## air travel – Can I reschedule a Non refundable international Flight ticket (AirFrance+Jet Airways; Barcelona-Pairs-India) with minimal additional charges?

Your ticket is non-refundable, but possibly changeable with a fee. So you probably can change your return date by paying the change fee plus the fare difference. You just need to call the airline office where you bought the ticket from, presumably in India (since you said you will return to India).

Now, before you call them, there’s a bit of homework you can do. If your date is flexible, try to see which date is the cheapest. As I stated before, you will need to pay the change fee plus the “fare difference”. If you’re lucky to find the same fare on the new return date, you will only need to pay the change fee. On the other hand, if you pick a date with only expensive fares left, then you may pay a lot more than you would like.

Nonetheless, you will have to call the airline office or the agency in India to find out the exact amount.

## Ask the GM, the rules are not precise and exacting

There are no exacting dimensions on the biggest medium creature or the smallest small creature and whether the first could squeeze into a space the size of the latter. You’ll have to ask the GM. That said, there are rules:

### If you are not using a grid

Then a creature can squeeze into a space that it otherwise could not fit into but that a creature one size smaller could fit into without squeezing:

(…) A creature can squeeze through a space that is large enough for a creature one size smaller than it. (…)

What this means in terms of exact dimensions is never stated and so is up to the GM.

### If you are using a grid

We know a little more about creatures and size as the section on Creature Size states:

Each creature takes up a different amount of space. The Size Categories table shows how much space a creature of a particular size controls in combat. (…)

Of course, this isn’t their physical size, it’s what they control during combat. That said, there are clear definitions of this right afterwards.

A tiny creature controls a 2.5*2.5 space
A small or medium creature controls a 5*5 space
A large creature controls a 10*10 space
A huge creature controls a 15*15 space
A gargantuan creature controls at least a 20*20 space

This doesn’t tell us how much physical space creatures of a given size category take up, so any real limit on squeezing has to be made by the GM, but it is some sort of start.

### Personally, I abstract squeezing away almost entirely

If my party consists of medium creatures, I am simply going to design a dungeon with sections that either do not require squeezing, do require squeezing, or cannot be traversed even while squeezing. If there are creatures of various sizes, I’ll just decide which paths each size of creature can fit into. The exact dimensions don’t matter there.

The place I do use slightly more exact dimensions is when I simply apply the rules on control by letting a small creature squeeze into a 2.5*2.5 space and a large creature squeeze into a 5*5 space (such as to avoid an area of effect). Using this, a medium creature is unique in that squeezing mid-combat does not make it now control less space.

## recursion – How many distinct BST of minimal height are there for a BST with n distinct nodes?

Imagine we have a BST with n nodes . We know how to find number of all the possible binary search trees with that number of nodes . But the thing I am looking for is which of those BSTs have the minimum height . I want a recursive relation that represent all the possible BST with minimum height for given n nodes .

for example if n is 3 so we can have 5 different BST with those 3 nodes . But the ones that have height of 1 is valid for this question .
Actually I tried a lot for solving this question in recursion but I was not successful I could even write code for that in java (not in recursion) , but not the mathematical relation.

I have red same questions like this but they were for just binary trees not the BST and were so hard to absorb .

could you help me solve that .

## sql server – Minimal logging for bulk inserts?

I have many scripts running that truncate entire tables and rewrite data daily, however this fills my transaction logs very quickly. All these scripts use `INSERT INTO .. SELECT`. So recently I’ve changed my database to the Bulk-Logged recovery model, and I added the `with (TABLOCK)` to all my insert statements. This doesn’t seem to be doing anything, because according to https://www.mssqltips.com/sqlservertip/1185/minimally-logging-bulk-load-inserts-into-sql-server/ if the table has a clustered or non-clustered index, it still gets fully logged. Should I then drop all the indexes before inserting, and recreate them after the table is populated? Or is there a better method to do this?

