stochastic calculus – reference requirement: Ito formula for the function $ G (t, x) $ if $ G $ depends on $ omega $

Reference request.
Lemma is proven in the book: let the function $ G (t, x) $ is defined when $ t in (0, T), x in (- infty infty) $. $ G $ has continuous derivation in terms of $ t $ and twice continuously differentiable in terms of $ x $, Then $$ dG (t, w (t)) = (G & # 39; _t (t, w (t)) + 1 / 2G & # 39; & # 39; _ {xx} (t, w (t)) ) + G _ _x (t, w (t)) dw (t). $$
Here $ w (t) $ is Brownian motion.
Afterwards without proof there is an assertion that lemma is true if $ G (t, x) $ depend on $ omega $ . $ G (t, w (t)) $ is measurable in terms of $ sigma $-Algebra $ F_t $ and for everyone $ omega $ Lemma conditions are met.
My question: How can you prove this claim? Could you refer to an exact proof?

C ++ Tries Deletion function opertator == does not work

I am a bit new to C ++ and for this program I have to delete a word from the tree. The program searches the trie and receives the specified reference. My problem, however, is that using the overloader & # 39; operator == & # 39; does not work in the following if statement, although the reference is the same word as the delkey ​​variable.

Any help would be appreciated.

bool TrieType::DeleteTrie(Key delkey)
{
   int i;
   Trienode* current = root;
   bool found = false;

for (i = 0; i < MAXLENGTH && current; i++)
    if (delkey(i) == '')
        break;
    else
    {
        current = current->branch(delkey(i) - 'a');

        if (current->ref != NULL)
        {
            current->ref->PrintWord(); //Debug Seeing the path it takes

            **if (current->ref->operator==(delkey))
                cout << "The END of the route?" << endl;**
        }
        else if (current->ref == NULL)
            cout << "Empty NODE, No Word" << endl;
    }
if (!current)
    return NULL;
else
    if (!current->ref)
        return NULL;

return found;
}

product – Pass the function to the array in Magento 2.3

I have this code to get the quantity of items from the Magento 2.3 product

namespace HelloSourceItemDataModel;

use Exception;
use PsrLogLoggerInterface;
use MagentoFrameworkApiSearchCriteriaBuilder;
use MagentoInventoryApiApiDataSourceItemInterface;
use MagentoInventoryApiApiSourceItemRepositoryInterface;

class SourceItem
{
    /**
     * @var SearchCriteriaBuilder
     */
    private $searchCriteriaBuilder;

     /**
     * @var SourceItemRepositoryInterface
     */
    private $sourceItemRepository;

    /**
     * @var LoggerInterface
     */
    private $logger;

    public function __construct(
        SearchCriteriaBuilder $searchCriteriaBuilder,
        SourceItemRepositoryInterface $sourceItemRepository,
        LoggerInterface $logger
    ) {
        $this->searchCriteriaBuilder = $searchCriteriaBuilder;
        $this->sourceItemRepository = $sourceItemRepository;
        $this->logger = $logger;
    }

    /**
     * Retrieves links that are assigned to $stockId
     *
     * @param string $sku
     * @return SourceItemInterface()
     */
    public function getSourceItemDetailBySKU(string $sku): array
    {
        $searchCriteria = $this->searchCriteriaBuilder
            ->addFilter(SourceItemInterface::SKU, '24-UB02')
            ->create();

        $result = $this->sourceItemRepository->getList($searchCriteria)->getItems();

        return $result;
    }
}

It's called that

$sku = '24-UB02';
$result = $this->getSourceItemDetailBySKU($sku);

foreach ($result as $item) {
    print_r($item->getData());
}

I want this code to get a set of articles and put them into an array. So I have to take care of it $data() = $product->..........

Any ideas?

