction of the tradition) and I see benefit (the bringing of the new), and if the new outweighs the old, there is a net benefit and thus won’t be regarded as harmful but beneficial. People will refuse to acknowledge my take that there is harm because they want to reserve that term for post analysis only. If you write 3 checks ($100 a piece) and make 10 deposits ($100 a piece), I see the parts and label them for what they are. You may evaluate the transactions and see$700 and see a net gain, and that’s fine. I do too, but I see the destruction of tradition as harmful (not necessarily as a post analysis conclusion though). The net gain may not be harmful overall but in fact beneficial. Kinda silly of me to say it’s harmful huh, when generally people save such attribution for the final analysis.
How about this: are there two individual obligations that when evaluated yields a net obligation; or neither promise alone makes for an obligation and it’s the net difference of the promises that breeds the obligation?
Angra Mainyu
Veteran Member
fast,
Thanks; I also respect you and value your input.
Regarding your analysis, I'm not sure I'm getting it right, but I do think I am trying to assess the whole thing. But it's not only the whole thing combining the $100 and the$200 into a single obligation, but rather, trying to assess their respective obligations from the perspective of the whole interaction and the relationship between the two. For instance, in the first scenario you described here, I think he probably should pay $200 as you think, rather than only$100. On the other hand, it the scenario I described here, I think it's only $100. I make those assessments intuitively, but if I had to guess the reason, I think it has something to do with the entire context of their interaction. In particular, in one case, she needs the money, and while she failed to pay before, the reasons are unspecified, and he agreed to pay knowning she had already failed to pay. In the other scenario, she grants that she's immorally not paying just to get an extra$100. I think her callous behavior with respect to the previous agreement may well be what makes a difference.
Generally, the whole relationship between the two people matters. For example, suppose my mother asked me for $400 the day before yesterday, and told me she'd give them back to me on Friday. If, on Friday, she tells me she got a great offer for a tour and she spent the money, so she'll pay me back later, then she's not doing anything wrong, and has no obligation to give them back (actually, she may just keep them). Now, I'm not saying that that would be the case for every mother with respect to her son. It depends on the situation. But I know she would not have an obligation. On the other hand, if a coworker did the same, she'd be acting immorally by spending the money on a tour when she promised to give it back to me. And this is so even if both my mother and the coworker use the same words, telling me that they'll give me the money back on such-and-such day, etc. I think you also consider the whole thing when making those assessments, by the way. When you focus on those separate promises in your anaysis, I think that's probably because, upon contemplating the whole thing intuitively, you reckoned that those two remain separate for the morally relevant matters at hand. But why do we have different intuitions in some of the cases we have presented? I can only speculate here, but I think that one potential reason is that sometimes, in hypothetical scenarios we are unfamiliar with (including but not limited to unrealistic ones), it's very difficult to fill in the blanks and make good probabilistic assessments about what is really going on in the interaction between the people whose obligations we are trying to assess, and that makes it difficult for us to get the right moral answer. In other words, the descriptions of the scenarios in this thread are not only incomplete (as always), but unfamiliar, and it may be that you and I are intuitively making different probabilistic assessments about other parts of their relationship, and things like intent, information available to each of the parties, etc., so we are actually assessing considerably different scenarios 'in our heads' so to speak. If so, the moral disagreement may not be fundamental after all, even if we can't find a way out. Still, there is an alternative possibility: it might happen also that the sense of right and wrong of different people diverge in some unrealistic scenarios, and this is happening here. I believe the human sense of right and wrong is generally reliable in realistic and in many unrealistic scenarios, but there are unrealistic scenarios when it is not so reliable, so either of us might be going wrong. I do not know for sure. But as I said before, I do not think in an actual scenario we would have much trouble figuring out our moral obligations. In an actual scenario, we would have plenty of further information about our respective relations with the other person, so we would both very probably be able to make an informed and correct moral assessment (even if we might not be able to pinpoint the reasons for our assessment). At any rate, as I said, I would agree that you're not being stupid. I think your friend probably made the following mistake: she failed to put herself properly into your