General topology – Does the total space of a set correspond to the Tietze extension property when fiber and basic space satisfy this property?

We say that a topological space $ Y $ satisfies the extension property of Tietze, property TE, if in the formulation of the theorem of extension of Tietze $ Y $ can be replaced by "$ mathbb {R} $".

It is obvious that the product of two TE spaces is again a TE space. But what about a twist product? Suppose more precisely that the fiber and base space of a fiber bundle satisfy the TE property. Is the total space necessarily a TE space?

Find general differential equation solution

The task is to find $ u_ {xy} + yu_x + xu_y + xyu = 0 $ this equation of general solutions.

First of all I wrote it as $ frac {d} {dx} (u_y + yu) + x (u_y + yu) = 0 $

Then marked $ u_y + yu = t $ and got the equation $ t_x + xt = 0 $

And found the solution: $ t = e ^ {- frac {x ^ 2} {2}} c (y) $

And I do not understand how to solve this differential equation $ u_y + yu = e ^ {- frac {x ^ 2} {2}} c (y) $

ordinary differential equations – Resolution of an ODE to find the general solution in the form of an infinite series for $ u (r, t) $

I'm trying to solve the following problem.

I have both ODE
begin {align}
T + alpha lambda T & = 0 \
frac {d} {dr} left (r frac {dR} {dr} right) + lambda rR & = 0,
end {align}

with boundary conditions $ R (b) = 0, R & # 39; (0) = 0 $ and $ T (0) = f (r) $. I'm trying to solve the ODE for $ T $ and therefore write the general solution of $ u (r, t) = R (r) T (t) $ as an infinite series.

Transform the ODE for $ R $ in a Bessel order equation $ 0 when $ lambda = k ^ 2> 0 $ and $ p = kr $ give the solution
$$ R_n (p) = A_nJ_0 (p) + B_nY_0 (p) implies R_n (r) = A_nJ_0 (kr) + B_nY_0 (kr). $$ Solve the ODE for $ T $ given $$ T (t) = This ^ {- alpha lambda t}, $$ as the characteristic equation is $ beta + alpha lambda = 0 implies beta = – alpha lambda $. Does this mean that the general solution for $ u $ is,

begin {align}
u (r, t) & = sum_ {n = 1} ^ { infty} R_n (r) T_n (t) \
u (r, t) & = sum_ {n = 1} ^ { infty} e ^ {- alpha lambda t} left (A_nJ_0 (kr) + B_nY_0 (kr) right)?
end {align}

I do not know how to define $ lambda $.

Content Marketing 55 Roundup Experts – Tips and Tricks for 2019 and Beyond – SEO Help (General Discussion)

You struggle with creating and promoting content marketing? We asked 55 experts to share their best tips and tricks that will work in 2018 and beyond.

Let's face it, the Internet is full of content of all kinds on every topic imaginable. It has become a real challenge for online marketers to attract readers, capture their attention and generate leads.

<img alt = "55_content_marketing_expert_roundup-770x" class = "ipsImage" height = "411" src = "×"

It's clear that creating good content and just marketing it, as you did last year, is not even enough. You need to be a lot more creative with your marketing strategy to get the desired results from your campaign.

I'm sure you're wondering now what exactly you should do to improve your strategy. How to effectively promote content to increase the number of conversions and make it exceptional?

Well, we asked for the opinion of 55 content marketing experts and, if I were you, I would certainly read their thoughts on this hot topic. If you do not have time to read all the contributions, go to the bottom of the article and download the conclusions in a nice PDF booklet.

General formula for sequences

Find the general formula of a sub n for the following: {11, 15, 11, 15 …}
I'm confused about how to do it because it's only about repeating integers.

What are the best ways to get real backlinks on your site? – SEO help (general discussion)

1. Allow others to credit their work for you

2. Develop sharable content

3. Link back from your own website

4. Write more guest messages

5. Online Network

6. Be creative

7. Collaborate on creative projects

8. Stay true to your niche

SEO Services in Warrington – Warrington Web Design – SEO Help (General Discussion)

Welcome to Warrington Web Design, the website design partner for your business. We are a web design company that understands the needs of your business like no other. And these are also the local experts for everything related to the Web, including e-commerce, website design, SEO, online marketing, and more. Get your website at the top of Google search results with our team of SEO Marketing Warrington experts!

data structures – Explain how to resolve hash conflicts in HAMT or hashtables in general

A hash table is a bucket array, where the bucket index is the hash values ​​of the keys (modulo the length of the array).

When collisions occur (two different keys mapped in the same bucket), you need a strategy to fix them. Here are two popular strategies.

