probability – independent and uniformly distributed random variable

Consider three independent sources uniformly distributed (taking values ​​between $ 0 and $ 1 $) Random variables. What is the probability that the middle of the three values ​​(between the smallest and the largest) is between $ a $ and $ b $ or $ 0 ≤ a <b ≤ 1 $?

$ A) 3 (1 – b) a (b – a) $

$ B) 3 ((b – a) – (b ^ {2} – a ^ {2}) / 2) $

$ C) 6 (1 – b) a (b – a) $

$ D) (1 – b) a (b – a) $

$ E) 6 ((b ^ {2} – a ^ {2}) / 2 – (b ^ {3} – a ^ {3}) / 3) $.


Now, formula for uniform distribution $ int_ {a} ^ {b} xdx = left [ frac{x^{2}}{2} right ]_ {a} ^ {b} $

According to the question average value of $ 3 $ the values ​​are inside $ a $ and $ b. $

So, here are 4 possibilities. Let's say that the numbers are x, y, z.

Now,

Case $ 1: $ Only $ y $ can be inside $ a $ and $ b. $

Case $ 2: $ Only $ x, y $ can be inside $ a $ and $ b. $

Case $ 3: $ Only $ y, z $ can be inside $ a $ and $ b. $

Case $ 4: $ $ x, y, z $ everything can be inside $ a $ and $ b. $

So the probability should be $ frac { frac {^ {4} textrm {C} _ {1} times left (b ^ {2} -a ^ {2} right)} {2}} { frac {^ { 8} textrm {C} _ {1} times left (b ^ {2} -a ^ {2} right)} {2}} $

Where am I wrong?

seo – Google selects an independent page like Canonical for many other pages, blocking the indexing of our pages

Since early April, we have many pages such as:

https://www.example.com/index.pl?page=directcore

for which Google continues to select this page as canonical:

https://www.example.com/index.pl?page=hw

(Replace "example" with "signalogic" to get the correct link). Our pages all have a canonical rel = https tag, which Search Console correctly displays as canonical declared by the user.

Why Google indexing persists in this situation? The two pages are linked only in that they are different products. The first page contains a brief mention and a link to the second. They each contain a different and unique content. no human would call them identical. What we declare canonical is not it "credible" or credible? In one way or another, Google is forced to access the independent page. What method do I need to overcome this?

Update. As of June 7, 19, the problem persists. It's actually worse, with more and more pages reputedly identical to this page, like this one which is even more different:

https://www.example.com/index.pl?page=codec_samples

Clicks are decreasing day by day because of this. I've documented the problem here:

https://www.signalogic.com/index.pl?page=google_canonical_page_algorithm_problems

including the formal complaints that I filed with the FTC, the DoJ, and so on. I have sent innumerable comments to Google, as well as emails to John Mueller. I do not know of any other way to get Google to fix everything that is wrong with its canonical page algorithm other than to continue to draw attention to the problem.

Any advice appreciated on how to "break" Google's attachment to an incorrect canonical page.

go

BlackHatKings: Proxies and VPN Section
Posted by: Quintondum
Post time: June 8, 2019 at 02:42.

ai – Development of independent games using machine learning for business intelligence