## riemannian geometry – Examples of bundles with minimal fibers

There is a result of Chen

A Riemannian submersion $$pi : F hookrightarrow (E,g) to B$$ with minimal fibers $$F$$ and such that $$g$$ has negative sectional curvature is such that the induced metric on $$F$$ has negative scalar curvature.

I would like very much to know: is there any explicit example of bundles of this kind?

Moreover, are there any Riemannian submersions with torus as fibers or with any other aspherical manifold as fiber, such that the fibers are minimal?

## dg.differential geometry – Extensions of minimal hypersurfaces

Let $$B subset mathbf{R}^{n+1}$$ be the unit ball, and $$M subset B$$ be a minimal hypersurface. By this we mean that $$M$$ is an embedded $$n$$-dimensional submanifold with vanishing mean curvature. We allow for the closure $$overline{M}$$ of $$M$$ in $$B$$ to not be embedded, write $$mathrm{sing} , M = overline{M} setminus M$$ and call this the singular set of $$M$$. However this is assumed to be small enough for $$M$$ to be stationary in $$B$$: compactly supported deformations $$X in C_c^1(B;mathbf{R}^{n+1})$$ do not change the area of $$M$$ up to first order. For example one might take $$n geq 2$$ and consider a surface $$M$$ embedded outside the origin with $$mathrm{sing} , M = { 0 }$$.

Question 1. Are there conditions that allow the extension of $$M$$ to a globally defined immersed minimal hypersurface in $$mathbf{R}^{n+1}$$? That is, when is there a minimal hypersurface $$tilde{M}$$ in $$mathbf{R}^{n+1}$$ (immersed away from a small singular set) with $$tilde{M} cap B = M$$?

Let me make some remarks summarising my own conclusions.

• The Cauchy–Kovalevskaya theorem could be relevant, but I am not sure whether this can be used to construct a globally defined extension. Moreover, one would have to worry about pieces coming together and meeting tangentially.
• This is not a purely PDE-theoretic question. If one considers the case where $$M$$ is the graph of a smooth function $$u$$ defined on $$mathbf{R}^n cap B$$—this function satisfies the (quasi-linear) minimal surface equation—then it is not hard to see that $$u$$ can in general not be extended to a globally defined function $$tilde{u}: mathbf{R}^n to mathbf{R}$$. The Bernstein theorem is one way to see this, but also simple examples can be constructed using a suitable portion of the catenoid.
• One can use the unique continuation property of minimal surfaces against the question, by taking $$M$$ to be a portion of a known surface. For example, by taking $$M$$ to be an embedded portion of an immersed minimal surface $$tilde{M}$$ one can see that one cannot hope for a globally defined and embedded minimal extension. Moreover, if one chooses $$M$$ to be portion of a singly-periodic Scherk surface one sees that $$tilde{M}$$ may have unbounded area growth: $$lim_{R to infty} mathcal{H}^n(tilde{M} cap B_R)/R^n = infty$$.

I am especially interested in the case where $$M$$ is one of the surfaces constructed by Caffarelli–Hardt–Simon. These are defined in $$B$$, embedded outside the origin, where they are prescribed to be tangent to a given minimal cone $$mathbf{C}$$.

Question 2. How does the answer change if $$M$$ is one of those surfaces? Is there $$tilde{M}$$ extending $$M$$, perhaps even with bounded area growth, that is with a constant $$C > 0$$ so that $$mathcal{H}^n(tilde{M} cap B_R) leq C R^n$$ for all radii $$R > 1$$?

## security – Is there a standard for the minimal lenght an application should support for the maximal characters count to support for the passwords?

I’m looking for a standard (or likewise) document that provides a minimal length an application should support for the maximal characters count for the password?

Of cause I know that there is the longer the better. And best is (maybe) not to limit at all (would be subject to discuss for other questions).

But is there a standard (form NIST) or something like a standard that provides a guideline for the minimum of the maximal character count for the password lenght.

## Building a minimal finite deterministic connected automaton

I need to build a minimal finite deterministic connected automaton that is equivalent to this automaton:

What are the steps?