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Having regard to the Treaty on the Functioning of the European Union,

Having regard to Regulation (EC) No 1107/2009 of the European Parliament and of the Council of 21October 2009 concerning the placing of plant protection products on the market and repealing Council Directives 79/117/EEC and 91/414/EEC ( 1 ) , and in particular the second alternative of Article 21(3) and Article 78(2) thereof,

Whereas:

HAS ADOPTED THIS REGULATION:

Article 1

Amendment to Implementing Regulation (EU) No 540/2011

The Annex to Implementing Regulation (EU) No 540/2011 is amended in accordance with the Annex to this Regulation.

Article 2

Transitional measures

Member States shall in accordance with Regulation (EC) No 1107/2009, where necessary amend or withdraw existing authorisations for plant protection products containing bifenthrin as active substance by 19June 2018 at the latest.

Article 3

Grace period

Any grace period granted by Member States in accordance with Article 46 of Regulation (EC) No1107/2009 shall be as short as possible and shall expire by 19June 2019 at the latest.

Article 4

Entry into force

This Regulation shall enter into force on the twentieth day following that of its publication in the Official Journal of the European Union .

This Regulation shall be binding in its entirety and directly applicable in all Member States.

Done at Brussels, 26February 2018.

For the Commission

The President

Jean-Claude JUNCKER

( 1 ) OJL309, 24.11.2009, p.1 .

( 2 ) Commission Implementing Regulation (EU) No 582/2012 of 2July 2012 approving the active substance bifenthrin, in accordance with Regulation (EC) No 1107/2009 of the European Parliament and of the Council concerning the placing of plant protection products on the market, and amending the Annex to Commission Implementing Regulation (EU) No 540/2011 ( OJL173, 3.7.2012, p.3 ).

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EFSA (European Food Safety Authority), Technical report on the outcome of the consultation with Member States, the applicant and EFSA on the pesticide risk assessment of confirmatory data for bifenthrin. EFSA supporting publication 2015:EN-780. 23 pp.

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EFSA (European Food Safety Authority), Technical report on the outcome of the consultation with Member States, the applicant and EFSA on the pesticide risk assessment of confirmatory data for bifenthrin. EFSA supporting publication 2016:EN-1019. 39 pp.

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Commission Implementing Regulation (EU) No 540/2011 of 25May 2011 implementing Regulation (EC) No 1107/2009 of the European Parliament and of the Council as regards the list of approved active substances ( Ann Demeulemeester hi top sneakers Black Clearance With Mastercard Buy Cheap Best Wholesale Explore Best Place Online Outlet 2018 Unisex 0wAnRNN
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Surprising Patterns in the Square Numbers (1, 4, 9, 16…)

A quick puzzle for you — look at the first few square numbers:

And now find the difference between consecutive squares:

Huh? The odd numbers are sandwiched between the squares?

Strange, but true. Take some time to figure out why — even better, find a reason that would work on a nine-year-old. Go on, I’ll be here.

We can explain this pattern in a few ways. But the goal is to find a convincing explanation, where we slap our forehands with “ah, that’s why!”. Let’s jump into three explanations, starting with the most intuitive, and see how they help explain the others.

convincing

It’s easy to forget that square numbers are, well… square! Try drawing them with pebbles

Notice anything? How do we get from one square number to the next? Well, we pull out each side (right and bottom) and fill in the corner:

While at 4 (2×2), we can jump to 9 (3×3) with an extension: we add 2 (right) + 2 (bottom) + 1 (corner) = 5. And yep, 2×2 + 5 = 3×3. And when we’re at 3, we get to the next square by pulling out the sides and filling in the corner: Indeed, 3×3 + 3 + 3 + 1 = 16.

Each time, the change is 2 more than before, since we have another side in each direction (right and bottom).

Another neat property: the jump to the next square is always odd since we change by “2n + 1″ (2n must be even, so 2n + 1 is odd). Because the change is odd, it means the squares must cycle even, odd, even, odd…

And wait! That makes sense because the integers themselves cycle even, odd, even odd… after all, a square keeps the “evenness” of the root number (even * even = even, odd * odd = odd).

Funny how much insight is hiding inside a simple pattern. (I call this technique “geometry” but that’s probably not correct — it’s just visualizing numbers).

Drawing squares with pebbles? What is this, ancient Greece? No, the modern student might argue this:

For example, if n=2, then n 2 =4. And the difference to the next square is thus (2n + 1) = 5.

Indeed, we found the same geometric formula. But is an algebraic manipulation satisfying? To me, it’s a bit sterile and doesn’t have that same “aha!” forehead slap. But, it’s another tool, and when we combine it with the geometry the insight gets deeper.

Calculus students may think: “Dear fellows, we’re examining the curious sequence of the squares, f(x) = x^2. The derivative shall reveal the difference between successive elements”.

And deriving f(x) = x^2 we get:

Close, but not quite! Where is the missing +1?

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