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2,2019 6x

2,2019 6x[IMG]https: //i110.fastpic*****big/2019/0524/dc/d3bcbcc3ccf43f907914e17119c712dc.jpg[/IMG] I 2 I 2 I 2 HTH 28 4 2014 (). 08.30 .19: 30.209: 35 HTH ,,, 6. 2019 ,. .2 2019 03 2019, 11:40 "": .24. 2018 ,,: & # 39; 19921993. ,, – .242. – , – , , HIGH DEFINITION; . (2). ; ; . (2); (2); (2) YUS 24 13:26. HIGH DEFINITION , , ,. 2 ,,,,) -Page 97! & # 39;: ,, 0: 002: 30 & # 39;,. , 2, ()., 2019.18. 20162), .21), .64). – 2019 (2); 2019 (2); 2019 (39); 2018 () The article examines two films on miners' strikes The July STORM (Produced by UkrNewsReel, Ukrainian 31 13 2015 -, .29. 2018 & # 39; – (VOX LUX ): Slashfilm 31: 2019?: .- (CD-) 6. 6. 13. 19. 26. 34. 34. 43. 50. 57. 65 (2). "" 3, .2019, 11:22:30 2 .. HD., ""; 09:45 "!!!", 1, 43. ""; 09:55 1, 35. "-"; 22:10 "", 1, 36 .7 (3 HD) .19 (2 HD) .24. 2016 – 42 – 1 + 1, 2 39. Toggle the camera. 0:00. 42:08. 0: 0042: 08 Live 170, HD-2019, 2019: 7. 2017, 2, 13: .5: 00, 9, 12. Triumph TR6.22: 00, 2, 7, 7: 15, 7: 20, … 0. 29. "-2": 21:37, 12 2010 1192 12:33 .: – 24. () v.2.200 – 500 .. 25 & 2019, 11:00 : 19 2019.:., -1000.,. The goal of the dog: 2017 ::: Universal Pictures, DreamWorks SKG: ,, (): () :: 120 (): 6: UFD -: 12 292 460. BDIM : -: 2,4610: 2186., ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,. .-,: 2019, – 2017, 2018, 2019. ::: 2017, 2018 ::. – 2019. 1.2019 2019. 2.2019 2019. 3.2019 2019. 4.2019 2019. 5.2019 2019. 6 .2019 2019.38. UFD Independent Films 23 Sep 2016views. 2:39. – () planetakino 26 September 2016 17,2K views. 12:08. . "" "" 24 Oct 23rd 2017views. 2:44. – August 18, 2018 5,2K new views. 5:35. : -! ! ,,,. . ,, – ,,. ,,,. : 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26 , 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38 (in line). , 39, 40, 41.. , -. . 1 – 5.. . 17 2016 6 .41 (1072). . ,,,,. ,, ,,,, & # 39; ,,. 2 + 1 2016, 2 + 1 2016. 2 + 1 2016. 2 + 1 2016 2 + 1 2016.,,. (()) 2019 – 2019. ,,,, & # 39; 2019, 2019. 2019. 2019 2019.? ? 2 2 2. 2019-24201921 2019, 22:23. . . ,. ? 65.:. Warner Bros. . . : 2 2 262019 :. . 25 .. – 2, ,,,. ,,,,. . ,.:. 2? ? ? ? : Andersen ,. . . + 10.5K, +4. 6. Kovaleva08. +522, +1. 7. Serebro. + 495, + 3.: 30 2019! ,,,,,, -. . , 2019 90 2 + 2 HD. 2 + 2 19. ,,,,. 2 + 2. 2017 1 + 1 video ,,,. . , 2 + 2.: 2017 :: ,,,,. . . . 16 1 16.. XVI. (47-68). . – 350 -. 20- XIX. 1932-1933 (). 1932-1933. 225. – rmx (3:42) 13. rmx (3:28) 14. rmx (3:16) 15.,. 80, 2 ,: 2 i 2 i 2019 2 2 2019 2 2019 2: https: //adrenalineprovinggrounds.nin…/j0basirh60pqn.

MervinROX
Reviewed by MervinROX sure
.
2,2019 6x
2 2019 6xhttps: //i110.fastpic*****big/2019/0524/dc/d3bcbcc3ccf43f907914e17119c712dc.jpg i 2 i 2 i 2 HTH 28 4 2014 (). 08.30 .19: 30.209: 35 HTH ,,, 6. 2019 ,. .2 2019 03 2019, 11:40 "": .24. 2018 ,,: & # 39; 19921993. ,, – .242. – , – , , HIGH DEFINITION; . (2). ; ; . (2); (2); (2) YUS 24 13:26. HIGH DEFINITION , , ,. 2 ,,,,) -Page 97! & # 39;: ,, 0: 002: 30 & # 39;
Evaluation: 5

.

algorithm – Gram-Schmidt process in Java for the calculation of independent bases in linear spaces

Given a set of $ k $ $ n $-vecteurs $ x_1, points, x_k $, Gram-Schmidt proces calculates a base $ y_1, dots, y_m $ ( $ m leq k $) whose vectors cover the same space as $ x_1, points, x_k $ but are orthogonal to each other: $ (y_i, y_j) = 0 $ for everyone $ i neq j $, where parentheses denote the inner product
$$
(x, y) = sum_ {i = 1} ^ n x_i y_i.
$$

Below my code:

net.coderodde.math.Additive

package net.coderodde.math;

/ **
* This interface defines the API for adding both elements.
*
* @param  the type of the left operand.
* @param  the type of the right operand.
* @param   the type of sum.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 17, 2019)
* /
public interface Additive {

/ **
* This method adds {@code a} and {@code b} and returns the sum.
*
* @param has the first element.
* @param b the second element.
* @back the sum of the two given numbers.
* /
public O add (I1 a, I2 b);
}

net.coderodde.math.Demo

package net.coderodde.math;

import net.coderodde.math.impl.ComplexVectorProductByScalar;
import net.coderodde.math.impl.ComplexNumber;
import net.coderodde.math.impl.ComplexVectorAdditive;
import net.coderodde.math.impl.ComplexVectorDivisible;
import net.coderodde.math.impl.ComplexVectorInnerProduct;
import net.coderodde.math.impl.ComplexVectorNegative;
import net.coderodde.math.impl.RealVectorAdditive;
import net.coderodde.math.impl.RealVectorDivisible;
import net.coderodde.math.impl.RealVectorInnerProduct;
import net.coderodde.math.impl.RealVectorNegative;
import net.coderodde.math.impl.RealVectorProductByScalar;

