IEEE 754 addition wrong result floating point numbers

I want to add two IEEE 754 numbers.
I followed the steps to add two 754 numbers. However the result it not correct.
Number 1:
S:0
E:01111111
M:11111111111111111111111

Number 2:
S:0
E:01111111
M:00000000000000000000000

Here is my calculation:

enter image description here

The site http://weitz.de/ieee/ gives this result:
S: 0
E: 10000000
M: 10000000000000000000000

in my calculation the mantissa is 01111…
Why?

Fuchsian groups and Eicher’s result

Let $G$ be a Fuchsian group of first kind contained in $text{PSL}_2(mathbb{R})$. A result of Eichler says, there exists a finite set $Ssubset G$ such that any $gamma$ in $G$ can be written as a product $prod_{i=1}^{k} gamma_i,$ where each $gamma_i$ are either in $S,$ or power of some parabolic element coming from $S,$ for some $kll log ||gamma||.$ Howerver, the original Eichler’s paper is in German, (http://matwbn.icm.edu.pl/ksiazki/aa/aa11/aa11111.pdf) and this is giving me trouble to understand the proof. Does anyone know if I can find the proof written in English somewhere else ?

javascript – How can i stop woocommerce checkout event based on api request result?

I’m building a custom woocommerce payment gateway and the following code is running on the woocommerce checkout page, and I’m trying to prevent the user from submitting the order till he writes his credit card details in the Tap payment gateway (card js) form.

if the user wrote his card details correctly a request will be sent to Tap to get a payment token and set it inside a hidden field that will be sent and processed on the server-side.

if the user wrote invalid card details I have to prevent him from submitting the order until he corrects his card details.

the problem I’m facing is I cannot get the result after Tap (card js) validates user inputs to make my condition to stop checkout_place_order event execution or continue with the valid data

is there is another way to stop woocommerce jQuery checkout_place_order event?


var tap = Tapjsli('pk_test_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); //public API key
var elements = tap.elements({});
var style = {
    base: {
        color: '#535353',
        lineHeight: '18px',
        fontFamily: 'sans-serif',
        fontSmoothing: 'antialiased',
        fontSize: '16px',
        '::placeholder': {
            color: 'rgba(0, 0, 0, 0.26)',
            fontSize: '15px'
        }
    },
    invalid: {
        color: 'red'
    }
};

// input labels/placeholders
var labels = {
    cardNumber: "Card Number",
    expirationDate: "MM/YY",
    cvv: "CVV",
    cardHolder: "Card Holder Name"
};

//payment options
var paymentOptions = {
    currencyCode: ("SAR"),
    labels: labels,
    TextDirection: 'rtl'
}

//create element, pass style and payment options
var card = elements.create('card', {style: style}, paymentOptions);

(function ($) {
    $(document).one('updated_checkout', function () {
        card.mount('#element-container');//mount element
        //card change event listener
        card.addEventListener('change', function (event) {
            var displayError = $('#error-handler');
            if (event.error) {
                displayError.html(event.error.message);
            } else {
                displayError.html('');
            }
        });
    });

    function tapTokenHandler(token) {
        $('#tap-form-container').append('<input type="hidden" name="tapToken" id="tapToken" value="' + token.id + '">');
    }

    $('form.woocommerce-checkout').on('checkout_place_order', function (e) {
        tap.createToken(card).then(function (result) {
            // console.log(result);
            if (result.error) {
                console.log(result.error);
                // Inform the user if there was an error
                $('#error-handler').html(result.error.message);
                return false; //here I'm trying to stop the event
            }
            // Send the token to your server
            $('#success').css('display', 'block');
            $('#token').html(result.id);
            tapTokenHandler(token);
        });
    });

})(jQuery);



reference to card js docs here

How to get the convergence radius or region of the result of `Series`-function

The Taylor expansion of function is very useful, but the convergence radius of power series results after Taylor expansion is also important. But the result of Series function does not contain the information of convergence region. What should I do to get the information of convergence region at the same time?

