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1. 300+ keywords
2. Trends (Rising / Stable / Drop)
3. Avg. Monthly search volume (global)
4. Avg. Monthly search volume (local)
5. Pay per click (PPC)
6. Cost per click (CPC)
7. allintitle
8. Exact KW in the title
9. allinurl
10. Root domain / home page
11. Difficulty of classification (out of 100)
12. web 2./wiki/q.a/news portal / Social Domain / Sub-Domain / .gov / .edu
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User Research – What are some advanced techniques of UX Competitor Analysis?

What are some advanced techniques of UX Competitor Analysis and what is the number of competitors that must be analyzed to obtain relevant results and obtain enough data to create a solid product? Also, how complex should it be? My main concern is to have an endless list of data that is difficult to interpret.

According to the report of the "User Experience Careers" survey by Nielsen Norman Group, 61% of UX professionals prefer to make a competitive analysis of their projects and the benefits of performing this type of analysis are obvious, but there are few resources of how complex this research should be and how to find information that really matters.

In addition to unique features, how do you identify user loyalty and commitment in our competitors' applications and discover if their approach really works?

How to take advantage of this method when your product should be first in the market and not only in a small niche and also if the type of business is in a relatively new activity domain?

Functional analysis. – Reference for compact embedding between the Holder space (weighted) in $ mathbb {R} ^ n $

Suppose $ 0 < alpha < beta <1 $Y $ Omega $ is a limited subset of $ mathbb {R} ^ n $. Then the space of the holder $ C ^ { beta} ( Omega) $ is in a compact way inside $ C ^ { alpha} ( Omega) $. But yes $ Omega = mathbb {R} ^ n $, then the compact incrustation is not true.

However, if we consider the weaker weighted holder space $ C ^ { alpha, – delta} ( mathbb {R} ^ n) $ (For any $ delta> 0 $) instead of $ C ^ { alpha} ( mathbb {R} ^ n) $. Then it is $ C ^ { beta} ( mathbb {R} ^ n) $ integrated compactly to $ C ^ { alpha, – delta} ( mathbb {R} ^ n) $?

here
$$
| f | _ {C ^ { alpha, – delta}} = | (1+ | cdot | ^ 2) ^ {- frac { delta} {2}} f | _ {C ^ { alpha}}.
$$

I could not find an accurate reference of some books on functional analysis. Any comment is welcomed.

Functional analysis. Valdivia-Vogt isomorphism extension of $ mathscr {D} (K) $ a $ mathscr {E} & # 39; (K) $

Leave $ M $ be a $ d $smooth three-dimensional manifold (for example, Hausdorff, paracompact, connected and oriented), and $ K subset M $ compact with $ mathring {K} neq varnothing $. M. Valdivia has shown (based on previous results by himself and D. Vogt, see, for example, M. Valdivia, A representation of space. $ mathscr {D} (K) $, J. reine angew. Math. 320 (1980) 97-98) that Fréchet's nuclear space $ mathscr {D} (K) $ of smooth functions supported in $ K $ It is topologically isomorphic to space. $ s $ of rapidly decreasing sequences: $$ s = {(a_n) _ {n in mathbb {N}} | ((1 + n) ^ k a_n) _ {n in mathbb {N}} text {is delimited for all} k in mathbb {N} } . $$ Leave $ Phi: mathscr {D} (K) cong s $ Denotes the isomorphism of Valdivia-Vogt. It is clear that the transposition $ {} ^ t Phi $ of $ Phi $ A topological isomorphism occurs between the dual. $ s & # 39; $ of $ s $ $$ s & # 39; = {(a_n) _ {n in mathbb {N}} | ((1 + n) ^ {- k} a_n) n in mathbb {N}} text {is limited by some} k in mathbb {N} } $$ and the dual $ mathscr {D} (K) & # 39; $ of $ mathscr {D} (K) $, which can be identified as a vector space with $ mathscr {D} & # 39; ( wedge ^ d T ^ * M rightarrow M) / mathscr {D} (K) ^ perp $, where $$ mathscr {D} (K) ^ perp = {u in mathscr {D} & # 39; ( wedge ^ d T ^ * M rightarrow M) | u ( varphi) = 0 text {for all} varphi in mathscr {D} (K) } $$ It is the annihilator of $ mathscr {D} (K) $. It is clear that $ mathscr {D} (K) & # 39; $ contains $$ mathscr {E} & # 39; (K) = {u in mathscr {E} & # 39; ( wedge ^ d T ^ * M rightarrow M) | text {supp} u subset K } $$ as a subspace (closed) (I apologize for the unconventional notation). From the sequences $ e_j = (e_ {j, n}) _ {n in mathbb {N}} $ given by $$ e_ {j, n} = begin {cases} 0 & (n neq j) \ 1 & (n = j) end {cases} $$ form a Schauder base of both $ s $ Y $ s & # 39; $, it is clear that $ s $ It is dense in $ s & # 39; $.