/ **
* This class performs a simple demonstration for the Gram-Schmidt process.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 17, 2019)
* /
final class Demo {

public static void main (String[] args) {
Vector x1 = new vector <> (1., -1., 1., -1.);
Vector x2 = new vector <> (5., 1., 1., 1.);
Vector x3 = new vector <> (- 3., -3., 1., -3.);

Vector[]    orthogonalBasis1 =
new GramSchmidtProcess <> (new RealVectorInnerProduct (),
new RealVectorDivisible (),
new RealVectorProductByScalar (),
new RealVectorAdditive (),
new RealVectorNegative ())
.process (x1, x2, x3);

for (vector vector: orthogonalBasis1) {
System.out.println (vector);
}

System.out.println ("Orthogonal:" +
isOrthogonal (orthogonalBasis1[0],
orthogonalBasis1[1],
0.00001));

System.out.println ("------");

// [(1, -2), (3, 4)] = [1 - 2i, 3 + 4i]
        Vector c1 = new vector <> (new complex number (1, -2),
new ComplexNumber (3, 4));

// [(0, -3), (1, 1)] = [-3i, 1 + i]
        Vector c2 = new vector <> (new ComplexNumber (0, -3),
new ComplexNumber (1, 1));

Vector[]    orthogonalBasis2 =
new GramSchmidtProcess <> (new ComplexVectorInnerProduct (),
new ComplexVectorDivisible (),
new ComplexVectorProductByScalar (),
new ComplexVectorAdditive (),
new ComplexVectorNegative ())
.process (c1, c2);

for (vector c: orthogonalBasis2) {
System.out.println (c);
}

System.out.println ("Orthogonal:" +
isOrthogonalComplex (orthogonalBasis2[0],
orthogonalBasis2[1],
0.00001));
}

public static  booleanIsOrthogonal base (vector[]    based,
double epsilon) {
for (int i = 1; i <base.length; i ++) {
Vector target = base[i];

for (int j = 0; j <i; j ++) {
Vector current = base[j];

if (! isOrthogonal (target, current, epsilon)) {
returns false;
}
}
}

return true;
}

static public base booleanIsOrthogonalComplex (
Vector[]    base, double epsilon) {
for (int i = 1; i <base.length; i ++) {
Vector target = base[i];

for (int j = 0; j <i; j ++) {
Vector current = base[j];

if (! isOrthogonalComplex (target, current, epsilon)) {
returns false;
}
}
}

return true;
}

isOrthogonal private static boolean (Vector a vector b, double epsilon) {
double sum = 0.0;

for (int i = 0; i <a.getNumberOfDimensions (); i ++) {
sum + = a.get (i) * b.get (i);
}

return sum <epsilon;
}

private static boolean isOrthogonalComplex (Vector a,
Vector b
double epsilon) {
ComplexNumber sum = new ComplexNumber (0, 0);

for (int i = 0; i <a.getNumberOfDimensions (); i ++) {
ComplexNumber product = a.get (i) .multiply (b.get (i));
sum = sum.add (product);
}

returns Math.abs (sum.getRealPart ()) <epsilon &&
Math.abs (sum.getImaginaryPart ()) <epsilon;
}
}

net.coderodde.math.Divisible

package net.coderodde.math;

/ **
* This interface defines the API for the division operator.
*
* @param  the type of the divident.
* @param  the type of the divider.
* @param   the type of fraction.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 17, 2019)
* /
divisible public interface {

/ **
* Divide {@code a} by {@code b} and return the result.
*
* @param divide the object being divided.
* @param divide the divisor.
* @return the result of dividing {@code divident} with {@code divisor}.
* /
public division F (divider D1, divider D2);
}

net.coderodde.math.GramSchmidtProcess

package net.coderodde.math;

import java.util.Arrays;
import java.util.HashSet;
import java.util.Objects;
import java.util.Set;

/ **
* This class implements the method to execute
* https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process
 * on an independent basis given a linear space.
*
* @param  the type of vertex component.
* @param  the type of internal product.
* @param   the type of result of the division.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 17, 2019)
* /
Public class GramSchmidtProcess {

/ **
* This object is responsible for calculating the inner product of two
* vectors.
* /
Private domestic product innerProduct;

/ **
* This object is responsible for the IT division.
* /
private divisible divisible;

/ **
* This object is responsible for IT products (multiplication).
* /
private product <FT, Vector, Vector> product;

/ **
* This object is responsible for calculating the addition.
* /
private additive <vector, Vector, Vector> additive;

/ **
* This object is responsible for calculating negative elements.
* /
negative private <vector, Vector> negative;

