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pathfinder – What action is needed to activate the special abilities of the paladin's stuck weapon?

The special Paladin & # 39; s Divine Bond ability includes the following text under the first option:

These bonuses can be added to the weapon, stacking with existing weapons.
weapon bonus up to a maximum of +5, or they can be used to add
the following weapon properties: axiomatic, brilliant energy,
defend, disturbance, flamboyant, burst of flamesholy, quick, merciful,
and speed.

The Special Flaming Weapon ability contains the following text:

On command, a burning weapon is sheathed with fire and inflicts an additional charge.
1d6 points of fire damage if successful. Fire does not harm
the wearer. The effect remains until another order is given.

Flaming Burst weapons also act in accordance with the text above. What kind of extra action does the Paladin have to spend to activate the Flaming Special Property or Flaming Burst, or is it included in the Quick Action to activate the ability?

Aggressive Geometry – Definition of the removal of Chow groups under a special morphism

Let $ X $ be a complex complex projective variety (not necessarily smooth), and leave $ Y $ to be a smooth complex projective variety. Let $ Z subset X $ to be a smooth closed subvariety.

Let $ pi: Y rightarrow X $ to be a morphism with the property $ pi $ is an isomorphism on $ X setminus Z $, and further $ pi $ is a $ mathbb {P} ^ n $– bundle on $ Z $ for some people $ n $.

(Note that $ pi $ may not be an explosion if codim$ Z neq n + 1 $, for example.)

My question is: can we define withdrawal map $ pi ^ *: CH_k (X) rightarrow CH_k (Y) $ for Chow groups? In general, withdrawals can be defined when $ pi $ is flat or a complete local intersection morphism, but in my case, clearly $ pi $ is not flat, and I do not know if $ pi $ is in fact the complete local interection.

Any help or reference would be welcome.

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Google group member name no longer allows special characters.

Until recently, I could include our member's lot number in the member's name by putting in quotation marks:
"103.08 Jane Jones"
This now displays double quotation marks in the name.
How can I now add this name?

Counting non-isomorphic bipartite graphs with special properties

We are given a non-label bipartite graph with size parts $ m $ and $ n $.

It also has the following properties:

  • there are no isolated peaks
  • there are not two peaks with equal sets of neighbors

How should we count (generate) all non-isomorphic graphs with fixed sizes $ m $ and $ n $?
Change room when $ m = n $ is not allowed.
Is there a closed formula in terms of $ m $ and $ n $? If no, is there a recursive way of counting it? If there is a good recursive algorithm to count it, what would its pseudocode look like?

Thank you!

P.S. Is there a chance to apply Polya's enumeration theorem?

P.P.S. This question comes from the task of listing the so-called $ # $tables of relations (see, for example, the finite automata and the algorithms of WATERLOO-LIKE FINITE FOR THEIR AUTOMATIC CONSTRUCTION). The ultimate goal is $ m = $ 8 and $ n = $ 10.

Special conditional formatting if cell A is in a range of numbers to give cell B a different color

I'm trying to create a conditional format that, if an "A" cell is in a range of two numbers, then cell "B" will change color. Google leaves. Please help. Thank you

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On the subgroups of a special semidirect product of two groups abelian

Let H and K tow abelian groups. It is well known that a subgroup of the semi-direct product $ HK $ is not usually semi-direct product of two subgroups $ H & # 39; <H $ and $ K <$ K. But if $ G $ is a subgroup of $ HK $ such as $ K <G & # 39; $then $ G Simeq (G cape H) K $ (see How can we use this for the following problem:
Let $ G $ to be a group p such that $ G simeq (Z / pZ) ^ {m} rtimes (Z / pZ) $. Is there a sub-group of $ G $ of shape $ (Z / pZ) ^ {k} rtimes (Z / pZ) $ with $ k <m $.

Any help would be so appreciated. Thank you all.

The chromatic number list of some special toroidal grid graphics

  • A list-assignment $ L $ at the summits of $ G $ is the attribution of a list
    together $ L (v) $ of colors at each vertex $ v $ of $ G $; and one $ k-list-assignment is a list assignment such as $ | L (v) | geq k $, for each summit $ v $. Yes $ L $ is a list assignment to $ G $, then a $ L $-colors $ G $ is a coloring (not necessarily appropriate) in which each vertex receives a color from its own list;

  • The graphic $ G $ is $ k-list-colorable, or $ k-choosableif it is good $ L $-colors for all $ k-list-Mission $ L $ at $ G $. The chromatic number $ chi (G) $ of $ G $ is the smallest number $ k such as $ G $ is
    $ k-colourable. the chromatic number list $ chi_l (G) $, is the smallest number $ k such as $ G $ is $ k-list-colorable or $ k-choosable.

  • It is obvious that $ chi_l (G) geq chi (G) $, since if $ k < chi (G) $ then $ G $ is not $ L $-colourable
    when each summit $ v $ of $ G $ is given the same list $ L (v) $ of $ k colors.

Consider the graph $ S_n $ which has for
summit define the $ n ^ 2 $ cells of our $ n times n $ array with two adjacent cells if and only if they are in the same row or column.
The graphic $ S_n $ Since n cells in one line are adjacent two by two, we need at least n colors.
Moreover, any coloring with n colors corresponds to a Latin square,
with the cells occupied by the same number forming a color class. Since
We have seen that the Latin squares exist, we deduce $ chi (Sn) = n $and the Dinitz
the problem can be stated as $$ chi_l (S_n) = n? $$

By the solution of the Dinitz problem, we know that the list of the chromatic number of $ C_3 Box C_3 $ is 3, it's $ chi_l (C_3 Box C_3) = $ 3.

The attack method for the Dinitz problem is this: we have to
find an orientation of the graph $ S_n $ with outdegrees $ d _ + (v) ≤ n – 1 $ for everyone $ v $
and which ensures the existence of a kernel for all induced subgraphs.
I want to know the $ chi_l (C_3 Box C_5) $ and $ chi_l (C_5 Box C_5) $.
If anyone can give suggestions or comments, I will appreciate it. Thank you.