## amazon web services – AWS Cloud Front, how to request origin using correct url

I’m trying to cache a website on an EC2 using the URL xyz.com, so i created an Cloud Front with the origin pointed to xyz.com,

But all information returned by the server (like button urls) are not relative and include the request URL, meaning that if Cloudfront access the origin with xyz.com, the contents returned by the CDN (for any cname used) will contain the origin url like an <a href="xyz.com/info"><a>
instead of a “cached” url that points to the CloudFront distribution, like an cdn.xyz.com.

tl:dr
CloudFront should return:
<a href="cached.xyz.com/info"><a> (which is the url accessed that points to the distribution)
But it returns:
<a href="uncached.xyz.com/info"><a> (which is the Origin URL that contains the data to be cached)

Is there a way to spoof the Origin server to it think that URL that is being used to access it is the URL being used to access the CloudFront distribution, so it returns correct URLs?

## reference request – Regularity for stationary Navier-Stokes equation in $mathbb R^2$

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## Is there a way to get UPS billing data through QuantumView API, or in any automated request to UPS billing center?

I am working on UPS API integration and have noticed that QuantumView excludes the cost that the shipper paid from their result XML.

So I have turned to the UPS Billing Center where it’s possible to generate reports

https://www.apps.ups.com/ebilling/trackNumReport.action?reportId=ups_trck_nr_dummy

The UPS API documentation is a disaster. I can’t find anything about how to automate this.

Would prefer not to scrape the web site to re-generate a canned “batch” report and download that, or have my client do it manually, if there is a way to do this in an automated fashion.

If I have to generate a batch billing report on a schedule then merge it with the QuantumView API response, that is do-able although not optimal.

Would prefer some way to pull the billing data in with the QV request, however it seems that UPS does not want you to know how much you paid for a shipment.

## reference request – Name for a logarithmic ratio of roots

I’m trying to find a name for the following quantity that came up in my research. I’ve asked some people and looked around myself but can’t find a name, yet it seems like something that has probably been studied before.

Let $$K$$ be a field and $$f(x)$$ a polynomial in $$K(x)$$, and further assume that $$bar K$$ has a norm $$|cdot |$$. Let $$alpha,beta$$ be the roots of smallest and largest norm, respectively. What would one call, and are there any references you know of related to:
$$frac{log|alpha|}{log|beta|}?$$
(or its reciprocal, of course)

I’m mainly interested in the case where $$K$$ is a local field, so really $$log|alpha|$$ is the valuation of $$alpha$$ – for this reason I prefer not to assume that $$f(x)$$ is irreducible over $$K$$.

## In IIS Request Filtering, is the case of the string important?

When in the Edit Filtering Rule dialog in IIS, is the case of the string, e.g. cast( important?

We’re seeing SQL injection attack attempts that have the string in various combinations of upper- and lower-case, like cAsT(. Do we need to be specific? I would expect that the module doesn’t expect one to think of all the possible combinations but I can’t find it clearly stated as the case in any of the online re

## reference request – “Old-Fashioned” O-level Maths Book

I’m looking for recommendations for an “old-fashioned” style of maths textbook for O-level/GCSE, i.e., one which is concise (not full of pictures) with plenty of exercises. Ideally something which is available in PDF format online. I don’t necessarily mean an old book, more a book written in a style which is typical of the early 20th century or earlier. (For instance, Gwynne’s Latin is a modern book for learning Latin which I would consider to fall under this category.)

I am quite fond of this one which I own a physical copy of, but am struggling to find anywhere online in PDF format.

Also I would appreciate if it is just one book rather than many volumes. A lot of maths textbooks made for school come in many volumes with titles like “School Maths 1A, 1B, 2A, 2B”, etc.