/ **
* Constructs the object with the method of execution of the Gram-Schmidt process
* on a given basis.
*
* @param innerProduct the object for the calculation of internal products.
* @param divisible the object to perform the division.
* @param produces the object to perform the multiplication.
* @param additive the object to perform the addition.
* @param negative the object for calculating inverses.
* /
public GramSchmidtProcess (InnerProduct innerProduct,
Divisible divisible,
Product <FT, Vector, Vector> product,
Additive <Vector,
Vector,
Vector> additive,
Negative <Vector, Vector> negative) {
this.innerProduct =
Objects.requireNoneNull (
innerProduct,
"The InnerProduct entry is null.");

this.negative = Objects.requireNonNull (negative,
"The negative entry is zero.");

this.product = Objects.requireNonNull (product,
"The input product is zero.");

this.divisible = Objects.requireNonNull (divisible,
"The Divisible input is null.");

this.additive = Objects.requireNonNull (additive,
"The input additive is zero.");
}

/ **
* Execute the Gram-Schmidt process on {@codecode}.
*
* @param bases the database to be processed.
* @returns the orthogonal base.
* /
public vector[]    process (vector... base) {
// Validate the entry database:
checkBasis (base);

// Treat the very first basic element:
Vector[]    orthogonalBasis = new vector[basis.length];
orthogonalBasis[0] = (Vector) new vector (base[0])

// The current process:
for (int i = 1; i <base.length; i ++) {
// copy the build x & # 39; from & # 39; base[i]& # 39 ;:
Vector x = new vector <> (base[i])

// For each basic item before 'x', do:
for (int j = 0; j <i; j ++) {
// Let's take the inner product of the divident:
IPT innerProductDivident =
this.innerProduct.innerProductOf (x, orthogonalBasis[j])

// take the inner product of the divisor:
IPT innerProductDivisor =
this.innerProduct.innerProductOf (orthogonalBasis[j],
orthogonalBasis[j])

// Divide the divident by the divisor:
Fraction FT = divisible.divide (innerProductDivident,
innerProductDivisor);

// Multiply the above with the current base:
Vector term = product.multiplier (fraction, base[j])

// cancel the above:
term = negative.negate (term);

// Add the above to "x". Indeed, it subtracts the term "term" from
// x # since we have denied 'term':
x = additive.add (x, term);
}

orthogonalBasis[i] = x;
}

// Removes duplicates and returns all that remains:
return removeDuplicates (orthogonalBasis);
}

/ **
* This method validates the input data sent to the Gram-Schmidt process.
* implementation above.
*
* @param             the type of element component.
* @param baseCandidate the basic candidate.
* @throws IllegalArgumentException if the candidate is not valid.
* /
private static  empty checkBasis (Vector[]    baseCandidate) {
// Check not null:
Objects.requireNoNull (baseCandidate, "The input base is null.");

// Check is not empty:
if (baseCandidate.length == 0) {
throws new IllegalArgumentException ("No vectors given.");
}

int expectedDimensions = baseCandidate[0].getNumberOfDimensions ();

// Each element of the basic candidate must have the same
// dimensionality:
if (expectedDimensions == 0) {
throws a new IllegalArgumentException exception (
"The element of index 0 has no component.");
}

for (int i = 1; i <baseCandidate.length; i ++) {
if (baseCandidate[i].getNumberOfDimensions () == 0) {
// Oops. An empty element:
throws a new IllegalArgumentException exception (
"The item at the index" + i + "has no components.");
}

if (expectedDimensions
! = baseCandidate[i].getNumberOfDimensions ()) {
// Oops. All basic elements are not equal
// dimensionality:
throws a new IllegalArgumentException exception (
"Dimension mismatch: expected" +
expectedDimensions + "but was" +
baseCandidat[i].getNumberOfDimensions () +
"at the index" + i + ".");
}
}
}

private static  Vector[]    removeDuplicates (Vector[]    base) {
Set <Vector> set = new HashSet <> (Arrays.asList (base));
Vector[]    vectors = new vector[set.size()];
return set.toArray (vectors);
}
}

net.coderodde.math.InnerProduct

package net.coderodde.math;

/ **
* This interface defines the API of the internal product with respect to a given vector component.
* type.
*
* @param  the left vector type.
* @param  the right kind of vector.
* @param   the type of value of the internal product.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 17, 2019)
* /
InnerProduct public interface {

/ **
* Calculates the inner product of the two given vectors.
*
* @param has the first vector.
* @param b the second vector.
* @return the inner product
* /
inner IPT innerProductOf (vector a vector b)
}

net.coderodde.math.Negative

                package net.coderodde.math;

/ **
* This interface defines the API for calculating negative data values.
*
* @param  the type of entry.
* @param  the type of output.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 17, 2019)
* /
public interface Negative {

/ **
* Returns the negative of {@code element}. The negative of {@code a} is
* {@code -a} such as {@code a + (-a) = O}, where {@code O} is zero
* element.
*
* @param element the element to be denied.
* @return the negative of {@code element}.
* /
public O negate (I element);
}

net.coderodde.math.Product

package net.coderodde.math;

/ **
* This interface defines the API for multiplication (product).
*
* @param  the type of the left element to multiply.
* @param  the type of the good element to multiply.
* @param   the type of result of the product.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 17, 2019)
* /
public interface Product {