shoes, and consider how your sense of right and wrong was assessing the matter. Maybe she is thinking of a scenario very different from the one you had in mind, by filling in the blanks differently. fast said: If there is a tradition that is outdated and it’s replaced with a more progressive appeal, I see harm (the destruction of the tradition) and I see benefit (the bringing of the new), and if the new outweighs the old, there is a net benefit and thus won’t be regarded as harmful but beneficial. People will refuse to acknowledge my take that there is harm because they want to reserve that term for post analysis only. I'm not sure I'm getting this right, but if you're talking about a tradition about how to evaluate obligations, I see both the tradition and the new idea as approximations that may yield the right verdict in cases that may be more or less common depending on the place, time, country, etc., but not as a replacement for the basic method of considering things on a case by case basis, and using the intuitive human sense of right and wrong. There is no need to destroy the tradition, or to replace it. Rather, it's about considering that neither theory or method (the traditional or the new one) is general, but a shortcut applicable to some specific cases (maybe a good shortcut in some social environments, in the sense it works in nearly all cases in those environments, but we should take into consideration it might not work in others). fast said: How about this: are there two individual obligations that when evaluated yields a net obligation; or neither promise alone makes for an obligation and it’s the net difference of the promises that breeds the obligation? I tend to think there is no simple answer. Rather, I think the relationship between two people results in many obligations, forming a very complex network. Promises do create some of those obligations, but the extent and conditions of them depend not only on what is said, but also on all sorts of complex interactions (e.g., consider the scenarios with my mother vs. my coworker above: they may both say the exact same words, and yet the resulting obligations are very different; that is so because of the whole context of the relationship between each of them and me). In short, I think that we can generally make proper assessments in realistic cases (and many unrealistic ones), but the study of the rules by which the obligations are governed (including those involving promises) is a very difficult matter for future research in human psychology and moral philosophy. Gun Nut Veteran Member By paying back only$100 you ARE keeping to the deal. You paid her $200... it's just that$100 of it evaporated with the closing of the previous deal.
I do not think the thought experiment survives past the "How can she have $200 to lend you if she didn't have the$100 to reimburse you" observation.
zorq
Veteran Member
I agree with Gun Nut... who is agreeing with Treedbear back on post #7.
It is an unrealistic scenario. The exploration of moral intuition between fast and AM is fascinating but so implausible that it is impractical, at least to my POV.
Suspending my disbelief for a moment though; I have to say that I agree with Angra Mainyu. The context is key, and we gain more information when we consider all the aspects of the relationship between the two parties rather than segregating individual aspects of their relationships into self contained units. Choosing to ignore ANY part of the relationship context when coming to a final evaluation of which course of action to proceed with is a mistake.
Fast's insistence on separating the agreements into discreet moral choices reminds me of the runaway trolly problem. Would fast be willing to divert the trolly onto the side track killing one person or would he abstain and let the trolly kill 5? Taken as a seperated choice, I would never choose to deliberately kill one person by my intentional action. It's the larger context that gives that option some merit.
Fast insists that the moral quandary under consideration is not a dichotomy like the trolly problem in which the two agreements have a necessary link. In the trolly problem we are not given the option to both divert the trolly away from the 5 workers and NOT divert the trolly into the lone worker. We are FORCED to take both options into consideration because the two are inextricably linked. But is this moral quandary really that different? Not a single scenario presented in this thread involves instantaneous decisions by the two parties. Each one happens over a period of time which gives one of the parties experience and knowledge about the other before the final judgement is made. This establishes the relationship between the two people. I have never made a decision in my life in which I did not bring all of my knowledge, experience, and intuition to bear to reach a judgement. It is unrealistic to me for a person to blind themselves to knowledge they know might be relevant.
To me, the two agreements are inextricably linked.
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fast
Contributor
It’s an unrealistic scenario.”
I don’t think this is as unrealistic as it seems. I say this because some older people have recollected similar situations where similar circumstances have occurred. As to the issue of whether an obligation continues to exist, I just don’t know.
