white balance – For a given lens/camera, will a ND filter always need same WB correction in all conditions?

I’ve taken a few photos with a new B+W ND 6-stop filter and found that it leaves them quite warm. I’m able to correct this in ACR using temperature/tint sliders. For the few photos I’ve taken so far, the same temp/tint settings seem to work for each one.

I’ve heard that color cast from a given ND filter can vary between cameras and lenses. But presuming I continue to use this filter with the same camera and lens, is it safe to assume my WB correction will be the same every time, for any photo? Or will it be dependent on other conditions like lighting and exposure/aperture?

Note that I ask, because if the color cast varies based on some conditions, then I will probably take no-filter companion shots for any filter shots that are important, so I’ll have a reference point for matching WB later. Though, it would be nice to not have to always do this.

Why double error correction and quadruple error detection cannot occur at the same time?

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What does ( we cannot both correct double errors and detect quadruple errors because this would require us to interpret a received codeword in two different ways) means? I understand how double error correction works but I cannot imagine quadruple error detection. Can anybody show me example why double error correction and quadruple error detection cannot occur at the same time because it requires different interpretation?

For example, if double error correction occur,

will be something like this. How about quadruple error detection?

special functions – Correction of HeavisideTheta in MM11.3 to generate the same results with UnitStep in MM5.2

the UnitStep has been replaced by the HeavisideTheta after version 6.0 (reference here), but some differences confused me between the old and the new version as follows (For convenience, the f (x) is simplified). I want to know how to correct the HeavisideTheta in Mathematica V11.3 to generate the same results with UnitStep in MM5.2. For the problem, I have proposed a few methods (here and here), but which have not given the result I want. Thank you.

Code in V11.3

f(x_) := 1;
Integrate(f(x)*HeavisideTheta(x), {x, 0, (Infinity)})
Integrate(f(x)*HeavisideTheta(x), {x, -(Infinity), (Infinity)})
Integrate(f(x)*D(HeavisideTheta(x), x), {x, 0, (Infinity)})
 f(x)*D(HeavisideTheta(x), x), {x, -(Infinity), (Infinity)})

Code in V5.2


Results in V11.3

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The results in V5.2

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automata – Correction of an error in CFG

Here is a CFG that generates the language of basic arithmetic expressions. These expressions allow the 4 basic operations on the arithmetic values ​​a, b and c. It implements an order of operations where multiplication and division take precedence over addition and subtraction, and all operations are associative on the left. It also implements parentheses. There is an error in this CFG.

S → S * T | S / T | T
T → T + V | T-V | V
V → (S) | a | b | vs

You must rewrite this CFG to accomplish as many of the following tasks as possible:
a) Correct the error in this CFG to make it work as described.
b) Add an exponent operation. This operation must have a higher priority than multiplication and division, but a lower priority than parentheses. The exponent operator is ^. For example, a ^ b would be ab, or "a to b". Give this operation, and only this operation, associativity on the right, so that a ^ b ^ c would be "a au (b to c)".
c) Transform these expressions into equations. An equation consists of an equality operator {=,<,>} with an expression on each side. The equality operator must have the lowest priority and the equality operator must not be allowed in parentheses.

Color correction – Why are high white balance temperatures redder when warmer objects are more blue?

As you know, the metal heated in a fire soon starts to shine. First the metal takes on a dull red glow, then cherry red. As the temperature of the metal increases, the color becomes warm white, then blue-white. It is these color changes observed with heating that inspired the color temperature system.

Also, you know that most of the world uses the Celsius system. This sets water freezing to zero (0) and boiling water to 100. The unit degree translates to "step". Early experimenters discovered that a hydrogen thermometer is super accurate. It is a hollow tube, filled with hydrogen with a float at the top of the column. The float rises and falls uniformly with changes in temperature. Other substances like mercury and alcohol don't have this uniformity. In addition, when the environment cools, the float falls near the bottom of the tube. The lowest possible temperature has been calculated to be an absolute zero and, if reached, the float would bottom out. This is how the absolute temperature scale was born. This scale has been favored by many, because all temperatures are positive, without confusing +20 with -20. This temperature scale was renamed the Kelvin scale after the document of the scientist Lord Kelvin of 1848, on absolute zero.

Now, many disciplines use the color of glowing hot substances to measure temperature. To name just a few: blacksmiths, metallurgists, steel, ceramics, glass blowing, etc. Experiments have shown that the glowing color and its associated temperature are approximately the same for all materials. The key here is the lighting industry which was initially the carbon arc and glowing tungsten, adopted the Kelvin scale to connect the color output of the lamps.

Selected Kelvin temperatures:

Candle flame 1850K

7520 2820K Domestic Tungsten Light Bulb

200 watt General Service Electric Blub 2980K

500-watt 3200K photo-flood light bulb

500 Watt 3400K Photo-Flood Film Light Bulb

Flash bulb 3800K – 4200K

Caron 5000K arc lamp

Photographic Daylight 5500K

Sunlight standard US Bureau of Standards Noon 5500K

Blue sky 12000K -18000K at various times of the day

Color films were manufactured to operate under specialized conditions.

