Does Aura of Courage end the frightened condition if a frightened ally enters its area of effect?

So I just made level 10 with my paladin and got the added feature “Aura of Courage.” I understand that currently I and anyone within 10 ft of me will be immune to the frightened condition. My question then:
If one of my allies is currently frightened and runs into my Aura, do they lose their frightened condition automatically? Or would they just pass through and keep running around?

I’m interested in RAW and what other DMs have ruled here.

Clarification of the proof involving the regularity condition in Master Theorem

I was going the text Introduction to Algorithms by Cormen Et. al. Where I came across the following statement in the proof of the third case of the Master’s Theorem.

(Master theorem) Let $ a \geqslant 1$ and $ b > 1$ be constants, let $ f(n)$ be a function, and let $ T (n)$ be defined on the nonnegative integers by the recurrence( the recursion divides a problem of size $ n$ into $ a$ problems of size $ n/b$ each and takes $ f(n)$ for the divide and combine)

$ T(n) = aT(n/b)+ f (n)$ ;

where we interpret $ n/b$ to mean either $ \lceil b/n \rceil$ or $ \lfloor b/n \rfloor$ . Then $ T(n)$ has the following asymptotic bounds:

  1. If $ f(n)=O (n^{log_ba – \epsilon})$ for some constant $ \epsilon > 0$ , then $ T(n)=\Theta (n^{log_ba})$ .

  2. If $ f(n)=\Theta (n^{log_ba})$ , then $ T(n)=\Theta (n^{log_ba}lg n)$

  3. If $ f(n)=\Omega (n^{log_ba + \epsilon})$ for some constant $ \epsilon > 0$ , and if $ af(n/b) \leqslant cf(n)$ for some constant $ c < 1$ and all sufficiently large n, then $ T(n)=\Theta (f(n))$ .

Now in the proof of Master’s Theorem with $ n$ as exact power of $ b$ the expression for $ T(n)$ reduces to :

$ $ T(n)=\Theta(n^{log_ba})+\sum_{j=0}^{log_bn -1} a^jf(n/b^j)$ $

Let us assume,

$ $ g(n)=\sum_{j=0}^{log_bn -1} a^jf(n/b^j)$ $

Then for the proof of the 3rd case of the Master’s Theorem the authors prove that,

If $ a.f(n/b)\leqslant c.f(n)$ for some constant $ c<1$ and for all $ n\geqslant b$ then $ g(n)=\Theta(f(n))$

They say that as, $ a.f(n/b)\leqslant c.f(n) \implies f(n/b)\leqslant (c/a).f(n)$ then interating $ j$ times yeilds, $ f(n/b^j)\leqslant (c/a)^j.f(n)$

I could not quite get the mathematics used behind iterating $ j$ times.

Moreover I could not quite get the logic behind the assumption of $ n\geqslant b$ for the situation that $ n$ should be sufficiently large.(As the third case of the Master’s Theorem says).

Moreover in the similar proof for the third case of the general master theorem( not assuming $ n$ as exact powers of $ b$ ) there again the book assumes that $ n\geqslant b+b/(b-1)$ to satisfy the situation of sufficiently large $ n$ .

I do not quite understand what the specific value has to do and why such is assumed as sufficiently large $ n$

(I did not give the details of the second situation as I feel that it shall be something similar to the first situation)

Does gaining immunity to a condition apply immediately to a current condition?

What happens when a creature gains immunity to a condition while it currently has that condition? (For a list of conditions see Rules Compendium 229–35.)

For example, the level 6 battlemind daily utility power mental triumph (Psionic Power 39), in part, says, “You cannot be slowed, immobilized, or restrained until the end of the encounter.” If Sivart the battlemind presently possesses the condition immobilized and takes a minor action to use the power mental triumph, does he lose the condition immobilized? Or, after he uses the power, must the duration of the condition still expire normally and thereafter—for the encounter’s duration—he can’t be immobilized?

By way of metaphor, can an inoculation also cure the disease?

