## functional analysis: show that \$ G_ {1} \$ as the space of certain partial sums in \$[0,1]\$ is equitable

Define $$G_ {1}: = {f_ {n} (x): = sum limits_ {i = 1} ^ {n} frac {x ^ {i}} {i!} | N in mathbb N } subseteq C ([0,1]$$

The background to this question is that I want to show that $$G_ {1}$$ It is relatively compact. It is clear that I need to use Arzela-Ascoli, but to do that, first I have to demonstrate the continuity of equity, and this is where I am fighting.

I know that $$(f_ {n}) _ {n}$$ converges uniformly in $$[0,1]$$ For something $$f$$ Y $$f_ {n} (x) leq exp (x)$$. From this I know that by any $$epsilon> 0$$ exists $$N en mathbb N$$ so that $$vert vert f_ {n} -f vert vert _ { infty} < epsilon$$ for all $$n geq N$$, where $$vert vert f_ {n} -f vert vert _ { infty} = sup limits_ {x in [0,1]} vert f_ {n} (x) -f (x) vert$$ But how does this help me to show continuity and much less to continuity?

## partial order: Do all relations with partial order and its dual have the same number of topological orderings?

Given the Hasse diagram of a partial order relationship, is it true that both POSET itself and its dual POSET have the same number of topological orderings? I have tried some examples, and although it seems to be the case, I need a formal way to prove the same. So please help me with this.

## tracing: How to manipulate a partial derivative diagram of self-defined bivariate functions?

I have a linear function by parts (spline) that describes a progressive income tax program, with higher marginal rates for higher and higher incomes.

I want to understand the implications of a rule that some tax-exempt income could still increase your average rate in the taxable part. Basically, with `X` being taxable income and `Y` being exempt income, your taxes will be `f (x + y) / (x + y) * x`, where `F` It is the non-linear scheme that would apply to income without exemptions. I can define `F` as a linear function by parts, see above.

To calculate the marginal tax rates on taxable and exempt income, I would simply need the partial derivatives of this expression, with the particular function `F` plugged in, and this I can plot against the two variables. Or trace against one and use the other as a parameter to `Handle`.

The derivative looks good in Mathematica, although it is a bit difficult to verify with so many cases.

However, I have empty plots, which, of course, do not make sense to manipulate. Where is this going wrong?

``````Handle[Plot[D[Tax[x+y]/ (x + y) * x, y], {and, 0,200000}], {x, 0,200000}]
``````

Think about `Tax` in this way:

``````Tax [z_]: = By parts[{
{0,0    <=z< 11265},
{0+ 0.0856(z-11265),11265<=z}
}]
``````

## Partial and semi-partial correlation.

I am interested in knowing if there are incorporated. Mathematics Functions that perform partial and partial calculations.

If not, what would be a simple and efficient way to calculate them from the results of a LinearModelFit?

## of formulas – Formatting partial cells with CONCATENATE in Google Sheets

Is there any way to partially format using `CONCATENATE` in Google Sheets?

For example, `= CONCATENATE ("*", Sheet1! A1, Sheet1! B1)`and I want to do the `*` In bold or blue or something else.

I realize that I could:

1. Divide it into several cells and control the color (this does not work with the sheet on which I am working due to everything that is happening on the sheet) To begin with, I have combined two cells to adjust the text, which would cause the obstruction of the text. the width of the column would affect other entries in the same column.)
2. Convert it manually to plain text and make the necessary format changes. But that is also manual.

## magento2: the upgrade of Magento 2.2.6 to 2.3.1 broke the functionality of partial reimbursement of the credit note

On the credit note, there is a "Adjustment refund" field at the bottom. Before updating to 2.3.1 If I entered a value in this field, there was a "Update totals" button that would update the total. But after updating to 2.3.1 this button does not appear. Attaching screenshots for more details.

]two

## Calculation of partial sums \$ begin {aligned} sum_ {k = 1} ^ {n – 1} end {aligned} left (1+ cos left ( frac {k , pi} {n} right) right) ^ n \$

Having established that Mathematics The following sum can not be calculated:

``````sum = sum[(1 + Cos[k Pi/n]) ^ n, {k, 1, n - 1}]
``````

I implemented the classic "plan B", that is, I tabulated some values ​​and then I looked for a sequence function:

``````Table[sum, {n, 10}] // FullSimplify;
sum = FindSequenceFunction[%, n] // Expand
``````

obtaining:

-2 ^ (- 1 + n) + (2 ^ n (-1/2 + n)!) / (Sqrt[Pi] (-1 + n)!)

On the other hand, I also know that:

``````sum == -2 ^ (- 1 + n) + n / 2 ^ n Binomial[2 n, n] // FullSimplify
``````

and in fact:

True

So the question is: is there a way to "force" Mathematics To give me the result in this last way that is easier for me?

## asp.net mvc – Error trying to make a partial view in a view

I have a view (cshtml) and in it I need to call a partialView. This Partial is a table with the records of that Sale, which will be displayed in tabular format at the bottom of the View. The problem is that when I try to open the View (Index), this error:

The element model passed in the dictionary is of type & # 39; System.Int32 & # 39 ;,
but this dictionary requires a model type of type
& # 39; System.Collections.Generic.IEnumerable`1[SubscriptionCenter.Core.Domain.Logs.LogAlteracao]& # 39;

How do I solve this?

This is my html where I "register" to Partial View

``````
@ Html.Partial ("_ LogAlterarMarkup", Model.CustomerId)

``````

I already did it like this:

``````@ Html.Partial ("_ LogAlterarMarkup")
``````

it's like that

``````@ Html.Partial ("_ LogAlterarMarkup", Model.CustomerId)
``````

and also like that

``````@ Html.Partial ("_ LogAlterarMarkup", Model.OrderId)
``````

OBS: The partial view is another model (record)

## Scala partial functions that give coincidence error: strange behavior

I'm trying to use a partial function for some validations, let's take an example of a string:

``````def isLengthValid: PartialFunction[String, Option[String]]= {
case s: String if s.length> 5 => Some ("Invalid")
}

def isStringValid: PartialFunction[String, Option[String]]= {
case s: String yes s == "valid" => Some ("Valid")
}

isLengthValid ("valid") oElse isStringValid ("valid")
``````

Expected output => Some ("Valid")

But I'm getting a match error:

scala.MatchError: valid (from class java.lang.String)

Could someone help what is wrong here, because according to my understanding? .it defines It is called internally and should not be given. matchError.

## magento2.3.1 – Magento 2.3.1 authorizenet-acceptjs does not support partial refunds

After upgrading from 2.2.7 -> 2.3.1, we have successfully switched from obsolete MD5 hash-based authorize.net hash to SHA-512 signature key method.
The problem with the new authorization module now is that we can not create partial refunds.
Searching and comparing with the old module, I found provider / magento / module-authorizenet / Model / Directpost.php: 68 have `protected \$ _canRefundInvoicePartial = true;`

Question, what would be an appropriate way to extend the new authorization module to support partial reimbursements?

Thank you.