But, if I tell you (unrealistic as it might be) that’ll i’ll pay you $200 back, i’m not going to use that opportunity to balance the books for your failure to pay me as you had originally said you would. It seems dishonorable. Maybe it’s technically not if the obligation isn’t really there, but say what some might, it has the feel of being wrong. That’s not to say I might not grin if I see another otherwise good person say towards an otherwise bad person, “hey, you screwed me; I screwed ya back!” In the end, it may be an equitable and fair outcome, but I would not personally place trust in such a person should I enter into such an agreement with him, and that’s because his sense of obligation is in stark disaccord with my view on his willingness to keep his word. Treedbear Veteran Member It’s an unrealistic scenario.” I don’t think this is as unrealistic as it seems. I say this because some older people have recollected similar situations where similar circumstances have occurred. As to the issue of whether an obligation continues to exist, I just don’t know. But, if I tell you (unrealistic as it might be) that’ll i’ll pay you$200 back, i’m not going to use that opportunity to balance the books for your failure to pay me as you had originally said you would. It seems dishonorable. Maybe it’s technically not if the obligation isn’t really there, but say what some might, it has the feel of being wrong.
That’s not to say I might not grin if I see another otherwise good person say towards an otherwise bad person, “hey, you screwed me; I screwed ya back!” In the end, it may be an equitable and fair outcome, but I would not personally place trust in such a person should I enter into such an agreement with him, and that’s because his sense of obligation is in stark disaccord with my view on his willingness to keep his word.
Trust has to be mutual. That's why I don't understand how you could seek to borrow any money from her when she had already demonstrated her own ongoing lack of integrity. There's a distinct irony in assuming she should trust you when it's obvious to everyone you have no reason to trust her. The only exception I can see is as an act of charity, which would be commendable if that was the motive. But that would imply you've forgiven her debt.
Jimmy Higgins
Contributor
It’s an unrealistic scenario.”
I don’t think this is as unrealistic as it seems.
The unrealistic part is the whole, you don't discuss the owed $100 during the$200 borrowing episode.
But, if I tell you (unrealistic as it might be) that’ll i’ll pay you $200 back, i’m not going to use that opportunity to balance the books for your failure to pay me as you had originally said you would. It seems dishonorable. It seems passive aggressive, but from you, it fits I suppose. fast Contributor It’s an unrealistic scenario.” I don’t think this is as unrealistic as it seems. I say this because some older people have recollected similar situations where similar circumstances have occurred. As to the issue of whether an obligation continues to exist, I just don’t know. But, if I tell you (unrealistic as it might be) that’ll i’ll pay you$200 back, i’m not going to use that opportunity to balance the books for your failure to pay me as you had originally said you would. It seems dishonorable. Maybe it’s technically not if the obligation isn’t really there, but say what some might, it has the feel of being wrong.
That’s not to say I might not grin if I see another otherwise good person say towards an otherwise bad person, “hey, you screwed me; I screwed ya back!” In the end, it may be an equitable and fair outcome, but I would not personally place trust in such a person should I enter into such an agreement with him, and that’s because his sense of obligation is in stark disaccord with my view on his willingness to keep his word.
Trust has to be mutual. That's why I don't understand how you could seek to borrow any money from her when she had already demonstrated her own ongoing lack of integrity. There's a distinct irony in assuming she should trust you when it's obvious to everyone you have no reason to trust her. The only exception I can see is as an act of charity, which would be commendable if that was the motive. But that would imply you've forgiven her debt.
If I’m the borrower, the trustworthiness of the lender is irrelevant. If you tell me you have to have it back, I should not say I will pay it back if I tell you I will but won’t.
Treedbear
Veteran Member
It’s an unrealistic scenario.”
I don’t think this is as unrealistic as it seems. I say this because some older people have recollected similar situations where similar circumstances have occurred. As to the issue of whether an obligation continues to exist, I just don’t know.
