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Note that in addition to avoiding the somewhat clumsy "Tree" syntax, the postponed evaluation of annotations will also speed up your code, since type hints are not executed. Forward references are already supported by .

By far, the most common use of annotations is type hinting. Still, you have full access to the annotations at runtime and can use them as you see fit. If you are handling annotations directly, you need to deal with the possible forward references explicitly.

Let us create some admittedly silly examples that show when annotations are evaluated. First we do it old-style, so annotations are evaluated at import time. Let contain the following code:

Note that the annotation of name is print() . This is only to see exactly when the annotation is evaluated. Import the new module:

As you can see, the annotation was evaluated at import time. Note that name ends up annotated with None because that is the return value of print() .

Add the __future__ import to enable postponed evaluation of annotations:

Importing this updated code will not evaluate the annotation:

Note that Now! is never printed and the annotation is kept as a string literal in the __annotations__ dictionary. In order to evaluate the annotation, use typing.get_type_hints() or eval() :

Observe that the __annotations__ dictionary is never updated, so you need to evaluate the annotation every time you use it.

In Python 3.7, the module gains some new functions as described in Benedetta Bruzziches Ariel Rainbow Clutch Blue CbXdVB
. In particular, the following six functions are added:

clock_gettime_ns() : clock_settime_ns() : monotonic_ns() : perf_counter_ns() process_time_ns() : time_ns()

In a sense, there is no new functionality added. Each function is similar to an already existing function without the _ns suffix. The difference being that the new functions return a number of nanoseconds as an int instead of a number of seconds as a float .

For most applications, the difference between these new nanosecond functions and their old counterpart will not be appreciable. However, the new functions are easier to reason about because they rely on int instead of float . Floating point numbers are by nature inaccurate :

This is not an issue with Python but rather a consequence of computers needing to represent infinite decimal numbers using a finite number of bits.

A Python float follows the IEEE 754 standard and uses 53 significant bits. The result is that any time greater than about 104 days (2⁵³ or approximately Asos Design Fastrack Tie Leg Sandals Grey zOgX4Y
) cannot be expressed as a float with nanosecond precision. In contrast, a Python int is unlimited , so an integer number of nanoseconds will always have nanosecond precision independent of the time value.

Schröder Points Database / Darij Grinberg

This page contains some results and questions about the Schröder points of a triangle and configuration related to these. The dates are the dates of last changes.

The idea of this page was to collect all known results about the Schröder points of a triangle from different sources (Hyacinthos messages, MathLinks discussions). Feel free to mail me (see main site for address) if you have something to add.

[Schroeder2] The Schröder points, Darij Grinberg, 4 Jul 2004 Fendi Geometric Stud Mini Bag Blue E2rsR3Smv
Incentral Triangle Question, Darij Grinberg, 27 Feb 2004 Ritch Erani NYFC Braided Wedge Sandals Women Leather Suede Plexiglass 39 White 4kAjwy91Kc
Re: Incentral Triangle Question, Eric Danneels, 3 May 2003 [Schroeder5] Poristically fixed points, Darij Grinberg, 25 Mar 2004 Dolce amp; Gabbana Peplum Hem Midi Dress Pink Purple CNtKya3ni
Re: Incentral Triangle Question, Darij Grinberg, 27 Feb 2004 Balmain Disco Shoulder Bag Black PsfY5Kcc6
Some newer results from MathLinks, Darij Grinberg, 4 Jul 2004

[Schroeder2] [Schroeder3] [Schroeder4] [Schroeder5] [Schroeder6] [Schroeder7]
[Schroeder2] The Schröder points 1. The Schröder point by inversion Schröder point 2. Trilinears of the Schröder point Gergonne-Schröder point X(1155) = SCHRÖDER POINT 3. Jean-Pierre Ehrmann's approach 4. The Schröder point as inversive image of X(55) Weill point 5. The Nagel-Schröder point Nagel-Schröder point 6. The Stutensee point Stutensee point 7. The Mitten-Schröder points Mitten-Schröder points 8. The Bevan-Schröder point Bevan point Bevan-Schröder point 9. Trilinears of the Bevan-Schröder point 10. Some synthetic conjectures about the Bevan-Schröder point 11. Poristically fixed points poristically fixed Fundamental Poristic Theorem. 12. A generalization of the Schröder and Bevan-Schröder points leading to the Darboux cubic Schoute point Longchamps-Schröder point 13. A generalization of the Schröder and Nagel-Schröder points and the Feuerbach hyperbola Droussent pivot
[Schroeder3] Incentral Triangle Question