/ **
* Returns the product of {@code a} and {@code b}.
*
* @param has the first element.
* @param b the second element.
* @back the product of the two input elements.
* /
public O multiplies (E1 a, E2 b);
}

net.coderodde.math.Vector

package net.coderodde.math;

import java.util.Arrays;
import java.util.Objects;

/ **
* This class implements a vector / element in a three-dimensional space {@code n}.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 17, 2019)
* /
public final class vector {

/ **
* The content of the real vector.
* /
private final E[] components;

/ **
* Builds the vector from the data provided.
*
* @param composes the vector data.
* /
public Vector (E ... components) {
Objects.requireNonNull (components, "The input vector is null.");
this.components = Arrays.copyOf (components, components.length);
}

/ **
* Copy-built this vector.
*
* @param vector the vector to copy.
* /
public vector (vector vector)
this.components = Arrays.copyOf (vector.components,
vector.components.length);
}

/ **
* Returns the {@code index} component of this vector.
*
* @param indexes the index of the component.
* @return the value of the component {@code index}.
* /
public E get (int index) {
return components[index];
}

/ **
* Sets the value of the {@code index} vector component theme to the given value
* value.
*
* @param indexes the index of the target vector component.
* @param value the value to define.
* /
public empty set (index int, value E) {
components[index] = value;
}

/ **
* Returns the number of components in this vector.
*
* @return the number of components in this vector.
* /
public int getNumberOfDimensions () {
return components.length;
}

@Override
public channel toString () {
StringBuilder stringBuilder = new StringBuilder ("<");
        String separator = "";

        for (E component : components) {
            stringBuilder.append(separator);
            separator = ", ";
            stringBuilder.append(component);
        }
        return stringBuilder.append(">") .toString ();
}

@Override
public int hashCode () {
return Arrays.hashCode (components);
}

@Override
public boolean equals (Object o) {
if (o == null) {
returns false;
}

if (o == this) {
return true;
}

if (! o.getClass (). equals (this.getClass ())) {
returns false;
}

Vector other = (vectoro;
return Arrays.equals (components, other components);
}
}

net.coderodde.math.impl.ComplexNumber

package net.coderodde.math.impl;

/ **
* This class implements a complex number. The complex number consists of a real
* part and an imaginary part. The imaginary part is a real number equipped with
* the imaginary unit {@code i}, for which {@code i ^ 2 = -1}. This class is
* immutable.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 18, 2019)
* /
public final class ComplexNumber {

/ **
* The real number.
* /
private final double realPart;

/ **
* The imaginary number.
* /
private double final imaginaryPart;

/ **
* Build a new complex number.
*
* @param realPart the real part of the newly built complex
* number.
* @param imaginaryPart the imaginary part of the newly built complex
* number.
* /
public ComplexNumber (final double realPart, final double imaginaryPart) {
checkNotNan (realPart);
checkNotNan (imaginaryPart);
checkNotInfinite (realPart);
checkNotInfinite (imaginaryPart);
this.realPart = realPart;
this.imaginaryPart = imaginaryPart;
}

/ **
* Returns the real part of this complex number.
*
* @return the real part of this complex number.
* /
public double getRealPart () {
return realPart;
}

/ **
* Return the imaginary part of this complex number.
*
* @return the imaginary part of this complex number.
* /
public double getImaginaryPart () {
returns imaginaryPart;
}

/ **
* Returns the complex number equal to the sum of this complex
* number and the {@code other} complex number.
*
* @param other the complex number to add.
* @return the sum of this and {@code other} complex number.
* /
public ComplexNumber add (ComplexNumber other) {
returns the new ComplexNumber (realPart + other.realPart,
imaginaryPart + other.imaginaryPart);
}

/ **
* Returns the negative of this complex number.
*
* @returns the negative of this complex number.
* /
public ComplexNumber negate () {
return new ComplexNumber (-realPart, -imaginaryPart);
}

/ **
* Returns the complex number representing the product of the two inputs
* complex numbers.
*
* @param has the first complex number.
* @param b the second complex number.
* @return the product of {@code a} and {@code b}.
* /
public ComplexNumber multiply (ComplexNumber complexNumber) {
double a = realPart;
double b = imaginaryPart;
double c = complexNumber.realPart;
double d = complexNumber.imaginaryPart;
double resultRealPart = a * c - b * d;
double resultImaginaryPart = a * d + b * c;
returns the new ComplexNumber (resultRealPart, resultImaginaryPart);
}