But, if I tell you (unrealistic as it might be) that’ll i’ll pay you $200 back, i’m not going to use that opportunity to balance the books for your failure to pay me as you had originally said you would. It seems dishonorable. Maybe it’s technically not if the obligation isn’t really there, but say what some might, it has the feel of being wrong. That’s not to say I might not grin if I see another otherwise good person say towards an otherwise bad person, “hey, you screwed me; I screwed ya back!” In the end, it may be an equitable and fair outcome, but I would not personally place trust in such a person should I enter into such an agreement with him, and that’s because his sense of obligation is in stark disaccord with my view on his willingness to keep his word. Trust has to be mutual. That's why I don't understand how you could seek to borrow any money from her when she had already demonstrated her own ongoing lack of integrity. There's a distinct irony in assuming she should trust you when it's obvious to everyone you have no reason to trust her. The only exception I can see is as an act of charity, which would be commendable if that was the motive. But that would imply you've forgiven her debt. If I’m the borrower, the trustworthiness of the lender is irrelevant. If you tell me you have to have it back, I should not say I will pay it back if I tell you I will but won’t. Well the way I see it if a friend is willing to lend money to me and I'm willing to accept a loan from a friend then it means I'd be willing to lend money to them also. It needs to be a two way street. That's the way interpersonal relationships work. Banks are different and have stricter means of accounting that don't always reflect how honorable and trustworthy they or the individual are, but are simply based on balancing out accounts. Which means you'd get to keep your$100.
fast
Contributor
Friend or no friend, if you’re the borrower and capable and willing to keep your word, then you should. I don’t particularly feel too inclined or somehow obligated to lend someone money just because they would lend it to me, especially if they a proven track record of failing to live up to their end of the bargain.
I’ve met a few people (and believe me when I say they’re far and few between) that would not dream of reneging on their word. They wouldn’t be swayed in the slightest by some argument that they had no obligation to do as they said.
If you borrowed fifty dollars from someone and later you caught them stealing from you, you may net keep your word. You may feel justified. You may feel that the obligation has gone away. Heck, you may be justified and no longer have an obligation, but for a proud few, no matter what you say, you will never have good reason to call them a liar.
fast
Contributor
Clear? Clear. CLEAR?? Crystal.
People are always capable of coming up with excuses for why they don’t do what they said they would—and don’t do what they said they would.
People (but substantively fewer) may have a legitamate justifiable reason for why they didnt do what they said they would—and also don’t (forgivably so) do what they said they would.
Then, you have people who let’s neither justification nor good sense stand in their way. Of course, there’s numerous hypotheticals where one cannot do as they said they would, but there’s plenty of justifiable reasons that can be overcome.
Some people will accept a little inconvenience before not keeping their word, but how many would down right suffer?
fast
Contributor
Yeah. Prisoners don't choose.
They are held against their will. But even still, they can choose which of their sides to sleep on.
If you’re saying we’re trapped to choose what we must, like prisoners of our limitations, or some such jazz, then even though we are bound by our abilities, we can freely choose between our available choices.
Treedbear
Veteran Member
Friend or no friend, if you’re the borrower and capable and willing to keep your word, then you should. I don’t particularly feel too inclined or somehow obligated to lend someone money just because they would lend it to me, especially if they a proven track record of failing to live up to their end of the bargain.
I’ve met a few people (and believe me when I say they’re far and few between) that would not dream of reneging on their word. They wouldn’t be swayed in the slightest by some argument that they had no obligation to do as they said.
If you borrowed fifty dollars from someone and later you caught them stealing from you, you may net keep your word. You may feel justified. You may feel that the obligation has gone away. Heck, you may be justified and no longer have an obligation, but for a proud few, no matter what you say, you will never have good reason to call them a liar.