  • Using a list: You design a bucket data structure that supports multiple key / value pairs, for example. a linked list of pairs. In case of collision (the list is not empty), you simply add a second / third / … pair to the list.
  • Using the next free bucket: Your bucket supports a single key / value pair. If the "correct" bucket (depending on the hash value) is already busy, you are looking for the next free linear and place the key / value pair at this location.

With both strategies, performance degrades in linear search when the number of collisions is large. The second strategy is deteriorating faster.

If you are in a tight memory situation, you may prefer the second because it does not generate an overload of a list per bucket.

With the second approach, it can be difficult to implement properly, especially the action of deletion.

architecture – General question on REST principles

To understand REST, you must understand that there are at least two totally opposite interpretations. The first is the original, from the author who invented it. The arguments of this interpretation are used all the time to justify implementations that do not really follow it. Then there is the familiar interpretation of "CRUD via JSON / HTTP".

Because writers rarely say what interpretation they speak, things get really confusing.

To understand the original REST, just think of the Web and people as customers. On the web, we are presented with options and we choose options. I have my own logic (the client logic) that I want to achieve, but every resource I talk to can have its own logic. For example, I want to book a flight, I can start with google, then go to a flight aggregator site, enter data (which I do not normally have to enter again!), Choose a provider, go there, enter other information. payment data maybe, and so on. I know what I want and interact with things from their own field to do my job. I must of course know them all and understand what they say (Google results page, flight assistant, etc.).

In the familiar interpretation, none of these things are of importance. You just have a few CRUD endpoints and you often hear about URI, sub-resources, POST versus PUT, and so on. Rarely, if ever, media types, links, or forms are mentioned, although REST (original) does not exist without Hypermedia.

So now, to ask you questions (and I guess you want the "original" REST, because the spoken language does not really have any specific rules):

  1. Where is the business logic: the client and the server each have their own logic. But, the server logic is not shared with the client. Think of the customer as a person. Do you want someone to enter URLs and data with each new request? Of course not, you use forms, links, hidden fields no matter what it takes.

  2. How is it possible to add abstractions? How does Google Search work? How do assistant dialogues work on the web? How can you book a hotel on the internet? All of these applications are REST applications, with a human being as a client. This is not a hyperbole, REST applications with programmatic clients work in exactly the same way.

  3. How to avoid transferring the entire database? Again, look at all the millions of web applications. This is not difficult.

  4. How is the server stateless? Statelessness! = No data. The state refers to the current interaction, not the data. For example, if I use a wizard type dialog to book a hotel, the progress I make is not tracked (in REST mode) on the server. I return each time my state (via hidden fields, which I do not really need to know). If I can for example save a preliminary version of my reservation, the server can very well save this version.

Here is an article with more information: 5 signs that your REST API is not RESTful

Best lens for landscapes / general zoom with Nikon D7200?

The whole point of a interchangeable lens system The camera allows you to use different lenses that are better or excellent, but are not suitable for other things. Fixed-lens cameras require you to use a single lens that is mediocre or worse for many things, but better for nothing. Insist on the use of a single lens with an interchangeable lens camera is not fundamentally different from using a camera with a zoom lens permanently attached .

The best goals are all first lenses. It means a single focal length. No.Zoom.At.All. They are really good when they provide the field of vision and other features you need. This is because they can be optimized to do one thing at a focal distance. A good flat field 100mm macro lens is different from a good 85mm, 105mm or 135mm portrait lens. But these specialized goals are not always very flexible, so you need them for different things. Some are good enough for little money (eg, EF 50mm f / 1.8 STM @ $ 120). Others are incredibly good for a boat full of money (eg, EF 400mm f / 2.8 L IS II @ $ 10,000). Most are somewhere in between.

Short ratio zooms, ie zooms with a difference of less than 3X between their longest and shortest focal lengths, can also be very good. But the best ones are expensive. A lens like the Canon EF 24-70mm f / 2.8 L II runs around $ 2K and can match the image quality, if not the maximum aperture, of a STM at $ 120 EF 50mm f / 1.8. It is also built a little better and can shoot at 24mm (with an IQ almost identical to a 24mm premium) and at 70mm and anywhere between the two.

When you move outside the 3x limit, the quality of the image begins to drop noticeably. Some 4-5X zooms that fall entirely within the telephoto range can be very good. But when you're trying to design a lens from wide-angle to telephoto and covering a zoom range of 5X-10X or more, you're starting to have a hard time keeping it affordable and affordable in terms of size and weight. by offering excellent image quality. You will usually get better picture quality and spend less on a 18-55mm or 55-250mm lens than if you were using an 18-200mm "all-in-one".

Do you get better picture quality with the AF-S 24-120mm f / 4G ED VR than with the AF-S DX 18-140mm f / 3.5-5.6G ED VR? You are probably going. This will probably not make the difference that you seem to hope or want, however. The difference will not be as great as what you would see using different lenses specifically designed for specific photographic tasks.