Some confusion about cpanel and directadmin panel

Hello friends,

I have some confusion about the following position in my reseller account.

1. Can I have both Cpanel and Directadmin Panels? I want to ask if I have 10 Cpanels accounts and if I need to add more websites. Can I then set up DirectAdmin panels?

2. According to the reseller seller plans, Maria DB and MySQL DB are the same. Some of my websites are currently running on MySQL DB and I will switch to another reseller with Maria DB. A new reseller transfers my account free of charge. But my question is whether all freeware web applications like Osticket, WordPress and e-commerce apps support Maria DB. Does Softaculous AutoInstaller support Maria DB and is there no error during installation? Can I just switch from Maria DB to MySQL DB again?

I have confusion about these points. Help kindly.

Probability Theory – Contingency Table Confusion NLP

Hello for the contingency table: [really positive, false negative, wrong positive, really negative]. It is difficult for me to remember the difference between these terms, because all concepts consist of words that are very similar to each other but used in such contrasting contexts. The only ones that make sense are true positives and false negatives, but the others that I am always confusing and wondering is there a brief mnemonics that I can use?

Lens confusion in defining f-number: f / D or 1 / (2NA)

I have seen two different definitions for the f-number of a universal lens. Are they consistent?

I assume that the subjects are far away (no macro, the magnification is low), and we have a lens that is corrected for coma and spherical aberration.

I mean f-number in the sense that it indicates the brightness of a lens that has no internal losses.

The 1 / (2 * Numerical_Aperture) definition results in f / 0.5 as the limit; The F / D definition is not.

I searched: 20half% 20the% 20opening% 20angle & hl = it & pg = PA25 # v = onepage & q = The% 20F number% 20of% 20a% 20lens & f = false

Supplement – Clarification attempt:

My background:
I have a mathematics degree with an applied / physical focus, so I understand Trig Identities & Approximations, though my work does not take up so much of my math training.

I have not studied optics since graduation.

As a photographer, I understand the everyday use of F-numbers when photographing non-macro subjects and that T-numbers are sometimes more relevant. I am aware of the changes in the effective f-number in macro cases, but I do not actually make macros.

Confusion and question:

The question relates to photographic lenses that are at least somewhat corrected for coma and spherical aberration, are focused almost infinitely, with negligible magnification and negligible internal losses in a medium having a refractive index near 1 at points on the sensor near the axis of the lens.

The most common formula for the f-number is: N = f / D

Numerical aperture ("NA") numerical aperture formulas in combination with numerical aperture formulas sometimes appear to yield results for f-number ("N") that differ from N = f / D when f / D is small (say f-number <2).

How should these contradictory results be reconciled?

The NA approach makes it clear that there is a lower limit to the f-number at 0.5 because the cone angle of the light that hits the center of the sensor can not exceed 180 degrees. This lower limit is not immediately apparent from the N = f / D formula.

My confusion is for small f-numbers above this f-number of 0.5.

As I said, I do not know much optics. I wonder if the inconsistencies are related to the assumed shape of the "second major plane" of the lens.

If the half-cone angle is θ & # 39 ;, I seem to get different values ​​for θ & # 39 ;, depending on the assumed shape of the second principal plane:

  • If the second principal plane is assumed to be flat, I get tan θ = = D / 2f
  • If the second principal plane is assumed to be spherical with the radius f, I obtain sin θ = = D / 2f

Perhaps, as indicated in the comments, none of the forms is a very An accurate representation of a real lens and an accurate response can only be predicted by ray tracing.

In any case, sin θ = = D / 2f is a better approximation than tan θ #. = D / 2f for a universal lens?

(For slow lenses, θ ~ = sin θ = = tan θ ~ = D / 2f, where & im is in radians.)

I do not really understand this, but I read that a (near) spherical second major plane is desirable to correct for spherical aberrations.

If NAi = n sin θ und and f-number = 1 / (2 * NAi):

  • If sin θ = = D / 2f, we get f-number = (1 / n) (f / D), even for fast lenses
  • If tan θ = = D / 2f, we obtain f-number = (1 / n) (f / D) sqrt (1+ (D / 2f) ^ 2)

general topology – confusion about boundary and accumulation points of a sequence

I'm reading the textbook "Theory of Statistics" by James E. Gentle. I start with Chapter 0, which contains a series of predicted mathematics. I've come to the Topology section of the chapter and have some confusion about the definitions the author sets for limits and accumulation points. I will copy the definitions word by word:

boundary point: A sequence $ {x_n } $ should converge to the point $ x $, or to have a limit $ x $if an open sentence is given T contains $ x $there is an integer N so that $ x_n in T forall n geq N $

Accumulation point or cluster point: one point $ x $ is called the accumulation point or cluster point of the sequence $ {x_n } $ if an open sentence is given T contains $ x $ and any integer Nthere is an integer $ n geq N ni x_n in T $

I was wondering if anyone could give some examples of sequences and their respective bounding and accumulation points. Thanks.

Confusion about P against NP

I am sure that my reasoning in the following question is extremely simple and erroneous, but I think that if anyone answers, I can better understand what the P vs. NP puzzle is. So here's my question: Why is the following not proof that NP is not equal to P?

Scenario: A computer is assigned an n-digit number that it must guess. The numbers of this number were selected at random. Since the digits are randomly selected, there is no pattern a computer could detect, and this simplifies the problem. All solutions must be tried, of which there are 9 ^ n.

Does the problem with my argument lie in the assumption that the numbers are really random? Randomness is impossible and there will always be an underlying pattern for how seemingly "random" numbers have been selected

magento2 – shipping price and grand total excluding VAT. confusion

Our calculation for shipping, taxes and total (excluding taxes) is incorrect. We have set the shipping and handling fees to include the taxes in the settings. Shipping will still be added to the total amount (excluding taxes).

See the example below (here VAT is 24%).

Subtotal                €141.05
Shipping & Handling     €7.90
Grand Total (Excl.Tax)  €148.95     (141.05+7.90 = 148.95)
Total Tax               €33.85      (141.05*0.24 = 33.85)
Grand Total (Incl.Tax)  €182.80

As you can see, shipping is added to the total without taxes, but the total tax is only calculated from the subtotal. We want the total (without tax) + total + shipping = total (tax included) to be clearly displayed. How should we handle this?

Magento 2.3.2