reference request – What inequalities for convex sets are known since the work of Scott and Awyong?

In 2000, Paul R. Scott and Poh Way Awyong published the paper Inequalities for Convex Sets, which nicely collates the known results relating various natural geometric functionals (diameter, area, etc.) on convex planar sets.

Given that some of the inequalities in the paper cite results published just a few years prior (or in one case, 18 years later!), it seems that the state of knowledge about these inequalities is still evolving, so I would expect some new results to have arisen in the two decades since its original publication.

Which new results are known relating geometric functionals on planar convex sets? In particular, I would love to find an equivalent version of this paper with up-to-date information on the current state of knowledge, existing conjectures, etc., or a reliably-updated webpage tracking the same.

Two related extensions of the original paper I would be interested to see:

  • An extension of the table on relationships between pairs of functionals giving results for additional measurements, of which there are many possible choices: packing density, area of maximal inscribed triangle, etc.

  • An analogous collection of results for convex bodies in $mathbb{R}^3$, though of course the number of natural functionals grows substantially and obtaining exact results is likely much harder. In the $mathbb{R}^n$ case, this thread is a good start, though I’d be interested in seeing conjectural relationships as well.

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

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naming convention – Proper name for reference tables in OLTP

I know this might be a silly question. But I really appreciate accepting and answering this question.

When I have an OLTP database with some big tables like orders and items. I have other tables (similar to dimension tables in OLAP) where we store reference values, such as: currency, city, category.

What is the proper name for those reference tables? Can we still call them dimension tables in OLTP or do they have their own generic name?

c# – Cannot perform binding on null reference when on async operastion

I’ve got a series of functions and methods to authenticate to a web service and control various hardware parameters.

Of which, almost all of them are async – aside from the ones where I’m specifically steering some parameters.

Where I’ve come unstuck over the last few days (and finally can see now) is that I have set a new value, sent it to the server, and am waiting for a boolean to come back to tell me if it’s successful.

What’s worse – is that if I’m explicitly awaiting everything I still get the same error.

I’m got it called from a timer, so I can consolidate all updates into a single JSON object, and correctly serialise it for the endpoint.

private async void SendTimer_Elapsed(object sender, ElapsedEventArgs e)
    var timer = sender as Timer;
    if (Device.JsonToSend != null && Device.JsonToSend.Count > 0)  //ensure I've got a valid dict of endpoints and JSON updates
        foreach (var json in Device.JsonToSend)
            //Key is path, Value is payload.
            if(await Device.putValue(json))  //true if update was successful
                await Device.readConfigJsonFromServer(this);
                await Device.readStatusJsonFromServer(this);
            logger.Debug($"JSON to Send:n{json}");

    Device.JsonToSend = new Dictionary<string, JObject>();


Timer above, putValue below.

public async Task<bool> putValue(KeyValuePair<string, JObject> json)
    // Initialization.  
    var handler = new HttpClientHandler()
        ServerCertificateCustomValidationCallback = HttpClientHandler.DangerousAcceptAnyServerCertificateValidator
    // Prepare JSON - serialise CONFIG token

    string s = JsonConvert.SerializeObject(json.Value.SelectToken("config"));
    dynamic tempJson = json.Value;

    using (var client = new HttpClient(handler))
        // Access test instance
        client.BaseAddress = SNPDeviceUri;
        string putPath = "/api/elements/" + SNPDeviceUri.Host + json.Key; // construct my putValue query
        putPath += "/?partial=true";

        int retryCount = 3;
            // Setting content type.  
            HttpResponseMessage putResponse = null;
                else if(putResponse.IsSuccessStatusCode)
                    //DeviceModel.CommsStatus = DeviceState.Connected;
                    logger.Trace($"PUT Succeeded to {SNPDeviceUri.Host}{putPath}nt{putResponse.StatusCode}:{putResponse.ReasonPhrase}nnt{json.Value.ToString()}n");
                    return true;

            } while (retryCount > 0);
        return false;

Even if I declare a boolean explicitly for await Device.putValue – I still get the same error – Cannot perform binding on null reference.

I think I’ve spent way too much time looking at this, and have evidently done something wrong.

Any thoughts?
Many thanks

9 – View to get information for the user entity reference using contextual filters

I have two content types and each one has a user entity reference field. I want a view using contextual filter that shows the information of the content types when I pass the user ID referenced for the user entity reference field.

content-type 1: field -> studies, field -> id-user-entity-reference
content-type 2: field -> experience, field -> id-user-entity-reference

I want to get for example studies and experience in a view when I have a path similar like that:

/content/id-user-entity-reference (not the logged user, not the author id of the content type)

I need these results can be exposed via rest.

How can I configure my view to achieve that?

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:
(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 $K$.

magento2.3 – Anybody know the Reference block name for the Footer->Miscellaneous HTML

Within Content->Design->Configuration->Theme->Footer->Miscellaneous HTML I have added some HTML and it works correctly

However, I use a popup and it also displays at the bottom of the popup window

Through the pop-ups Layout.xml I would like to remove the Miscellaneous HTML using something like

<referenceBlock name="XXXXXXXXXX" remove="true"/>

Can anyone please give me the referenceBlock name for the Miscellaneous HTML?

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.

profinite groups – Reference requested to (possible) consequences of a theorem about verbal subgroup

I studied the paper “On the verbal width of finitely generated pro-p groups” by Andrei Jaikin-Zapirain (link at ProjectEuclid).

Theorem. Let $omega neq 1$ be an element of the free group $F$. The the following are equivalent:

  1. $omega(H)$ is closed for every finitely generated pro-$p$ group $H$;
  2. $omega notin (F’)^pF”$.

This is the main theorem of the paper (and can be extended to pronilpotent groups). Since this paper is from $2009$, is there some consequences of this theorem? If yes, someone knows a reference? By “consequences” I mean some corolaries or something like that.