Petrified Condition and Magic Items

Here is an extract of the Petrified condition (from PHB p291):

Petrified: A petrified creature is transformed, along with any nonmagical object it is wearing or carrying, into a solid inanimate substance (usually stone) […] (Emphasis mine)

My question is: what happens to magical object(s) worn or carried by petrified character?

As a DM, I’d rule: said magical object(s) not petrified, somewhat intact (inside the stone backpack, magical sword in scabbard, potion still magical in a probably non-magical glass, etc…), which fits my…erh…style, but is there somewhere something resembling sage advice? Could not find anything about it.

Function minimization as genetic algorithm stop condition

I have implemented genetic algorithm for a problem where I have an objective function which I need to minimize:

Cost = ax + by + cz -> min 

The genetic algorithm should have found the optimal solution if objective function is satisfied.

The function will never reach 0 or below, so I just need to minimize it. Now, since there are no objective values to be reached, how do I know whether the objective function is satisfied or not?

Is there a Dijkstra like pathfinding with condition satisfication algorithm?

Say we have a place-transition digraph system. A transition can fire if all input places have marks. A transition fires by consuming items from input places and placing one into each output place. A number near the transition is a transition price. So, for example, we can get an image like this: enter image description here

We want to find the cheapest path from From to To. So it is quite simple to see how one can modify Dijkstra to find a path in algorithm terms, yet in terms of formal theory in generalised case it does not look so simple and there can appear loops and loop step related conditions. So Is there a Dijkstra like pathfinding with condition satisfaction algorithm?

add_action works outside condition but not inside it

I am developing a theme framework for my own purposes.

So this time i am facing a problem, that is add_action works out side conditional.

add_action( 'meanz_before_main_wrap', 'meanz_entry_header_structure_open', 5 ); add_action( 'meanz_before_main_wrap', function(){echo "<div class='title_cat'>";}, 6 ); add_action( 'meanz_before_main_wrap', function(){echo meanz_post_cats();}, 7 ); add_action( 'meanz_before_main_wrap', 'meanz_do_title', 25 ); add_action( 'meanz_before_main_wrap', function(){echo "</div>";}, 49 ); add_action( 'meanz_before_main_wrap', 'meanz_do_thumbnail', 50 ); add_action( 'meanz_before_main_wrap', 'meanz_entry_header_structure_close', 100 ); 

Otherwise if is use a conditional like this, it doesn’t work

if(is_single()){ add_action( 'meanz_before_main_wrap', 'meanz_entry_header_structure_open', 5 ); add_action( 'meanz_before_main_wrap', function(){echo "<div class='title_cat'>";}, 6 ); add_action( 'meanz_before_main_wrap', function(){echo meanz_post_cats();}, 7 ); add_action( 'meanz_before_main_wrap', 'meanz_do_title', 25 ); add_action( 'meanz_before_main_wrap', function(){echo "</div>";}, 49 ); add_action( 'meanz_before_main_wrap', 'meanz_do_thumbnail', 50 ); add_action( 'meanz_before_main_wrap', 'meanz_entry_header_structure_close', 100 ); } 

Don’t know why it doesn’t work. Any comments?

Sorry for wrong code. Updated the question.

Can you negate the Frightened condition by not looking at the source of your fear?

As the title says, if you cause a creature to be Frightened of you, as in the Frightened condition, but they can somehow manage to not see you, do they stop rolling with disadvantage to attacks/ability checks?

Below are scenarios to illustrate my question.

Scenarios:

  • If a creature is frightened of you, and they turn their back against you to hit someone else, would they no longer have disadvantage to attack rolls/ability checks?

  • If a creature is frightened of you and they have Blindsight, can they close their eyes to stop seeing you, and hence stop rolling with disadvantage?

  • If a creature has 60 ft of movement and is frightened of you, and there is a corner they can reach in 15 ft that will block you from sight, can they run to that corner to stop being frightened, then run back to attack without disadvantage? Assume they would not provoke OA to do this, although the OA is immaterial to the question.