Examples for testing:

    Series(Power(Log(1-x)^2, (2)^-1)/Sqrt(x),{x,0,5})
    Series(Tan(x),{x,0,5})
    Series(Sin(m*x), {x, 0, 5})

plotting – Is there an alternative way instead of increasing the number of plotpoints in ContourPlot to get a better result?

I have this function and I use ContourPlot to see in which part of the domain, the function is negative:


f := 1/4 x^2 Sinh((2 (Pi) x)/
     3)^2 Sinh((Pi) x)^2 (-512 Sinh(((Pi) x)/3) + 
      128 x^2 Sinh(((Pi) x)/3) + 64 Sinh((Pi) x) + 
      32 x^2 Sinh((Pi) x) + 4 x^4 Sinh((Pi) x) - 
      128 Sinh((5 (Pi) x)/3) - 64 x^2 Sinh((5 (Pi) x)/3) - 
      8 x^4 Sinh((5 (Pi) x)/3) + 576 Sinh((7 (Pi) x)/3) - 
      96 x^2 Sinh((7 (Pi) x)/3) + 4 x^4 Sinh((7 (Pi) x)/3))^2 - 
   4 (256 Cosh((2 (Pi) x)/3)^2 - 128 x^2 Cosh((2 (Pi) x)/3)^2 + 
      16 x^4 Cosh((2 (Pi) x)/3)^2 + 
      256 x^2 Sinh((2 (Pi) x)/
        3)^2) Sinh((Pi) x)^2 (64 Sinh(((Pi) x)/3)^2 - 
      32 x^2 Sinh(((Pi) x)/3)^2 + 4 x^4 Sinh(((Pi) x)/3)^2 - 
      16 Sinh(((Pi) x)/3) Sinh((Pi) x) - 
      4 x^2 Sinh(((Pi) x)/3) Sinh((Pi) x) + 
      x^4 Sinh(((Pi) x)/3) Sinh((Pi) x) + 
      1/4 x^6 Sinh(((Pi) x)/3) Sinh((Pi) x) + Sinh((Pi) x)^2 + 
      x^2 Sinh((Pi) x)^2 + 3/8 x^4 Sinh((Pi) x)^2 + 
      1/16 x^6 Sinh((Pi) x)^2 + 1/256 x^8 Sinh((Pi) x)^2 - 
      256 Cosh((2 (Pi) x)/3)^2 Sinh((Pi) x)^2 + 
      128 x^2 Cosh((2 (Pi) x)/3)^2 Sinh((Pi) x)^2 - 
      16 x^4 Cosh((2 (Pi) x)/3)^2 Sinh((Pi) x)^2 + 
      32 Sinh(((Pi) x)/3) Sinh((5 (Pi) x)/3) + 
      8 x^2 Sinh(((Pi) x)/3) Sinh((5 (Pi) x)/3) - 
      2 x^4 Sinh(((Pi) x)/3) Sinh((5 (Pi) x)/3) - 
      1/2 x^6 Sinh(((Pi) x)/3) Sinh((5 (Pi) x)/3) - 
      4 Sinh((Pi) x) Sinh((5 (Pi) x)/3) - 
      4 x^2 Sinh((Pi) x) Sinh((5 (Pi) x)/3) - 
      3/2 x^4 Sinh((Pi) x) Sinh((5 (Pi) x)/3) - 
      1/4 x^6 Sinh((Pi) x) Sinh((5 (Pi) x)/3) - 
      1/64 x^8 Sinh((Pi) x) Sinh((5 (Pi) x)/3) + 
      4 Sinh((5 (Pi) x)/3)^2 + 4 x^2 Sinh((5 (Pi) x)/3)^2 + 
      3/2 x^4 Sinh((5 (Pi) x)/3)^2 + 1/4 x^6 Sinh((5 (Pi) x)/3)^2 + 
      1/64 x^8 Sinh((5 (Pi) x)/3)^2 - 
      144 Sinh(((Pi) x)/3) Sinh((7 (Pi) x)/3) + 
      60 x^2 Sinh(((Pi) x)/3) Sinh((7 (Pi) x)/3) - 
      7 x^4 Sinh(((Pi) x)/3) Sinh((7 (Pi) x)/3) + 
      1/4 x^6 Sinh(((Pi) x)/3) Sinh((7 (Pi) x)/3) + 
      18 Sinh((Pi) x) Sinh((7 (Pi) x)/3) + 
      6 x^2 Sinh((Pi) x) Sinh((7 (Pi) x)/3) - 
      1/4 x^4 Sinh((Pi) x) Sinh((7 (Pi) x)/3) - 
      1/8 x^6 Sinh((Pi) x) Sinh((7 (Pi) x)/3) + 
      1/128 x^8 Sinh((Pi) x) Sinh((7 (Pi) x)/3) - 
      36 Sinh((5 (Pi) x)/3) Sinh((7 (Pi) x)/3) - 
      12 x^2 Sinh((5 (Pi) x)/3) Sinh((7 (Pi) x)/3) + 
      1/2 x^4 Sinh((5 (Pi) x)/3) Sinh((7 (Pi) x)/3) + 
      1/4 x^6 Sinh((5 (Pi) x)/3) Sinh((7 (Pi) x)/3) - 
      1/64 x^8 Sinh((5 (Pi) x)/3) Sinh((7 (Pi) x)/3) + 
      81 Sinh((7 (Pi) x)/3)^2 - 27 x^2 Sinh((7 (Pi) x)/3)^2 + 
      27/8 x^4 Sinh((7 (Pi) x)/3)^2 - 
      3/16 x^6 Sinh((7 (Pi) x)/3)^2 + 
      1/256 x^8 Sinh((7 (Pi) x)/3)^2);
RegionPlot(a f < 0, {x, 3.46572, 3.46574}, {a, 0, 1}, 
 PlotPoints -> 60)