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The Antcar had a great visit to Bugfest 2016, sponsored by the North Carolina Museum of Natural Science in Raleigh. Science comedian Brian Malow was on hand, too, and he made this nice video about the Ant Car.

Check it out!

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The Chattanooga Scenic City Art Car Parade was a blast! Lots of great cars, great people, new friends! (Click on each photo for larger view.)

Watch the Ant Car twinkling at the riverfront in Chattanooga. The Scenic City Art Car Parade 2016 was a blast, especially the Illuminated Cruise! Thanks to Art120.0rg!

Click for larger image!

Click here to tour the Ant Car while singing the blues on the Blue Ridge Parkway. Be sure to look for the happy passenger!

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The Ant Car had a great time at Artscape 2012 in Baltimore. Billed as the nation’s largest free arts festival, Artscape draws 350,000 visitors over a three day weekend. Organizer Jim Lucio and curator C.K. Laster put together a great collection of art cars from all over the country. Below are pictures of just a few. Click on each image for larger view.

Art car artists exhibiting at Artscape 2012 included Cindy Albano, Clarke Bedford, Randy Blair, Howard Davis, Dr. Bob Hieronimus, Chris Hubbard, David Schwartz, Selena Schreyer, Robert Seven, Jim Shores, Daniel Stuelpnagel, Dan Van Allen, Erika Nelson and others. Also on hand was the World’s Largest Collection of the World’s Smallest Versions of the World’s largest Things.

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The Ant Car had a fabulous time at the 2011 Houston Art Car Parade! In fact, it was one ofa handfulselected to be a ‘Star Car’ anddisplayed on the infield of Discovery Green Park in downtown Houston. To see more pics from the parade and the fantastic cars(over 260!) that took part in May 2011, please visit

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Industrious Human Ant Readies Car for Huge Houston Parade Click here to see newspaper article and pictures >

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Antcar on TV

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This winter has of course battered the antcar with a variety of precipitation, including 20 inches of fluffy snow and several inches of ice. Here are pics of the antcar hanging in there, and sometimes even lighting up!

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A stability analysis for an oscillation equation should be given at this point.

A stability analysis for a relaxation equation should be given at this point.

Figure 2.2 Oscillatory and damping response of quasi-second order Adams-Bashforth scheme for different values of the ϵ A B parameter (0.0, 0.1, 0.25, from top to bottom) The analytical solution (in black), the physical mode (in blue) and the numerical mode (in red) are represented with a CFL step of 0.1. The left column represents the oscillatory response on the complex plane for CFL ranging from 0.1 up to 0.9. The right column represents the damping response amplitude (y-axis) function of the CFL (x-axis).

Vertical diffusion and viscosity can be treated implicitly in time using the backward method which is an intrinsic scheme. Recently, the option to treat the vertical advection implicitly has been added, but not yet tested; therefore, the description hereafter is limited to diffusion and viscosity. For tracers, the time discretized equation is:

(2.20) τ n + 1 Δ t r κ v r τ n + 1 = τ n + Δ t G ( n + 1 / 2 ) τ

where G ( n + 1 / 2 ) τ is the remaining explicit terms extrapolated using the Adams-Bashforth method as described above. Equation (2.20) can be split split into:

(2.21) τ = τ n + Δ t G ( n + 1 / 2 ) τ
(2.22) Senso Sandals Dark Blue WxKwKes
τ n + 1 = L 1 τ ( τ )

where L 1 τ is the inverse of the operator

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