Re-reading the OP it looks like the two people involved actually never were described as friends. So I guess you'd say I was mistaken. It was confusing because you were discussing a hypothetical with a friend who also happened to be a she, and I guess I conflated them. But then again the two of you were taking on the roles pretty well. Be that as it may, it seems logical to ask why you would lend $100 to her in the first place. There has to be something in it for you, if only friendship. I told you what I believe friendship means and that it needs to be reciprocal. The same goes for her when she lends you the$200. Why would she do that for a stranger? Is there interest involved? First born son perhaps? No and no. Playing you for a fool does start to make sense. Of course it's just a hypothetical situation so that's not an attack on your character. The scenario just doesn't seem plausible, and so I think you may be using it as a stage for moral self-righteousness. Yeah, I think that's why my mind keeps going back to the Merchant of Venice. You promised a pound of flesh?? Really? A pound of your own flesh? What rational, moral reason is there for anyone to ever ask for that?
jab
Veteran Member
I would definitely have said something. Like “Do you want me to just pay back the $100 so we’re even up now? I’m prepared to pay what I borrowed, but if you want to use the opportunity to square up, let me know.” I wouldn’t say “stupid”, but I would definitely have used the opportunity to discuss. So you (like me) would have been willing to pay the entire$200; granted, it’s post discussion, but ultimately, you wouldn’t have just commingled the agreements and adjusted accordingly.
It's no longer an agreement if it's commingled without the agreement of both parties. The sensible thing is to ask clearly, "How much of this 200 dollars is to be paid back, in light of the 100 dollars you owe me?"--then, if the answer is $200, and if you need the 200, take it, and pay the whole thing back with the reminder, "You still owe me$100."
Jimmy Higgins
Contributor
Didn't really need a bump, however, I was getting tired of the previous thread that is still on the main page list.
fast
Contributor
Okay.
When the tables are turned, and my reliance on you to keep your word is more important than woulda coulda shoulda justifications, I won’t be so stupid.
fast
Contributor
fromderinside,
Even a statement with no obligatory thrust is true or false. If I say, “I will pay,” even the absence of obligation will not twirl a falsity into a truthhood.
If I adopt a second class sentiment, be wary of me, for I am shrewd.
fromderinside
Mazzie Daius
Why are you defending yourself fast. I applauded OLDMAN because he probably just used the wrong form of you. I took him to be intentional which resulted in both stupid and well played.. Hooked you didn't it?
ruby sparks
Contributor
I overheard a conversation she was having, and in light of it decided to pose a hypothetical scenario question. We’ve known each other a long time, and we speak our minds, so trust me when I say calling me stupid was mild. Although I’ve been called a whole lot worse by her over the years, truth is, we’ve become friends and there’s just no telling what we might say. At any rate, my hypothetical was meant to simplify and parallel the jist of something she said in the conversation I heard. I’ll now pose it to you all.
Let’s say someone comes to you to borrow $100 — with the agreement that it will be paid back next Friday. You lend it to her. Next Friday comes, but you are not paid back. So, this someone still owes you$100.
Fast forward a couple months later. The person still hasn’t paid nor has forgotten, but you need to borrow $200 —with the agreement that it will be paid back next Friday. She lends it to you. When Friday comes, do you A) pay back a hundred dollars (of the$200) thereby balancing the books such that no one owes either any money, or
do you B) pay back the entire two hundred dollars, with that person still owing you $100? She said “A” She said, “what, you’d pay [$200]?”
I said yes and she called me stupid.
She said her not being paid back is partly why she’s in the mess now—would of only had to borrow $100. My reasoning is that two wrongs don’t make it right; they’re independent agreements. A person not honoring her agreement doesn’t justify me breaking mine. I told a couple others what had happened. Both said they’d only pay back$100. One also thought I was stupid. One understood where I was coming from. She tried to explain that people that lend shouldn’t expect it back. I said, as the borrower, I can still decide to keep my word and honor my agreement regardless of the choices others make. If she wants to turn around and pay me back the $100 she owes, that’s her choice. On moral grounds, I think I have the upper hand, but on stupidity grounds, that’s still up in the air. If this were a legal transaction with extra zeros and there was a caveat for me to take an “A” type position, morality be damned, I wouldn’t be stupid, but with little money, I don’t see the advantage of doing what’s wrong—even if the person you’re doing it to would actually understand and accept it. I think some may hold that it wouldn’t be wrong to pay back only the$100, but for those that think it is actually wrong but also thinks it’s stupid, if they are right, it would be stupid to do what’s right.
Any thoughts?