/ **
* Returns a simple textual representation of this complex number.
*
* @return the textual representation of this complex number.
* /
@Override
public channel toString () {
if (realPart == 0.0 && imaginaryPart == 0.0) {
returns "0.0"
}

if (realPart == 0.0) {
returns imaginaryPart + "i";
}

if (imaginaryPart == 0.0) {
return Double.toString (realPart);
}

if (imaginaryPart <0.0) {
return realPart + "-" + Math.abs (imaginaryPart) + "i";
}

returns realPart + "+" + imaginaryPart + "i";
}

/ **
* Check that the input value {@double code} is not {@NaN} code.
*
* @param of the value to check.
* @throws IllegalArgumentException in case {@code d} is {@code NaN}.
* /
private checkNotNan (double d) {
if (Double.isNaN (d)) {
launch the new IllegalArgumentException ("NaN");
}
}

/ **
* Verifies that the value entered {@double code} is finished.
*
* @param of the value to check.
* @throws IllegalArgumentException in case {@code d} is not finished.
* /
private vacuum checkNotInfinite (double d) {
if (Double.isInfinite (d)) {
launch the new IllegalArgumentException ("Infinite");
}
}
}

net.coderodde.math.impl.ComplexVectorAdditive

package net.coderodde.math.impl;

import net.coderodde.math.Additive;
import net.coderodde.math.Vector;

/ **
* This class implements the addition operation on complex vectors.
*
* @author Rodion "rodde" Efremov
* @version 1.6: P (May 18, 2019)
* /
public final class ComplexVectorAdditive
implements additive <vector,
Vector,
Vector> {

/ **
* Add complex vectors {@code a} and {@code b} and return the
* copy by component of the object. The two complex vectors entered remain
* intact.
*
* @param has the left summation operand.
* @param b the right summation operand.
* @returns the sum vector.
* /
@Override
public vector add (vector a,
Vector b) {
Complex number[] complexNumbers =
new ComplexNumber[a.getNumberOfDimensions()];

for (int i = 0; i <a.getNumberOfDimensions (); i ++) {
complex numbers[i] = a.get (i) .add (b.get (i));
}

return the new vector <> (complexNumbers);
}
}

net.coderodde.math.impl.ComplexVectorDivisible

package net.coderodde.math.impl;

import net.coderodde.math.Divisible;

/ **
* This class implements the division operator on complex numbers.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 18, 2019)
* /
public final class ComplexVectorDivisible implements Divisible {

/ **
* Divide the {@code divident} complex with the {@code divisor} complex and
* returns the fraction. The two complex numbers entered remain intact.
*
* @param divide the divident complex.
* @param divides the complex divider.
* @return the fraction after dividing the divident by the divisor.
* /
@Override
public ComplexNumber divide (ComplexNumber divident, ComplexNumber divisor) {
// TODO: could do the multiplication of Karatsuba here, I suppose.
double a = divident.getRealPart ();
double b = divident.getImaginaryPart ();
double c = divisor.getRealPart ();
double d = divisor.getImaginaryPart ();

double resultRealPart = (a * c + b * d) / (c * c + d * d);
double resultImaginaryPart = (b * c - a * d) / (c * c + d * d);

returns the new ComplexNumber (resultRealPart, resultImaginaryPart);
}
}

net.coderodde.math.impl.ComplexVectorInnerProduct

package net.coderodde.math.impl;

import net.coderodde.math.InnerProduct;
import net.coderodde.math.Vector;

/ **
* This class implements the internal IT product on complex vectors.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 18, 2019)
* /
public final class ComplexVectorInnerProduct
implements InnerProduct {

/ **
* Calculates the inner product of {@code a} and {@code b} and returns it to
* the caller.
*
* @param has the first operand.
* @param b the second operand.
* @return the inner product.
* /
@Override
public ComplexNumber innerProductOf (vector a, // 1 -2i
Vector b) {// 1 -2i
ComplexNumber innerProduct = new ComplexNumber (0.0, 0.0);

for (int i = 0; i <a.getNumberOfDimensions (); i ++) {
ComplexNumber complexNumber1 = a.get (i);
ComplexNumber complexNumber2 = b.get (i);
ComplexNumber product = complexNumber1.multiply (complexNumber2);
innerProduct = innerProduct.add (product);
}

return innerProduct;
}
}

net.coderodde.math.impl.ComplexVectorNegative

package net.coderodde.math.impl;

import net.coderodde.math.Negative;
import net.coderodde.math.Vector;

/ **
* This class implements the negation operation on complex numbers.
*
* @author Rodino "rodde" Efremov
* @version 1.6 (May 18, 2019)
* /
public final class ComplexVectorNegative
implements negative <vector,
Vector> {

/ **
* Cancels each component in {@code element} and returns the result
* vector. The input vector remains intact.
*
* @param element the element to be denied.
* @return the element with all the components reversed in relation to the
* input vector.
* /
@Override
public vector deny (vector element) {
Vector result = new vector <> (element);

for (int i = 0; i <element.getNumberOfDimensions (); i ++) {
result.set (i, result.get (i) .negate ());
}

return the result;
}
}

net.coderodde.math.impl.ComplexVectorProductByScalar

package net.coderodde.math.impl;

import net.coderodde.math.Product;
import net.coderodde.math.Vector;