Question: Make $ Phi $ extend to a topological isomorphism between $ mathscr {E} & # 39; (K) $ Y $ s & # 39; $? Also, the restriction of $ {} ^ t Phi $ to $ s $ yield another topological isomorphism between $ s $ Y $ mathscr {D} (K) $?

My question is inspired by the known characterization of $ mathscr {D} ([0,1]$ Y $ mathscr {E} & # 39; ([0,1]$ through the decay / growth of their Fourier coefficients in $[0,1]$.

Fourier analysis: test the inverse transform of the unilateral Laplace transform.

I am reading this article and I have a question.

Consider a function $ f $ and its Laplace transform

$ hspace {3.0cm} F (s) = int_0 ^ infty f (t) e ^ {- st} dt $, with $ {s | text {Re} (s) = 0 } in text {ROC}[F(s)]$

The inverse transform would be $ f (t) = lim _ { omega to infty} int _ { sigma – i omega} ^ { sigma + i omega} F (s) e ^ {st} ds $.

Now, consider the case where $ text {Re} (s) = 0 $, We can see that

$ hspace {3.0cm} f (t) = lim _ { omega to infty} int_ {i omega} ^ {- i omega} F (s) e ^ {st} ds = int_ {- infty} ^ infty F (i omega) e ^ {i omega t} d omega $

It is an inverse Fourier transform.

According to the Fourier transform, we know that

$ hspace {3.0cm} F (i omega) = cal {F} {f (t) } = int _ {- infty} ^ infty f (t) e ^ {- i omega t} dt $

But the Laplace transform of $ f $, when $ text {Re} (s) = 0 $, suggests that

$ hspace {3.0cm} F (i omega) = int_0 ^ infty f (t) e ^ {- i omega t} dt $

It turns out that $ int _ {- infty} ^ infty f (t) e ^ {- i omega t} dt = int_0 ^ infty f (t) e ^ {- i omega t} dt $ ? This seems wrong to me? Am I wrong somewhere?

Functional analysis. Chern projection number. Can you explain the magic?

Attached a calculation where the Chern number of Landau's first level is calculated (the result claimed is $ -1 $) and the complete document can be found here
Click on me I have difficulties to understand
what happened here.

The projection is given by the integral nucleus.

$$ Pi (x, y) = frac {qB} {h} e ^ {- (qB / 4 hbar) (xy) ^ 2-i (qB / 2 hbar) x wedge y}. $ PS

The authors calculate a "derivative" of this expression and obtain an integral expression for Chern's character and affirm that it is equal to $ -1 $. It does not seem to be a very sophisticated calculation, but it is very difficult to understand, so I would like to ask here because it is very likely that I am missing something.

Fafunctional analysis: Kaehler compact submanifolds of the projectized Hilbert space

If we take a separable complex Hilbert space. $ H $, its projective space $ PH $ it is a variety of Kähler of infinite dimension in a quite obvious sense (see below). Suppose $ M subset PH $ is a submenu of Kähler compact finite-dimensional of $ PH $. There must be a linear subspace of finite dimension. $ V subset H $ such that $ M subset PV $?