Imo, it would be generous to repay all the $200. It wouldn't be particularly stupid though. It seems to me like some sort of game theory scenario. A long-term strategy involving paying back the$200 might work out better. The repayer can decide their views on that. Generosity can be rewarded via reciprocity (or reputation) later.
fast
Contributor
Why are you defending yourself fast. I applauded OLDMAN because he probably just used the wrong form of you. I took him to be intentional which resulted in both stupid and well played.. Hooked you didn't it?
Prostitution is illegal ... in some places, you hooker, he he
fromderinside
Mazzie Daius
Captain? Captain Hook is that you? I hear something ticking ..... actually it's just clock.
Oooh. That hurts even Schmee ....
fast
Contributor
Imo, it would be generous to repay all the $200. Tipping a waitress is generous. There is no obligation to tip. There is a social expectation, but that doesn’t produce a responsibility, duty, or obligation—morally, legally, or socially. Satisfying the check is not an act of generosity. I would in fact owe that bill. There is an actual obligation to pay. There too is an expectation to pay, but the originating thrust behind that is spawned elsewhere. If it turns out there was no obligation and I unwittingly payed anyway, it would not be considered generosity. If it turns out there was no obligation and I willing paid anyway, it would be generosity but not expected. In the borrowing situation, it’s not the case that I don’t have an obligation to pay, and not paying you because you so happen to also owe me is a rationalization and at least akin to an attempt to justify immoral behavior. It’s similar in form to revenge; you screwed me so I screw you back. I should be judged by my actions. I don’t have to wrong you when you yourself have wronged me. However, let’s say (in light of many posters comments) that I somehow do not in fact have an obligation to pay. There’s still the everpresent issue that I gave my word. I said I would do something, and if I don’t, then I will not have done what I said I would. Does our word not mean anything anymore? To many in this world, they not only don’t care, they don’t understand why they should. Not even the absence of obligation alters the fact that my word is unkept if I choose to reconcile the books by balancing them. If there is no obligation, payment (the$200) would still not be born out of generosity. That is not the spark igniting the flames (it is not the rationale behind the gesture to pay). So why pay? Because I said I would. When I looked into your eyes and said I would do something, you can expect that I will do just as I said I would. I don’t care why you haven’t lived up to your end of an entirely different bargain. That’s on you. Whether you keep your word is on you.
When a patron sits down at a restaurant, there is no tacit agreement between the help and the patron, but there is an obligation to pay the business whether I verbally express my word to pay or not, but let’s say I do promise to pay for my meal, there is a tacit agreement that an exchange is in order. If you don’t provide the meal, it is not the breaking of my word if I don’t pay, for what I gave my word to was to pay for a provided meal. If the meal is not provided, there is no word to live up to. It would be like me promising to pay you $20 for you selling me your$50,000 car. If you don’t sell it to me, I haven’t went against my word to pay.
It wouldn't be particularly stupid though.
fast
Contributor
I would try to avoid problems by having $200 on hand which I display to the other party. I then consciously put the two hundred on the table with my hand atop the cash. I remind the other party of their obligation to me and suggest they use$100 of the two hundred under my hand to settle their debt to me. The other party can object but they don't yet have possession of the two hundred. I take back the two hundred. But I remain in the room giving the other party time to reconsider the situation. All they have to do is ask for accounts to be settled whereupon I'll give then \$100 dollars and say accounts settled.
Nice try. But, you have only until Midnight to pay; otherwise, you have won to keep the upper hand—yet FAILED in another and important way. Recall, there was a time limit. If you’re a microsecond or more late to pay, you will not have done what it is you said you would.
Debtors are the most blind people I’ve ever met. You can’t just agree to one thing and later make a promise to do another thing and consider yourself a person of your word because you did what you said you would. You became a piece of shit the moment you made the latter promise and being a person of your word becomes irrecoverable the moment the clock strikes twelve.
fromderinside
Mazzie Daius
Naw. As I see it a contract spoken is a thing of honor and not one entirely of law. One can be called a liar by either party. So provisions are made in handshake law to permit such as I set forth.
fast
Contributor
Naw. As I see it a contract spoken is a thing of honor and not one entirely of law. One can be called a liar by either party. So provisions are made in handshake law to permit such as I set forth.