This is the result:

enter image description here

I am sure that the blue part should be a continuous domain. How can I get a better result? Is there an alternative way instead of increasing the number of plotpoints? Since it is not easy for my system and it takes much time.

How to show the search result to archive page without redirection to search result page

In the archive page, used Jet-Ajax-search widget/Elementor pro to filter products and products putted by using Jet-woo-builder product grid.
Just wanted to show search result to archive page with same layout of product grid without redirection to search result page.
How to solve the problem?

normalization – How can a ‘Request’ store a ‘Result’ code and its associated ‘Error’ code and still enforce the relationship between Result and Error?

I’m an application developer creating the database structure to represent a flat file message format. I’d like to ask the collective knowledge the best/correct way to represent the following scenario:

Request table (PK: RequestID) contains requests; a request has a Result property which is indeterminate (null) until the request has completed.

Result table (PK ResultID) is a lookup table containing (currently) two possible results:

  • Success (Result ID = 0)
  • Failure (Result ID = 1)

ErrorCode table (PK ErrorCodeID) is a lookup table containing error details and their parent ResultID:

  • No Error (ErrorCodeID = 0, ResultID = 0)
  • Generic Error (ErrorCodeID = 1, ResultID = 1)
  • Queue Full (ErrorCodeID = 2, ResultID = 1)
  • Unsupported Interface (ErrorCodeID = 3, ResultID = 1)
  • etc…

I’ve created a one to many relationship between Result (one) and ErrorCode (many). A ‘Success’ Result can only have a ‘No Error’ Error Code, while a ‘Failure’ Result can have a single error code of ‘Generic Error’, ‘Queue Full’, ‘Unsupported Interface’, etc.

When the Request has completed, I need to store the result and its associated error code.