(I do not know a good reference for Kähler varieties of infinite dimension, but the relevant concept here seems clear. $ PH $ is a soft variety of Hilbert that can be covered with graphics modeled in a complex Hilbert space, with transition functions that are holomorphic (given in a neighborhood of each point by a series of absolutely convergent powers). This makes each space tangent of $ PH $ in a complex vector space, and this complex vector space structure extends to a complex Hilbert spatial structure, which varies smoothly, in fact, analytically, from one point to another. The imaginary part of the inner product gives. $ PH $ A symplectic structure, and the real part gives. $ PH $ a Riemannian structure, both not strongly generated: that is, each one gives an isomorphism $ T_p PH to T ^ * _ p PH $ of the underlying real Hilbert spaces.)

What is cisco meraki doing as a reference in his analysis?

As for the references on my website, I noticed that the second highest source is n213.network-auth.com, which comes from the Cisco Meraki cloud management platform. I am surprised at why it is there and what exactly it means.

As I understand it, this site contains a link to mine and comes from path / splash /. Also, the behavior is strange: bounce 95% and 96% is pointing to my landing page. 100% would suggest that there is software behind the visits, a non-perfect score that IMHO suggests to humans.

Is this a ghostspam gone wrong attempt? A byproduct of a survey?

Complex analysis: Where does this "factorization" of a meromorphic function come from?

I find a comment when reading a book that says:

Yes $ f (x) in mathbb R[x]$ it's a monic polynomial, that is, $ f (x) = x ^ n + a_ {n-1} x ^ {n-1} + dots + a_0 $, so
begin {align *}
frac {f & # 39; (x)} {f (x)} = frac {n} {x} left (1- g (x) right),
end {align *}

where $ g (x) = frac {x ^ {n-2} + b_ {n-3} x ^ {n-3} + dots + b_0} {x ^ {n-1} + c_ {n-2} } x ^ {n-2} + dots + c_0} $ for some real coefficients $ b_i, c_j $& # 39; s

Expanding the right side and multiplying the numerator-denominator on both sides, then equaling the coefficients of each term, it seems to me that this is possible. But I wonder if there is a generalized theorem about the meromorphic function that can tell me this directly.

Technical analysis in all the main pairs | December 31, 2018 – Other opportunities to earn money

The Forex market is open 24 hours a day, but is not always active throughout the day. You can earn money when the market goes up and down. But you will have a hard time making money when the market does not move at all.

Hours of the Forex market

The forex market can be divided into four main trading sessions: the Sydney session, the Tokyo session, the London session, the New York session. ForexTrading Premium ForexTrading Course ForYou is always there to help you if you are interested.

The actual opening and closing times are based on local business hours, and most business hours start somewhere between 7 and 9 a.m. local time. The opening and closing times will also vary during the months of October / November and March / April, as some countries (such as the United States, England and Australia) change to / from daylight saving time (DST).

The day of the month in which a country changes to / from summer time also varies, which confuses us even more. And Japan does not observe summer time, so thank you Japan for keeping it simple.

Now, you're probably watching the Sydney Open and wondering why it changes two hours in the Eastern time zone.

You would think that the Sydney Open would only move one hour when the USA. UU It fits the standard schedule, but remember that when the US. UU Go back one hour, Sydney actually advances one hour (the seasons are opposite in Australia).

You should always remember this if you ever plan to trade during that period of time. Also keep in mind that between each trading session of currencies, there is a period of time in which two sessions are open at the same time. During the summer, from 3: 00-4: 00 AM ET, for example, the Tokyo session and the London session overlap, and during the summer and winter from 8:00 a.m. at 12:00 p.m. ET, the session of London and the New session of York overlaps.

Naturally, these are the busiest times during the trading day because there is more volume when two markets are open at the same time.

This makes sense because, at those times, all participants in the market are wheeled and dealt, which means that more money is transferring hands.

Now let's look at the average movement of the major currency pairs during each forex trading session.


From the table, you will see that the London session normally provides the most amount of movement.

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