dnd 5th – What is the maximum static positive modifier to the damage of a melee attack?

I'm building a level 20 warlock for maximum static damage (by static, I mean non-rolling damage) in a melee attack.

A level 20 Hexblade warlock with a charisma of 20 may have the following additions:

  • +5 from 20 cha
  • +5: Lifedrinker (based on charisma)
  • +6: Curse of Hexblade (skill bonus)
  • +10: Grand Master of Arms
  • +3: Magic Weapon

This totals +29 damage.

Aside from using volumes to increase my charisma or getting the legendary item that increases the skill bonus by 1, are there other ways to increase flat damage that I do not know?

The answer does not have to be about a Hexblade warlock; That's exactly what I've found to add the highest static bonus to a damage roll.

Multiclass tweets, RAW, RAI, Errata and Jeremy Crawford are all accepted. Simply explain your opinion or facts and cite your sources!

Find the intervals where a song is maximum

I have the following 3 functions in pieces and I would like to have the upper envelope sill.

a = Piecewise({{0.125 (0.1 + 0.1 (11.5 - 1 (Beta))), 
    8 < (Beta) < (11.4)}})
b = Piecewise({{0.375 (0.1 + 0.1 (10.5 - 1 (Beta))), 
    8 < (Beta) < (10.4)}})
c = Piecewise({{0.375 ((10.5 - 1 (Beta))), (10.4) < (Beta) < 12}})

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In other words, I would like to get the list {10.4,10.431}, where 10.4 is the threshold between b and c (here, there is no intersection between b and c) and 10.431, the threshold between a and c (their intersection).

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Maximum length in characters for SQL Server service accounts

I've envisioned a new naming convention for all SQL Server service accounts for instances of our company. I have encountered some problems on my lab environment. Is there a character limit for SQL Server service account names?

DOMAIN SQL-Service-COMPUTER_NAME
DOMAIN SQL-Agent-COMPUTER_NAME
DOMAIN SQL-SSRS-COMPUTER-NAME
DOMAIN SQL-SSAS-COMPUTER-NAME
DOMAIN SQL-SSIS-COMPUTER-NAME

symbolic – searches for a maximum parameter for a range of target eigenvalues ​​based on the size of the matrix

I have a symbolic tridiagonal matrix of this form

a = 0;
c = 0.25;
sa1[b_] :=SparseArray[{Band[{1, 1}] -> a, 
          Band[{2, 1}, {2 l, 2 l}] -> {I b/4, I c}, 
          Band[{1, 2}, {2 l, 2 l}] -> {-I b/4, -I c}}, {2 l, 2 l}];

or a and c are fixed parameters, b> 0 is a variable parameter and l is the rank of the matrix. Diagonalising this matrix according to b, I can get the greatest value for bLet's say bmax, so that the absolute value of the eigenvalues ​​is less than 1/10 ^ 5. Note that the eine values ​​always appear in pairs by symmetry. Find bmax, I used the Arnoldi method which was also used in this thread

closestEVtotarget[b_?NumericQ, target_?NumericQ] := 
  Abs[First@
    Eigenvalues[sa1[N[b]], -1, 
     Method -> {"Arnoldi", "Criteria" -> "Magnitude", 
       "Shift" -> target}]];
With[{target = 1/10^5}, 
  Plot[closestEVtotarget[b, target], {b, 0, 0.5}, 
   GridLines -> {None, {target}}]];
With[{target = 1/10^5}, 
  plot = Plot[{target, closestEVtotarget[b, target]}, {b, 0, 2}]; 
  bmaxval = Graphics`Mesh`FindIntersections[plot]];

For example for l= 6, printing the bmaxval would be

{{0.185999,0.00001}}

or bmax= 0.185999.
Now the question is how can I collect all bmax values ​​for different values ​​even from lLet's say

llist = {4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26};

and plot l against. bmax?

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dnd 5th – What is the maximum number of undead controlled by PC?

I decided to make an unreasonable request from the nearby city and get a benefit during a future conflict. I want a horde of undead reinforcing my arguments. I'm not looking for quality (after all, these jesters can not distinguish the skeleton from the lich), but the quantity.

My question is: how many undead creatures can a player character have under his control at the same time?

constraints:

  • Only the official content of WOTC.
  • Undead small and big only: it's hard to be intimidated by something you need to look for.
  • The target number should be achievable without the explicit cooperation of the DM. No dozens of tomes thrown on the character, no improbable situations, no fiat DM (so no Boons, for example).
  • No legendary magic object.
  • After reaching the desired amount of undead, the character must be able to keep that amount for at least seven days without outside help during a trip with the horde.

reference query – The maximum order of an isogeny class of rational elliptic curves is 8?

I am looking for a reference for the proof of the following question following Mazur theorem 5 Rational isogenies of the first degree.

Theorem 5 There is a constant $ C $ such as each elliptical curve $ E _ {/ mathbb {Q}} $ is isogenous (on $ mathbb {Q} $) at most $ C $ elliptic curves (not mutually non-isomorphic).

"Can we take $ C = $ 8? "

Has this question been proven? And if so, what is a reference to the proof of the result?

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dnd 3.5e – For damage due to falling objects, does the maximum of 20d6 apply only to additional damage caused by distance, or is it? a global maximum?

According to the DMG, page 303:

For 200 pounds of an item's weight, it deals 1d6 damage, as long as it falls at least 10 feet. The distance also comes into play, adding 1d6 additional damage for each 10-foot increment falling beyond the first (up to a maximum of 20d6 points of damage).

I read that it meant that the damage added by the distance of the hats dropped to 20d6, but that the damage based on the weight of the object had no hat.

One of my friends said that it remembers a lot of talk about the subject years ago and a decision that the damage caused by the fall of an object has a strict ceiling of 20d6, regardless extra weight.

Unfortunately, he can not find where the things he remembers have been told, and all we need to go on is the text of the book. Does anyone know what is the correct answer? Preferably with a source?