/ **
* This class implements the multiplication of complex vectors by a complex scalar.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 18, 2019)
* /
public final class ComplexVectorProductByScalar
implements the product <ComplexNumber,
Vector,
Vector> {

/ **
* Multiplies the complex vector by the given complex scalar and returns the
* result. All input objects remain intact.
*
* @param scalar the scalar to be multiplied by.
* @param vector the complex vector to multiply.
* @return the {@code code} multiplied by {@code scalar}.
* /
@Override
public vector multiply (Scalar ComplexNumber,
Vector vector)
Vector ret = new vector <> (vector);

for (int i = 0; i <vector.getNumberOfDimensions (); i ++) {
ret.set (i, ret.get (i) .multiply (scalar));
}

return ret;
}
}

net.coderodde.math.impl.RealVectorAdditive

package net.coderodde.math.impl;

import net.coderodde.math.Additive;
import net.coderodde.math.Vector;

/ **
* This class implements the addition on the evaluated vectors of a {@double code}
* Euclidean space.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 17, 2019)
* /
public final class RealVectorAdditive implements the <vector <additive,
Vector,
Vector> {

/ **
* Add component content in {@code a} and {@code b} and return
* the sum. Both input vectors remain intact.
*
* @param has the first operand.
* @param b the second operand.
* @back the sum of the two input operands.
* /
@Override
public vector add (vector a vector b) {
Vector result = new vector <> (a);

for (int i = 0; i <a.getNumberOfDimensions (); i ++) {
result.set (i, result.get (i) + b.get (i));
}

return the result;
}
}

net.coderodde.math.impl.RealVectorDivisible

package net.coderodde.math.impl;

import net.coderodde.math.Divisible;

/ **
* This class implements the division of values ​​{@double code}.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 17, 2019)
* /
Public final class RealVectorDivisible
implements Divisible {

/ **
* Returns the fraction of {@code divident} and {@code divisor}.
*
* @param divide the divisor value {@double code}.
* @param divides the value of divisor {@double code}.
* @return the fraction.
* /
@Override
public double division (double division, double divider) {
return divisor / divisor;
}
}

net.coderodde.math.impl.RealVectorInnerProduct

package net.coderodde.math.impl;

import net.coderodde.math.InnerProduct;
import net.coderodde.math.Vector;

/ **
* This class is responsible for calculating internal products in relation to actual values
* vectors.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 17, 2019)
* /
Public final class RealVectorInnerProduct
implements InnerProduct {

/ **
* Calculates and returns the inner product of vectors {@code a} and
* {@code b}
*
* @param has the left operand vector.
* @param b the right operand vector.
* @return the inner product of the vectors {@code a} and {@code b}.
* /
@Override
public double innerProductOf (vector a vector b) {
double internal product = 0.0;

for (int i = 0; i <a.getNumberOfDimensions (); i ++) {
innerProduct + = a.get (i) * b.get (i);
}

return innerProduct;
}
}

net.coderodde.math.impl.RealVectorNegative

package net.coderodde.math.impl;

import net.coderodde.math.Negative;
import net.coderodde.math.Vector;

/ **
* This class implements the negate operation on real vectors.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 17, 2019)
* /
public final class RealVectorNegative implements Negative <Vector,
Vector> {

/ **
* Inverts the input vector {@double code}. The input vector remains intact.
*
* @param is the {@code double} vector to cancel.
* @return the negative of {@code a}.
* /
@Override
public vector deny (vector a) {
Vector result = new vector <> (a);

for (int i = 0; i <result.getNumberOfDimensions (); i ++) {
result.set (i, -result.get (i));
}

return the result;
}

}

net.coderodde.math.impl.RealVectorProductByScalar

package net.coderodde.math.impl;

import net.coderodde.math.Product;
import net.coderodde.math.Vector;

/ **
* This class implements the multiplication operation of a vector by a scalar.
*
* @author Rodion "rodde" Efremov
* @version 1.6 (May 18, 2019)
* /
Public final class RealVectorProductByScalar
implements Product <Double, Vector, Vector> {

/ **
* This method multiplies the input vector {@code vector} component by s by
* the scalar {@code} and returns the result. The input vector
* remains intact.
*
* @param scalar the scalar.
* @param vector the vector to be multiplied by the scalar.
* @return the input vector multiplied by the input scalar.
* /
@Override
public vector multiply (double scalar, vector vector)
Vector x = new vector <> (vector);

for (int i = 0; i <vector.getNumberOfDimensions (); i ++) {
x.set (i, x.get (i) * scalar);
}

return x;
}
}

(The whole project is here.)

Request for criticism

As always, tell me everything that goes through your head!

seo – Google selects an independent page like Canonical for many other pages, blocking the indexing of our pages

We have pages such as:

https://www.signalogic.com/index.pl?page=surveillance_video_suspect_detection

for which Google continues to select this page as Canonical:

http://www.signalogic.com/index.pl?page=sw

Our pages all have a canonical rel = https tag, which Search Console correctly displays as canonical declared by the user.

