Complexity Theory – Master Theorem: When a $ f (n) $ is smaller or greater than $ n ^ {log_b a} $ less than a polynomial factor

I was reviewing the main theorem of https://brilliant.org/wiki/master-theorem/ and I was trying to solve a question.

Which of the following factors increases more rapidly asymptotically?

(a) $ T (n) = 4T (n / 2) + 10n $

(B) $ T (n) = 8T (n / 3) + 24n ^ 2 $

(C) $ T (n) = 16T (n / 4) + 10n ^ 2 $

(re) $ T (n) = 25T (n / 5) + 20 (nlogn) ^ {1.99} $

e) They are all asymptotically identical

My calculation says, (a) is $ theta (n ^ 2) $ (b) is $ theta (n ^ 2) $ (it is $ theta (n ^ 2logn) $. Now, how can I evaluate (d)?

Yes $ f (n) $ is smaller or bigger than $ n ^ {log_b a} $by less than a polynomial factor, how can I solve T (n)?

Is it a problem if , and are smaller than the normal text?

On many websites and website templates, the font size of

(sometimes) and

and

are often smaller than the normal text, that is to say, that of

without additional classes.

The word "Necromancer" is actually a level 5 title, and I took extra thoughts before I realized it.

When designing my own website (templates), I keep all topics (1-6) larger than normal text, with

being only 1.05x as big as

, with additional layout parameters like extra padding.

Would it be necessary to keep all the titles no smaller than the normal text? I'm mainly interested in text blocks and do not use headers as image captions or anything non-textual.

performance – Bullet Physics StepSimulation is really slow when TriangleMeshShape is smaller in BoxShape

I've observed that StepSimulation of bullet physics is very very slow when a rigid body with a TriangleMeshShape is entirely inside a rigid body with a simple BoxShape. I noticed that when I move the trianglemeshshape object a little outside the box in shape, my simulation started to run as fast as usual. How can I improve the performance of this scenario? At some point in my simulation, I have to test that all triangular shapes are entirely contained in a bounding box. Until now, I have to do the test on demand and I can not keep the form all the time in the simulation.

I've tried using ghostobjects but this has not helped improve performance. I guess the problem lies in the initial operation of bullet physics and how DynamicsWorld performs crash tests.

Does anyone have an idea of ​​how to improve the performance of many small triangles in a big box? all my forms are cinematic.

How to divide a FLAC file into a lot of smaller ones?

This is not music and there is no cue file. The size of the FLAC file can be several GB. I want to break down this large FLAC file into several smaller files depending on a file size setting using a Linux terminal command. . Thank you for your help!

email – The Gmail app on IOS does not accept font sizes smaller than 12px for Emailer

How can I add something specifically to fix my iOS problem in the gmail app?

my is below





    
    
    
    
    
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dump – SVN repo 3 times smaller after unloading / loading

I have a repo on an old SVN server running on RHL9. The version of svn is 1.1.4. The repo is 1.1 GB wide (from -sh $ REPO), its total size is 1.7 GB.
I load the dump on a recent svn server under ubuntu 16.04, svn version 1.9.3.
I run the following command:

svnadmin load --bypass-prop-validation -q "/path/to/repo.svn" <"/ path / to / repo.dump"

Now the repo is only 412MB (du -sh).

I only administer the server, I do not use svn myself. When I look at the repo logs on Tortoise, it looks like all the revisions and documents are here (impossible to check all manually, 3733 revs).

But I do not know how to check if this size difference has resulted in data loss.

How can I know ? (tortoise or server cli, I'm root) Does this difference in size shock you?

Lens design – What allows the Canon RF 70-200 f / 2.8 to be much smaller than the EF version?

It is possible to create an image with the help of a single element single objective. Sorry to report, the resulting images will be second-rate. This is because all goals suffer from aberrations that are degrading. Opticians reduce aberrations by combining many lens elements. Some are positive (convex) and some other negative (concave) with regard to power. In addition, some are cemented together; others are spaced. All this is needed to mitigate the aberrations. Nevertheless, the residual aberrations still remain.

If the camera were to be equipped with a single element lens and focused on a distant view, we could take a measurement from the center of the lens to the plane of the image. This value is the focal length. In a complex lens array, it is more difficult to find the point of taking this step. The point we must find is called the back nodal.

Opticians can and do move the position of the back nodal. Now, a long lens is a lens that has a long focal length. The longer the focal length, the higher the magnification. A long lens is very desirable if you are in sport or wildlife or the like. However, you might find a long lens a bit awkward.

Opticians have a stunt in their sleeve that physically shortens the lens barrel. This is accomplished by moving the back nodal forward. If the optician wishes, a complex set of lens elements can be constructed so that the back nodal falls in the air, in front of the front element.

Remember that the focal length is a measurement taken from the back nodal to the image plane. The advantage of such a design is a shorter and less delicate barrel length. Let me add that a real telephoto model differs from the long lens in that the telephoto is shortened as to the length of the barrel.

In addition, be aware that short wide-angle lenses often place the rear lens group too close to the plane of the image. If true, there is no room for the mirror mechanism of the SLR. The optician, desiring more space for the rear focus distance, will move the back knot backwards.

design – Is splitting a potentially monolithic application into smaller ones to avoid bugs?

Yes. Generally, two smaller and less complex applications are much easier to manage than a single large one.

However. You get a new type of bug when applications work together to achieve a goal. In order to make them work together, they have to exchange messages and this orchestration can go wrong in different ways, even if each application works perfectly. Having a million tiny apps has its own particular problems.

A monolithic application is really the default option with which you end up when you add more and more features to a single application. This is the easiest approach when you consider each feature separately. It's only once he's grown up that you can look at it and say "you know what, it would work better if we separated X and Y"

Is it possible to have a Hausdorff dimension smaller than the topological dimension?

"Normal" geometric shapes have Hausdorff dimensions equal to their topological dimensions. Mandelbrot defined fractures as shapes with a Hausdorff dimension greater than their topological dimension. Is there a class of shapes with a Hausdorff dimension smaller than the topological dimension or is it impossible? If there is such a form, what are the most common examples, if not, why are they impossible.

Dribbble Shot seems to be smaller

My strokes seem to look smaller despite the perfect size. Is there a reason for this?