Thanks a lot!

javascript – wants to clarify a little what this simple js function does and how

Hey guys, I have a balloon game that speeds up the balloon when I mouse over one of them. I have a few questions:
1.Does the acceleration function not only increase the speech bubble cell value?
it doesn't seem to change the pixels it should increase in any way, it just updates the object's speed value

2.this function: onmouseover = "speedUp (& # 39; + i + & # 39;)

When I hold the mouse pointer over the object, it gets a number that is linked to the object that was set as a data attribute by the "Render Speech Bubbles" function. I dont understand this

Here is the code:

& # 39; use strict & # 39 ;;

var gNextId = 101;
var gBalloons = createBalloons()

var gInterval;

function startGame() {

    renderBalloons();

    gInterval = setInterval(() => {
        moveBalloons();
    }, 500);
}

function renderBalloons() {
    var strHtml = '';
    for (let i = 0; i < gBalloons.length; i++) {
        var balloon = gBalloons(i);
        strHtml += '
' + balloon.txt + '
' } // console.log('strHTML', strHtml); document.querySelector('.balloon-container').innerHTML = strHtml; } function moveBalloons() { var elBalloons = document.querySelectorAll('.balloon'); for (let i = 0; i < elBalloons.length; i++) { var balloon = gBalloons(i); var elBalloon = elBalloons(i); balloon.bottom += balloon.speed; elBalloon.style.bottom = balloon.bottom + 'px'; if (balloon.bottom >= 800) clearInterval(gInterval); } } function popBalloon(elBalloon) { var popSound = new Audio('sounds/pop.mp3'); popSound.play(); elBalloon.classList.add('fade'); } function speedUp(idxBalloon) { console.log('Speeding up: ', gBalloons(idxBalloon)) gBalloons(idxBalloon).speed += 10; } function createBalloons() { var ballons = ( createBalloon('A'), createBalloon('B'), createBalloon('C') ); return ballons } function createBalloon(txt) { return { id: gNextId++, bottom: 0, speed: 45, txt: txt } }

the HTML when it's needed:




    
    
    
    Document
    


        

Convergence Divergence – What can I understand about a function through its Fourier series?

I've come across a question that looks at things from a different perspective, and I'm not sure how to do it. I have three functions $ f, g, h $ defined in the $ (0, 2 pi) $ Interval, the Fourier series of which are: $$ f (x): sum_ {n = 1} ^ infty {1 over sqrt n} sin (nx) $$ $$ g (x): sum_ {n = 1} ^ infty {1 over n ^ 2 + 1} cos (nx) + {1 over n ^ 4} sin (nx) $$ $$ h (x): sum_ {n = 1} ^ infty {1 over 2 ^ n} cos (nx) $$

Without going into detail because I want to understand the concept first, I am asked a number of questions about belonging to different ones $ L ^ p $Spaces, convergence and so on. The question is … what information can I collect in the Fourier series? What should I pay attention to in order to know my functions?

Thanks a lot!

Animation – manipulate control with tracking function under autorun

I am writing a demonstration that shows complex dependencies between controls that can be time-consuming to evaluate. It works fine, except it breaks when I try to use autorun. I think the problem is that when Autorun changes a variable, the TrackingFunction for controls associated with that variable is not called. Is there a way to intercept changes to a variable without copying all of my tracking functions into the body of the manipulate?

In this MWE I want the variable a to be updated by autorun as if the slider itself was being moved without adding "a = m + 1" to the body of the manipulate.

Manipulate(
{m, a},
 {{a, 2}, None},
 {{m, 2, Dynamic(m)}, 2, 10, 1,
   TrackingFunction -> (m = #; a = m + 1; & )},
 TrackedSymbols -> {m}, AutorunSequencing -> {2})

(I'm not sure if "animation" is a good day for it, but I'm new and can't create "animate" or "autorun".)

$ kerf $ of the linear function in Banach space $ f (x) = x (1) -x (0) $

We have Banach space $ C ((0,1), mathbb {R}) $ and a linear function $ f: C ((0,1), mathbb {R}) rightarrow mathbb {R} $ such as $ f (x) = x (1) -x (0) $ for each $ x in C ((0,1), mathbb {R}) $,

I have to find that $ kerf $. $ || f || $, and $ d (t, kerf) $, So I wanted to start $ kerf: = {x in X: f (x) = 0 } $

$ f (x) = 0 iff x (1) -x (0) = 0 $,

So, $ x (1) = x (0) $ and how we define that $ kerf $?