## logic – a conjunctive normal form that is a tautology

Take any clause in the formula. If all variables in that clause are different, we can always assign $$0$$ to a non-negated variable and $$1$$ to a negated variable. This makes that clause $$0$$. Therefore, it makes the CNF formula $$0$$. Thus, tautology is not possible unless there is $$A vee neg A$$ in every clause.

## c++ – Is there any difference between anonymous class and normal class initialization?

The following code will report an uninitialized error

``````        class A {
public:
int i;
double j;
};

// in main:

A a;
std::cout << a.i << std::endl;
``````

I know it can’t rely on the synthesized default constructor, but why does another piece of code work?

``````        class {
public:
int i;
double j;
} a;

// in main:
std::cout << a.i << std::endl;  // output: 0
``````

Is there any difference between anonymous class and normal class initialization?

## Is it normal for a level 2 character to have a +8 attack modifier?

One of my player’s character is an archer elf with a +4 Dexterity modifier. When she uses her longbow, she gets the +2 poficiency bonus, plus the +2 bonus given by her archer specialization. That gives us a +8 modifier on the attacks with the longbow. Is it normal ?

On one hand I’m a bit surprised because it seems high, but on the other I feel it would be unfair to nerf it.

I didn’t find where to look for the answer, can somebody help me ?

## fraud – Is it normal to be asked for an advance fee on a withdrawal?

No, when transferring or selling Bitcoin you don’t ever have to first pay any sort of extra fee in advance.

Being asked to pay in extra money for any sort of fee is a trick of confidence tricksters (conmen, scammers, fraudsters)

Ordinary Bitcoin transactions will deduct a small amount of Bitcoin from the balance as a transaction fee (not a transfer fee), but this is not something extra you pay in. Current transaction fees are very high at around \$30 per transaction (a year ago they were less than \$1). The actual fee you should pay depends on how complex the transaction is and how quickly you want the transaction to be processed. You should not be paying more than this and it should automatically be deducted from your Bitcoin balance, not paid in as an extra amount. This is a transaction fee not a transfer fee. There is no such thing as a transfer fee or transfer code in normal Bitcoin transactions.

When dealing with any business, no fees should ever come as a surprise. You should be able to find the business terms and conditions on their web page without talking to anyone at that business. Any fees that come as a surprise are a sign of possible fraud.

## Graphing a Normal Vector to a Plane from the origin

I’m trying to plot a normal vector to a plane. I know I’m doing something I should know better, but can’t seem to find. Vectors {0, 1, 2}, {1, 1, 3} obviously determine a plane. Their Cross Product is {1, 2, -1}, which is normal. Unfortunately this code (all from the origin):

``````Graphics3D({{Blue, Arrow({{0, 0, 0}, {0, 1, 2}})}, {Red, Arrow({{0, 0, 0}, {-1, -2, 1}})},
{Blue, Arrow({{0, 0, 0}, {1, 1, 3}})}})
``````

Yields,

Which doesn’t look quite right. Just don’t trust pictures? Any thoughts appreciated. Trying a different way I found some Mathematica code from a multivariable course for normals to a plane… and I got the same thing…

## linear algebra – Why the diagonal elements of the Smith normal form of a boundary matrix are the torsion coefficients of a homology module?

Can you help me in proving/justifying the isomorphism going between $$H_p$$ and $$left(bigoplus_{i=1}^{l_{p}} R / b_{p i} Rright)$$.

Where $$H_p$$ is the p-th homolgy module, R is a commutative PID, and $$b_{pi}$$‘s are the diagonal elements in the Smith normal form of the boundary matrix.

Please support in this. Any hints would be highly appreciated!!

P.S. From the generalized version of the structure Theorem, $$H_p$$ is uniquely decomposed into:
$$H_{p} simeq R^{beta_p} oplusleft(bigoplus_{i=1}^{l_{p}} R / b_{p i} Rright)$$, $$beta_p$$ is the p-th Betti number (the rank) of $$H_p$$.

## cpu – Is 2240 RPM normal fan speed?

I have a stock CPU fan and I was wondering if my fan’s RPM of around 2240 is considered normal or average. I should also bring up that my CPU temps right now is resting at around 25 degrees Celsius.

EDIT: I’m talking about the computer fan speed, not the CPU temp itself.

This is the image in question

## Context free grammar transformation to Normal Form

I found a task where you need to transform context free grammar to normal form.
I’m a High Shcool student at this moment. But my Brother learning this at the university. He don’t have much time to explan this, this is why I’m writting this question.

This is the task description: A chainless G grammar equivalent to G’ grammar, all symbols of which can be used.

``````G : S → BC | DB
A → BD
B → b | D
C → CD | BC
D → bC | a | bB
``````

If anybody can help me, please write a comment.
Thanks :]

## 3d – How to project a vector onto a plane, but not along plane normal?

Given a plane with normal vector $$vec n$$ and any arbitrary point $$vec p$$ on that plane, then for any other point $$vec p^prime$$ in that plane the following equation holds:

$$vec n cdot vec p ^ prime = vec n cdot vec p$$

Now let’s take your off-plane point $$vec q = (q_x, q_y, q_z)$$. We’re going to slide it along the y axis to a new point $$vec q ^prime = (q_x, y, q_z)$$ so that it lies in that plane. That means…

begin{align}vec n cdot vec q^prime &= vec n cdot vec p\ n_x q_x + n_y y + n_z q_z &= vec n cdot vec p\ n_y y &= vec n cdot vec p – n_x q_x – n_z q_z\ y &= frac {vec n cdot vec p – n_x q_x – n_z q_z} {n_y} end{align}

So, substitute your normal, point on plane, and x/z coordinates of your off-plane point $$vec q$$, and you’ll get the new y coordinate that will project it vertically onto this plane.

## pathfinder 1e – Do thistle arrows deal their bleed damage in addition to the normal effects of a bow shot, or instead of it?

Thistle arrows “deal damage as a bleed effect for 1d6 rounds after a hit”. Does it cancel their normal damage, or does it essentially double the total damage dealt on the round when the arrow is shot?

Is using such arrows at least once on every potentially vulnerable enemy optimal?