I’ve thought of combining the two tables but that strikes me as repeating columns.

I’ve also thought of having the Request table store the ResultID and the ErrorCodeID but this doesn’t enforce the Result to ErrorCode relationship.

I’m a big believer in database that ‘defends itself’ from bad data so I want the relationship to reject a Result/ErrorCode combination that is invalid; a.k.a. a Result of ‘Success’ and an ErrorCode of ‘Generic Error’ or a Result of ‘Failure’ and an ErrorCode of ‘No Error’.

I’m also a big believer in solid initial design so when changes come down the pike at a later date (as they always do) the structure will not need rework.

Thank you in advance for your time.

Regards,
John E.

aql – arangodb self join query result

Im trying to self join,merge parent field and get results as separate documents
data:

(
{_key="1",name":"a",mf:"xyz"},
{_key="2","name":"b", "parent":"1"},
{_key="3","name":"c", "parent":"1"},
{_key="4",name":"d",mf:"xyzw"},
{_key="5","name":"e", "parent":"4"},
)

query:

for i in data
let o=i.parent>0 ? (for d in data filter i._key==d.parent return merge(d,{mf:i.mf}) : i
return o

expected result:

(
{_key="1",name":"a",mf:"xyz"},
{_key="2","name":"b", "parent":"1",mf:"xyz"},
{_key="3","name":"c", "parent":"1",mf:"xyz"},
{_key="4",name":"d",mf:"xyzw"},
{_key="5","name":"e", "parent":"4",mf:"xyzw"},
}

is this possible to do in arangodb ?

numerical integration – NIntegrate with highly oscilatory result

I want to evaluate a function defined by the following numerical integral:

I1(y_) := NIntegrate((PolyGamma(0, 3*(0.6^2 - x*(1 - x)*y^2)/(4*0.001) + 1)), {x, 0, 1}, PrecisionGoal -> 15, MaxRecursion -> 30)

The PolyGamma function is singular if the argument is a negative integer or zero. In this case, singularities only appear after the point $$yapprox1.202$$. You can graphically check it:

Manipulate(Plot(PolyGamma(0, 3*(0.6^2 - x*(1 - x)*y^2)/(4*0.001) + 1), {x, 0, 1}), {y, 0, 2})

The plot of the integral defined above is:

Plot(NIntegrate(Re(PolyGamma(0, 3*(0.6^2 - x*(1 - x)*y^2)/(4*0.001) + 1)), {x, 0, 1}, PrecisionGoal -> 15, MaxRecursion -> 30), {y, 0, 2})

enter image description here

If I increase the number of recursions:

Plot(NIntegrate(Re(PolyGamma(0, 3*(0.6^2 - x*(1 - x)*y^2)/(4*0.001) + 1)), {x, 0, 1}, PrecisionGoal -> 15, MaxRecursion -> 500), {y, 0, 2})

enter image description here

The result is slightly better. The expected plot, roughly speaking, is the “average of these oscilations”(based in physical estimations). I’ve tried to improve the result:

Plot(NIntegrate(Re(PolyGamma(0, 3*(0.6^2 - x*(1 - x)*y^2)/(4*0.001) + 1)), {x, 0, 1}, PrecisionGoal -> 15, MaxRecursion -> 500, Method -> "GaussKronrodRule"), {y, 0, 2})

But the result is the same. How can I fix the highly oscilatory behaviour? Or at least compute a average of these oscilations.

MySQL result ORDER BY reverse order?

My query looks like ..

SELECT 
        uid
    FROM 
        user 
    
    WHERE 
        plz IN(24718,32326,32329,32328) 
    
    ORDER BY 
        FIELD(plz,24718,32326,32329,32328),
        uid DESC

Output:

97462
97407
97112
.
.
3037
891
15
91967
29360

I need to select / get first (97462) and last (29360) uid.

SELECT uid, MAX(uid), MIN(uid) does not work because of the ORDER BY.