## usability – Appropriate use of and child-proof alternatives to screwed-down battery covers

On lots of electronic devices with replaceable batteries, the battery cover is secured by a screw.

I understand that it may be necessary to protect against child access to the battery bay, but using a screw necessitates the use of a screwdriver to open the battery cover, which can be inconvenient. It annoys me to no end that I need to open my toolbox, grab my screwdriver, and unscrew the darn thing to replace the batteries.

When is using a screw appropriate for securing a battery cover? Under what circumstances is a simple latch closure inadequate for a battery cover? Are there safety regulations that cover this?

It appears that there are legal requirements that specify that toys intended for young children must have secured battery covers. However, this question covers more than just toys, but pretty much any electronic device that has replaceable batteries. Aside from safety and regulatory requirements, when is it better to use a screw instead of a latch closure to secure the battery cover?

Also, what alternatives are there to a screwed-down battery cover that can prevent young children from accessing batteries while being more convenient than a screw closure?

Any such battery compartment must be “inaccessible” such that “it is not physically exposed by reason of a sealed casing and does not become exposed through reasonably foreseeable use and abuse of the product” (source). This may be very difficult to attain in a toolless manner, but any ideas are welcome.

## Smooth covers rescaling the symplectic form

Let $$(M, omega)$$ be a connected closed symplectic manifold of dimension $$2n$$.

Assume there exist smooth covering maps $$phi_k:Mto M$$ such that $$phi_k^* omega=sqrt(n){k}omega$$ for all $$kgeq 1$$. Is $$n=1$$ then?

## dg.differential geometry – Covers of a 3-manifold pull back a cohomology class to any algebraic multiple

Thanks for contributing an answer to MathOverflow!

But avoid

• Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.

## Conformal covers of all degrees

Let $$M$$ be a connected closed conformal oriented manifold.

Assume there exist conformal covering maps $$phi_k:Mto M$$ of all degrees $$kgeq 1$$. Is $$Mcong S^1$$ then?

## ag.algebraic geometry – Open covers by ind-affine ind-schemes

Many apologies if this is totally standard! I couldn’t find it in the literature.

Background definitions:

• A presheaf $$X: textbf{Aff}^text{op} to textbf{Set}$$ is an ind-scheme if it is a filtered colimit of schemes, where we regard a scheme as a presheaf via the Yoneda embedding (and then restrict to affine schemes), and the colimit is taken in the category $$text{Psh}(textbf{Aff})$$ of presheaves (i.e. the colimit is taken “pointwise”). One can impose the condition that all of the transition maps are closed immersions, and then call the result a strict ind-scheme.

• Let’s say that $$X$$ is an ind-affine ind-scheme if it is a filtered colimit of affine schemes. (Side question: Is this the right terminology? It seems there are several distinct notions with this name in the literature.)

Context:

• It is well known that a presheaf $$X in text{Psh}(textbf{Aff})$$ is represented by a scheme if and only if it satisfies the following two conditions: 1) $$X$$ is a Zariski sheaf and, 2) There is a covering of $$X$$ by open affine subfunctors.

• Every ind-scheme is a Zariski sheaf (in fact satisfies the sheaf condition for the fpqc topology).

• The affine Grassmannian (which is an ind-scheme) admits an open cover by ind-affine ind-schemes. See, e.g. the extremely helpful paper by Timo Richarz “Basics on Affine Grassmannians”.

Question:

Is there a similar characterization for (strict or otherwise) ind-schemes? I.e. is something like the following true: a presheaf $$X$$ is an ind-scheme if and only if 1) $$X$$ is a Zariski sheaf and, 2) $$X$$ admits a covering by open subfunctors which are ind-affine ind-schemes? Is it at least sufficient? If not, is there a name for the presheaves that satisfy this property?

## graph theory – Complexity of optimally creating tours from cycle covers

A popular heuristic for the symmetric TSP is to first generate a near optimal cycle cover and then to repeatedly merge pairs of cycles until a single cycle covering all vertices has resulted.
To the best of my knowledge the decision of which pairs of cycles to merge in each step is also based on heuristics; either sequentially by greedy selection or by determining minimum weight matchings in a graph where the vertices represent the cycles and the weight of edges reflects the cost of merging the pair of cycles that are “adjacent” to such an edge.

Question:
what is the complexity of generating the shortest Hamilton Cycle that can be obtained by exchanging $$2left|Cright|-2$$ cycle edges with $$2left|Cright|-2$$ non-cycle edges, when $$left|Cright|$$ denotes the number of cycles in the cover?

To prevent from misunderstandings let me clarify that even with an optimal merging strategy the resulting tour need not be the shortest Hamilton Cycle in the underlying graph.

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## How do I remove Nikon strap rings with plastic covers?