I don’t care about the legality of it; moreover, I’m not phased by its enforceability. If we meet upon the stump in the wilderness and without even so much as a handshake or spit to seal a deal, if you look me in the eyes and I utter the words that I shall be back with food in exchange for fixing my broken leg, no boulder, storm, nor nary a reason, let alone an excuse, will stop my every efforts to honor my commitment.
fromderinside
Mazzie Daius
Hey. I was just providing ways to ensure one's commitment is remembered. Never can tell how old your patient may be yano. Your memory may fall short of your commitment.
just SAYIN' | 2022-06-29 18:23:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3392190635204315, "perplexity": 1404.1323879539389}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103642979.38/warc/CC-MAIN-20220629180939-20220629210939-00139.warc.gz"} |
http://bims.iranjournals.ir/article_1038.html | # Decay estimates of solutions to the IBq equation
Document Type: Research Paper
Authors
School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450011, China.
Abstract
In this paper we focus on the Cauchy problem for the generalized IBq equation with damped term in $n$-dimensional space. We establish the global existence and decay estimates of solution with $L^q(1\leq q\leq 2)$ initial value, provided that the initial value is suitably small. Moreover, we also show that the solution is asymptotic to the solution $u_L$ to the corresponding linear equation as time tends to infinity. Finally, asymptotic profile of the solution $u_L$ to the linearized problem is also discussed.
Keywords
Main Subjects
### References
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### History
• Receive Date: 26 November 2015
• Revise Date: 12 June 2016
• Accept Date: 16 July 2016 | 2020-08-11 03:40:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.578482449054718, "perplexity": 1231.3767187443195}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738727.76/warc/CC-MAIN-20200811025355-20200811055355-00274.warc.gz"} |
http://nrich.maths.org/1959 | 8 Methods for Three by One
This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different? Which do you like best?
Figure of Eight
On a nine-point pegboard a band is stretched over 4 pegs in a "figure of 8" arrangement. How many different "figure of 8" arrangements can be made ?
Sine and Cosine for Connected Angles
The length AM can be calculated using trigonometry in two different ways. Create this pair of equivalent calculations for different peg boards, notice a general result, and account for it.
Squ-areas
Stage: 4 Challenge Level:
The diagram shows three squares on the sides of a triangle $ABC$.
Their areas are respectively 18 000, 20 000 and 26 000 square centimetres.
If the squares are joined, three more triangular areas are enclosed. What is the area of this convex hexagon? | 2015-11-30 08:10:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6737669110298157, "perplexity": 884.2545556180974}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398461132.22/warc/CC-MAIN-20151124205421-00156-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://aas.org/archives/BAAS/v28n2/aas188/abs/S007004.html | Session 7 - Gas and Dust in the ISM.
Display session, Monday, June 10
Great Hall,
## [7.04] Correlation between Hydrogen-alpha and 100-micron Emissions
P. R. McCullough (Univ. of Illinois)
Observations of diffuse H\alpha emission in a \sim12 degree field at Galactic latitude --65 degrees show a correlation with infrared cirrus previously observed by IRAS. Anisoptropy of the H\alpha surface brightness is typically 0.2 Rayleighs (i.e. emission measure \sim0.5 cm^-6-pc) on angular scales of 0.1-1.0 degrees. Significantly for further observations of this type, sensitivity appears to be limited by confusion of real structures in the ISM, rather than by telluric sky brightness. The H\alpha emission associated with infrared cirrus likely is due to a combination of emission from gas at high latitude and emission from Galactic H II regions that has been backscattered by dust at high latitude. Observations of this type may provide a means to distinguish between Galactic foreground and cosmic background for both the free-free emission and the thermal dust emission associated with the warm ionized medium of the Milky Way. | 2016-07-23 14:44:11 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8646753430366516, "perplexity": 6281.73790622875}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257822598.11/warc/CC-MAIN-20160723071022-00245-ip-10-185-27-174.ec2.internal.warc.gz"} |
http://stackoverflow.com/questions/12449888/how-to-zip-upzip-a-folder-and-all-of-its-files-and-subdirectories-using-java?answertab=active | # How to zip/upzip a folder and all of its files and subdirectories using Java?