## reference request – On the state of the art on closed $(n-1)$-connected $2n$ manifolds

In the paper “Classification of $$(n – 1)$$-Connected $$2n$$-Manifolds” by C.T.C.Wall (Annals of Mathematics , Jan., 1962, Second Series, Vol. 75, No. 1 (Jan., 1962), pp. 163-189), Wall studies $$(n – 1)$$-Connected $$2n$$-Manifolds with a small ball removed and proves a classification result for such manifolds in terms of algebro-topological invariants, namely the intersection form on the middle cohomology and a homotopy theoretic invariant which varies finitely.

In the introduction Wall makes the following remark (I quote): “In a subsequent paper, the author intends to study the diffeomorphisms of the manifolds here obtained; in particular, to give a complete set of invariants of isotopy of a diffeomorphism, and to consider more carefully the actual diffeomorphism classification of closed $$(n-1)$$-connected $$2n$$-manifolds (which is not settled in this paper, even when our results are complete.)”

There are two parts to my question:

1. Did the mentioned paper appear?

I should mention that I have looked through the titles of Wall’s (100+) subsequent articles and not found a title directly related to this problem, hence the question.

I should also mention what is known in low dimensions. For $$2n = 4$$ this includes the smooth Poincare conjecture so is open to my knowledge, up to homeomorphism it has been settled by Freedman. In dimension $$2n = 6$$, I believe that it is known due to work of Wall, Jupp and Zubr that such a manifold should be diffeomorphic to a connect sum of $$S^3 times S^3$$‘s.

I ask a second part:

1. Let $$n$$ be an even integer, $$n geq 4$$. What is the state of the art of the homoemorphism classification of closed $$(n-1)$$-connected $$2n$$-manifolds?

Note also in Question 2 I have intentionally slightly modified the problem, since manifolds with dimension $$2 mod 4$$ and the issue of different smooth structures are not of primary interest to me.

## reference request – Specific criterion for the sum of two closed sets to be closed

Let $$Y$$ and $$Z$$ be two closed subspaces of a Banach space $$X$$ with $$Ycap Z={0}$$.

I know that $$Y+Z$$ is a closed subspace of $$X$$ $$iff exists α>0:quad ∥y∥≤α∥y+z∥forall y∈Y,forall z∈Z$$.

However, reading this question A criterion for the sum of two closed sets to be closed ? commenter posted that: the standard equivalence to the sum being closed is that the unit spheres of $$Y$$ and $$Z$$ are a positive distance apart i.e. $$∃r>0quad ∥y−z∥≥rquad ∀y∈Y,∀z∈Zquad s.t.quad ∥y∥=∥z∥=1$$.

Could anybody provide me with a proof or rather a reference to where I can see the proof of this equivalence?

## code request – Problem with chemical formula

Recently I learned that in Mathematica it is possible to create chemical structures here: Chemical formulas with Mathematica

I am having a problem with a structure called “Sucrose benzoate” (here’s the reference: https://www.sigmaaldrich.com/catalog/product/aldrich/458333?lang=en&region=US). Since the simple MoleculePlot@Molecule("Sucrose benzoate") doesn’t work, I am trying the following:

MoleculePlot@
Molecule("O=C(OC(C@H)1O(C@H)(O(C@)3(COC(=O)c2ccccc2)O(C@H)(COC(=O)
c4ccccc4)(C@@H)(OC(=O)c5ccccc5)(C@@H)3OC(=O)c6ccccc6)(C@H)(OC(=O)
c7ccccc7)(C@@H)(OC(=O)c8ccccc8)(C@@H)1OC(=O)c9ccccc9)c%10ccccc%10")
(*Sucrose benzoate*)


which gives (with no red circle):

The problem is that there are two rings on colliding with each other (as shown with the red circle). How can I fix that so that they look separated (at least not colliding)?.

## reference request – Hahn’s theorem on ordered fields

There is a theorem attributed to Hahn that every ordered field $$F$$ containing $$mathbb R$$ is a subfield of a formal power series field $$mathbb R[[X^Gamma]]$$, where $$Gamma$$ is an ordered abelian group. Can you give a nice reference in English for a proof of this theorem? Or if it is not too hard, please sketch a proof below.