I did this on my D800, I assume they are exactly the same.

So first remove the plastic clips and slide them HART towards the mounting post on the camera. You should just jump out.

Then remove the triangular rings, they are VERY stuff, so you may need a flat-head screwdriver to open the end. Just turn it around like a key ring and let's go.

I NEVER use a strap and these are very annoying all the time …

## dnd 5e – Is there a general rule that covers the interaction between effects that cause death at 0 hit points and features that prevent death at 0 hit points?

There are a number of questions on this website and online about the interaction between effects that cause death at 0 hit points and functions that prevent death at 0 hit points.

Effects that result in death if you reduce a character to 0 hit points include:

• Disintegrate Spell (Original): "If this damage reduces the target to 0 hit points, it will be resolved."
• Disintegrate Spell (PH Errata 2.0): "The target will be resolved if this damage leaves 0 hit points."
• Viewer Decay beam: "If this damage reduces the target to 0 hit points, its body becomes a pile of fine gray dust."
• Viewer Death ray: "The target dies if the beam reduces it to 0 hit points."
• A published adventure * contains a large number of effects with the language "If this damage reduces the creature's hit points to 0, it will be crushed to pulp."
• Immediate death: "If the damage reduces you to 0 hit points and there is still damage left, you die if the remaining damage equals or exceeds your maximum point maximum."

The effects that can prevent a character's death if a character is reduced to 0 hit points include (HT on this question for some of them):

• Halborcs Relentless perseverance: "If you were reduced to 0 hit points but were not killed immediately, you can drop to 1 hit point instead."
• Barbarian Relentless anger: "If you drop to 0 hit points during the rage and do not die immediately, you can make a constitutional roll of DC 10. If you are successful, you drop to 1 hit point instead."
• Druid Wild shape: "You automatically return when you pass out, drop to 0 hit points, or die. (…) If you return to your normal form, you will return to the number of hit points you had before your transformation."
• Death station Spell: "If the target first falls to 0 hit points due to damage, the target drops to 1 hit point instead and the spell ends."
• Polymorph Spell: "The transformation lasts for the duration or until the target falls to 0 hit points or dies. (…) When it returns to its normal form, the creature returns to the number of hit points it had before the transformation."

The interaction between these effects was an ongoing question. Sage Advice previously made the following decision:

If the damage from disintegrate reduces a halborc to
0 hit points, relentless endurance can prevent the orc
transform from ashes?
If disintegrate reduces you to 0 hits
Points, you will be killed immediately if you turn to dust. If you have one
Halborc, Relentless Endurance cannot save you.

What happens if a druid using Wild Shape is reduced to?
0 hit points from disintegrate? Does the druid just walk?
Animal shape?
The druid has turned to dust since the spell disintegrates The moment you drop to 0 hit points.

But then the wording of the disintegrate The spell was changed and in Sage Advice 2.0 the following decision appeared:

(NEW) If the damage from disintegrate reduced half
Orc at 0 hit points, relentless endurance can prevent that
Transform Orc of Ashes?
Yes. The disintegrate Spell turns
Turn them into dust only if the damage done by the spell leaves you with 0 hits
Points. If you're a Halborc, Relentless Endurance can spin
The 0 into a 1 before the spell can dissolve you.

(NEW) What happens when a druid uses wild shape?
reduced to 0 hit points by decay? Does the druid
Just leave animal form?
The druid leaves an animal shape. As
Normally, the remaining damage will apply to the druid's normal hit points. If the remaining damage leaves the druid with
0 hit points, the druid is dissolved.

The problem is, as I see it, a IF Condition that creates two opposite effects. With the Halborcs Relentless perseverance it seems clear (um) that it habit Protect yourself (because of the condition "and don't kill yourself immediately") while the subject polymorphic and wild shape is logically mud.

The change of wording from disintegrate seems to clarify polymorphic and wild shape while giving the Halborc a free boost. However, the language "reduces the target to 0 hit points" has a different problem. As stated in an answer to this question, it has the strange effect that "the spell would not Decay of creatures that already had 0 HP before being hit by the spell ". This also applies to Beam decay, Death rayfalling blocks of stone that crush creatures into porridge, or an effect that "reduces the target to 0 hit points".

Furthermore – and this is less a rule question than a metarule question – I find it irritating that the viewer Decay beam would work so differently from that disintegrate spell (assuming that the old answer from Sage Advice applies because the wording of has Decay beam has not changed). While there's nothing in a fantasy game that requires logical consistency, there are advantages (in terms of player clarity and fairness) when effects that use virtually the same name work the same way.

So the question is whether there is one General Rule that can regulate the interaction between these effects or that can only be solved on a case-by-case basis.

* Don't tell which one because of possible spoilers, but it's a WotC-published hardcover.