I was reading this to learn how to zip/unzip files using Java. I used this to guide me and it worked great when zipping all the files inside a folder, but when I tested it with a folder containing more folders inside of it, it didn't work, it threw the following error:
java.io.FileNotFoundException: assets (Access is denied) //assets is the name of the folder I tried to zip
at java.io.FileInputStream.open(Native Method)
at java.io.FileInputStream.<init>(Unknown Source)
at java.io.FileInputStream.<init>(Unknown Source)
at Zip.main(Zip.java:24)
This is the class I'm using, as you will see it's the same Code Sample 4: Zip.java class code from the previous link:
import java.io.*;
import java.util.zip.*;
public class Zip {
static final int BUFFER = 2048;
public void zip() {
try {
BufferedInputStream origin = null;
FileOutputStream dest = new
FileOutputStream("H:\\myfigs.zip");
CheckedOutputStream checksum = new
ZipOutputStream out = new
ZipOutputStream(new
BufferedOutputStream(checksum));
//out.setMethod(ZipOutputStream.DEFLATED);
byte data[] = new byte[BUFFER];
// get a list of files from current directory
File f = new File(".");
String files[] = f.list();
for (int i=0; i<files.length; i++) {
FileInputStream fi = new
FileInputStream(files[i]);
origin = new
BufferedInputStream(fi, BUFFER);
ZipEntry entry = new ZipEntry(files[i]);
out.putNextEntry(entry);
int count;
BUFFER)) != -1) {
out.write(data, 0, count);
}
origin.close();
}
out.close();
System.out.println("checksum: "+checksum.getChecksum().getValue());
} catch(Exception e) {
e.printStackTrace();
}
}
}
What changes should be made so this code can zip folders inside folder and all of its files into a zip file?
-
The zip entry needs to specify the path of the file inside the archive. You can't add a folder to a zip archive - you can only add the files within the folder.
The naming convention is to use forward slashes as the path separator. If you are zipping a folder with the following files/subdirectories:
c:\foo\bar\a.txt
c:\foo\bar\sub1\b.txt
c:\foo\bar\sub2\c.txt
the zip entry names would be:
a.txt
sub1/b.txt
sub2/c.txt
So to fix your algorithm, add isDirectory() inside your for loop, and then recursively add the files in any subdirectory to the zip. Probably the best way to do this is to have a method:
addDirectoryToZip(String prefix, File directory, ZipOutputStream out)
Here's a solution for the problem: java.util.zip - Recreating directory structure
-
The ZipEntry.isDirectory states ...A directory entry is defined to be one whose name ends with a '/', when adding entries to the Zip file, you only need to add the trailing slash to the entry name, you don't need to add any content, just the entry – MadProgrammer Sep 16 '12 at 20:36
Thank you so much, this helped me a lot. – Uriel Sep 17 '12 at 3:16
@MadProgrammer makes a good point - if you are trying to have the zip archive recreate an empty folder, you do need to insert a ZipEntry with the folder name ending in a forward slash, and don't add content. – Kevin Day Sep 17 '12 at 3:55 | 2015-05-05 16:57:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5565071105957031, "perplexity": 4538.414253314022}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430456823285.58/warc/CC-MAIN-20150501050703-00010-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://www.hackmath.net/en/math-problem/412 | # Compare
Compare fractions
$\dfrac{ 34}{ 3}$
and
$\dfrac{ 12}{ 4}$
. Which fraction of the lower?
Result
#### Solution:
$\dfrac{ 34}{ 3} = \dfrac{ 136}{ 12} \ \\ \dfrac{ 12}{ 4} = \dfrac{ 36}{ 12} \ \\ \ \\ 136 > 36 \ \\ \ \\ \dfrac{ 34}{ 3} > \dfrac{ 12}{ 4}$
Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!
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