Why Google indexing persists in this situation? The two pages are completely independent, not even close to the same content. What we declare canonical is not it "credible" or credible? In one way or another, Google is forced to access the independent page. What method do I need to overcome this?

Theory of complexity – Parameterized reduction of 3-SAT to independent group with bounded time under ETH assumption

I want to prove that, assuming that the exponential time hypothesis is true, no algorithm solves the independent game in $ 2 ^ {o (| V | + | E |}) $ time. I want to apply the strong reduction several parametric next $ f $ from 3-Sam to the independent set. Let $ psi $ be input to 3-SAT with parameter $ kappa_ {3-SAT} = #variables + # clauses $ and let $ (G = (V, E), k) $ be the entry for the independent game with parameter $ kappa_ {IS} = | V | + | E | $

For each clause of the entry formula $ psi $Add three vertices to the graph, corresponding to the respective literals. Add an edge between two vertices if:

a) They correspond to the literals of the same clause or

b) they correspond to a variable and its inverse

Then 3-Sat has a satisfactory assignment if and only if the graph defined by this reduction has an independent set of size $ m $, or $ m $ is the number of clauses in $ psi $. For example:
enter the description of the image here

I wonder now if this reduction is enough to show that (assuming ETH), the independent game can not be solved by $ 2 ^ {o (| V | + | E |)} $ time. If I understand correctly, the number of summits $ | V | = $ 3m and the number of edges $ | E | 3m + nm $since for each article we have $ 3 $ edges between the respective vertices and then for each variable we have at most $ m $ edges between a variable and its inverse. However, this is not linear in $ kappa_ {3-Sat} $ more.

Is my upper limit on the number of edges incorrect or should I use a different reduction to display the desired result?

Stochastic processes – Estimation of a random variable, independent decomposition

I have a question about an argument in this article: P.

Let $ S = (1, infty) times (-1,1) subset mathbb {R} ^ 2 $ and $ X = ( {X_t }, {P_x } _ {x in S}) $ to be a diffusion process on $ D $.

(Imagine something like a Brownian motion in $ (- infty, infty) times (-1,1) $ conditioned to hit $ {1 } times (-1,1) $)

We note by $ r (t) $, $ y (t) $ the first coordinate process of $ X $ and the second coordinate process of $ X $, respectively. Let $ tau_r = inf {t> 0 mid r_t = r } $ for $ r $ 1 $.

The author discusses whether
$$ text {(A)} quad lim_ {r to infty} inf_ {y in (-1,1)} P_ {r, y} left ( int_ {0} ^ { tau_1} r (s) ^ {- 2} , ds = infty right) = 1. $$

As proof, the following lemma seems to play a crucial role (See Proposition 1 in P).

Support. Let $ {Z_n } _ {n = 1} ^ { infty} $ be a sequence of non-negative bounded independent random variables. Then, $ sum_ {n = 1} ^ { infty} Z_n = infty $, $ Q $-as. Yes Yes $ sum_ {n = 1} ^ { infty} E ^ {Q}[Z_n]= infty $. Right here, $ E ^ {Q} $ denotes waiting w.r.t. $ Q $.

For simplicity, let's assume random variables $ { int _ { tau_k} ^ { tau_ {k-1}} 1 / r (s) ^ 2 , ds } _ {k = 2} ^ {n} $ are linked. Then, the random variables $ { int _ { tau_k} ^ { tau_ {k-1}} 1 / r (s) ^ 2 , ds } _ {k = 2} ^ {n} $ are non-negative, bounded and independent under $ P_ {n, y} ( cdot mid X _ { tau_2}, cdots X _ { tau_ {n-1}} $. Right here, $ P_ {n, y} ( cdot mid X _ { tau_2}, cdots X _ { tau_ {n-1}} $ denotes the conditional probability w.r.t. the random vector $ (X _ { tau_2}, cdots X _ { tau_ {n-1}}) $.

The random variable is broken down as follows

$$ int_ {0} ^ { tau_1} r (s) ^ {- 2} = sum_ {k = 2} ^ {n} int _ { tau_k} ^ { tau_ {k-1}} r (s) ^ {- 2} , ds, quadri P_ {n, y} ( cdot mid X _ { tau_2}, cdots X _ { tau_ {n-1}}) – text {as} $$

and considered as a sum of independent random variables.

The following condition is sufficient for (A) ?:

begin {align *}
text {(B)} quad lim_ {n to infty} inf_ {y in (-1,1)} E_ {n, y} left[sum_{k=2}^{n}int_{tau_k}^{tau_{k-1}}r(s)^{-2},ds mid X_{tau_2},cdots X_{tau_{n-1}} right]= infty.
end {align *}

Can we reach (A) if we combine (B) and Prop?

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