Daylight color balance

Color balance Tungsten cinema lamps

Color balance Tungsten photo flood

Color films for scientific work – other temperatures Kelvin

Note: the custom is to write the word kelvin scale in lowercase k and omit the sign of the degree °.

The manufacturers of digital cameras have logically adapted the photo film industry using their color balance ratings.

java – Correction of the Service Spring Boot method

Good evening, I create an API with spring based on a course. However, some methods are possibly deprecated in the version I use (2.2.6) of the course version (1.5.10).

I need to apply the update to the following:

Type mismatch: cannot convert from optional to user

insert description of image here

PageRequest constructor (int, int) is not defined

insert description of image here

Follow my class UserServiceImpl:

package com.br.helpdesk.helpdesk.api.service.impl;

import com.br.helpdesk.helpdesk.api.entity.User;
import com.br.helpdesk.helpdesk.api.repository.UserRepository;
import com.br.helpdesk.helpdesk.api.service.UserService;

import org.springframework.beans.factory.annotation.Autowired;
import org.springframework.data.domain.Page;
import org.springframework.data.domain.PageRequest;
import org.springframework.data.domain.Pageable;
import org.springframework.stereotype.Service;

public class UserServiceImpl implements UserService {

    private UserRepository userRepository;

    public User findByEmail(String email) {
        return this.userRepository.findByEmail(email);

    public User createOrUpdate(User user) {
        return this.userRepository.save(user);

    public User findById(String id) {
        return this.userRepository.findById(id);

    public void delete(String id) {

    public Page findAll(int page, int count) {
        Pageable pages = new PageRequest(page, count)
        return null;


Classroom User:

package com.br.helpdesk.helpdesk.api.entity;

import javax.validation.constraints.Email;
import javax.validation.constraints.NotBlank;
import javax.validation.constraints.Size;

import com.br.helpdesk.helpdesk.api.enums.ProfileEnum;

import org.springframework.data.annotation.Id;
import org.springframework.data.mongodb.core.index.Indexed;
import org.springframework.data.mongodb.core.mapping.Document;

public class User {

    private String Id;

    @Indexed(unique = true)
    @NotBlank(message = "Email required")
    @Email(message = "Email invalido")
    private String email;

    @NotBlank(message = "Passwor required")
    @Size(min = 6)
    private String password;

    private ProfileEnum profile;

    public String getId() {
        return this.Id;

    public void setId(String Id) {
        this.Id = Id;

    public String getEmail() {
        return this.email;

    public void setEmail(String email) {
        this.email = email;

    public String getPassword() {
        return this.password;

    public void setPassword(String password) {
        this.password = password;

    public ProfileEnum getProfile() {
        return this.profile;

    public void setProfile(ProfileEnum profile) {
        this.profile = profile;


Finally UserService:

package com.br.helpdesk.helpdesk.api.service;
import com.br.helpdesk.helpdesk.api.entity.User;
import org.springframework.data.domain.Page;
public interface UserService {
    User findByEmail(String email);
    User createOrUpdate(User user);
    User findById(String id);
    void delete(String id);
    Page findAll(int page, int count);

Has anyone experienced this and can they help me?

coding theory – correction codes for trinary errors

Given a word $ w = xyz $ are there any good known error correction codes which are coded as $ xyz f (y, z) f (x, z) f (x, y) $ ?

Such a family of LDPC codes would be the best.

Is there a reason why it won't be good (in terms of distance, price)?

This could be useful in a construction that I have. I just wanted to make sure before diving.

Thank you

depth of field – Does the offset-based perspective correction affect the focus?

Consider a photographer with a reflex camera and a PC lens fixed in its default position, not offset, standing on the ground at the base of a columned building whose height is X times that of the person and is located at Y feet from him.

The photographer composes a frame with the center of the building in the center of the frame with an empty space above, to do this, he must tilt the camera slightly upwards, which creates a keystone effect with the columns seeming to converge vertically towards a point above the frame.

Then the shooter maintains camera orientation upgrades the camera and adjusts the lens shift of the PC until the columns appear parallel in the image.

Is there a change of focus at the bottom of the columns and the focus at the top of the columns before and after the change?

Why is the proof of correction not tautological?

Consider the following function on binary trees, which is supposed to tell if a given int is a member of a binary tree t:

type tree = Leaf | Node of int * tree * tree;;

let rec tmember (t:tree) (x:int) : bool =
  match t with
      Leaf -> false
    | Node (j,left,right) -> j = x || tmember left x || tmember right x

If we want to prove that this function is correct, we should to define first what it really means to be a tree, but then I can't find any formal way to do it, except to say that x is a member of t if and only if it is equal to the root of t, or it belongs to the left or right subtree of t. It basically means that x is a member of t if and only if tmember t x the exits true.

What am I forgetting here?

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