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English translation: to decrease/decay at least as fast as (or no(t) slower than)

GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
Russian term or phrase:убывать не слабее, чем
English translation:to decrease/decay at least as fast as (or no(t) slower than)
Entered by: Nik-On/Off

19:16 Oct 17, 2003
Russian to English translations [PRO]
Science - Mathematics & Statistics / math
Russian term or phrase: убывать не слабее, чем
Функция убывает на бесконечности не слабее, чем exp().
Nik-On/Off
Ukraine
Local time: 05:57
to decrease at least exponentially (fast /quickly) / as fast as an exponential function / as exp ()
Explanation:
Повторяю варианты:

Если известно какая именно экспонента, то:
to decrease/decay at least as fast as exp ().
to decrease/decay at least exponentially as exp ()


Если просто сказано "не слабее экспоненты", то:

to decrease/decay at least exponentially (fast /quickly)
to decrease/decay at least as fast as an exponential function


Убывать на бесконечности = to descrease at infinity

Убывать на бесконечности не слабее чем экспонента = to decrease at least exponentially at infinity
А также все возможные перефразировки - см. варианты выше.


Примеры:



--------------------------------------------------
Note added at 1 hr 19 mins (2003-10-17 20:35:47 GMT)
--------------------------------------------------

... We simply quote the first one from Ref. [11]: Poincare lemma. Let ?(x) be a p-form that decreases at least exponentially at infinity. ...
http://arxiv.org/pdf/hep-lat/9906015

IF the parent has an unbounded tail that decreases at least as fast as an exponential function, and has finite moments (as does the normal, for example). http://www.statisticalengineering.com/extreme_value.htm

ss=(0.2*(exp(5.)-exp(-5.))) Interval ... quadrature scheme --
albeit a simple one -- whose fractional error decreases at least as fast as N. ...
http://www.ma.utexas.edu/documentation/nr/bookf/f7-6.ps

... if the probability of finding it outside a ball B r of radius r around the origin, ie in IR 3 \\B r , decreases at least as exp{-Kr} for large r ...
http://arxiv.org/pdf/quant-ph/9809030

. In opposite case coupling energy decreases exponentially as exp - 8 T DL . ...
http://arxiv.org/pdf/cond-mat/0209084

The Boltzmann factor decreases exponentially with increasing energy: exp (-Я E ) ...
ariadne.mse.uiuc.edu/390/lecture09a.pdf

... unstable unless the density of large spheres decreases at least exponentially as their ... ...
http://arxiv.org/pdf/cond-mat/9811150

... ref{T:main} shows that the spectral gap decreases at least exponentially fast in $N ... condition decays exponentially to 0 as the boundary recedes to infinity. ...
http://mpej.unige.ch/mp_arc/papers/00-230

... be reached from which there is a positive probability of escape to infinity. ... c0||x||. Hence g(x) <= exp{-hc0||x||}decreases at least exponentially quickly with ...
http://www.math.leidenuniv.nl/~spieksma/papers/Lyapunov.ps


... for some s ? 0. This means that the tail of G decreases at least exponentially fast ... It relates the behaviour of regularly varying functions at infinity to the ...
http://www.math.ethz.ch/~hjfurrer/mydiss.ps
Selected response from:

Vera Fluhr (X)
Local time: 04:57
Grading comment
Спасибо!
4 KudoZ points were awarded for this answer



Summary of answers provided
5 +2to decrease at least exponentially (fast /quickly) / as fast as an exponential function / as exp ()
Vera Fluhr (X)
4 +1function] decreases.....no more weakly than exp()
Jack slep
5см ниже
ttagir
3function decays at infinity not slower than...
Olga Demiryurek


Discussion entries: 1





  

Answers


22 mins   confidence: Answerer confidence 4/5Answerer confidence 4/5 peer agreement (net): +1
function] decreases.....no more weakly than exp()


Explanation:
Examples of "weakly decreasing function"

ASYMPTOTIC EXPANSION OF THE BACKSCATTERING STRENGTH FOR THE ...
File Format: Unrecognized - View as HTML
... The first term is similar in structure to the standard formula, dominant near
the normal direction and a weakly decreasing function of frequency. ...
www.worldscinet.com/jca/09/0904/S0218396X01000565.html - Similar pages

[PDF]improved regularity of harmonic map flows with hЁ older ...
File Format: PDF/Adobe Acrobat - View as HTML
... 0 in what follows.) Note that although u is not fixed on the boundary of B (and in
particular, E(u(·), B) need not be a weakly decreasing function) by keeping ...
www.maths.warwick.ac.uk/~topping/topping_holder.pdf - Similar pages

[astro-ph/0010253] Cosmic Mach Number as a Function of ...
... value of 0.37. We show from our simulation that the Mach number is
a weakly decreasing function of overdensity. We also investigate ...
arxiv



    see above
Jack slep
Local time: 22:57
Works in field
Native speaker of: English
PRO pts in category: 35

Peer comments on this answer (and responses from the answerer)
agree  Boris Nedkov: I find it's fine
10 hrs
  -> Thanks, Altair!
Login to enter a peer comment (or grade)

50 mins   confidence: Answerer confidence 5/5
см ниже


Explanation:
...the function descreases at infinity not slower than a negative exponent.
See, e.g.,
www.math.utah.edu/~beebe/software/ieee/timops.html
www.vib-bw.de/~mcclung/mathlets/bigO/ ("f(x) grows strictly slower than g(x ...)
Very USEFUL:
(...than g as n ? ?. If L = 0, then f grows slower than g as n ...)
www.nd.edu/~aarana/Math126/Handouts/fun_grow.pdf
sccm.stanford.edu/~drexler/research.html
arxiv.org/pdf/cond-mat/9907067 ( ? 0 at least not slower than 1/ ln N ...)

Another option is "...the function _vanishes_ at infinity not slower than a negative exponent."
Yours,
T.

ttagir
Local time: 05:57
Specializes in field
Native speaker of: Native in RussianRussian, Native in TatarTatar
PRO pts in category: 8
Login to enter a peer comment (or grade)

20 mins   confidence: Answerer confidence 3/5Answerer confidence 3/5
убывать не слабее, чем
function decays at infinity not slower than...


Explanation:
-

--------------------------------------------------
Note added at 41 mins (2003-10-17 19:57:57 GMT)
--------------------------------------------------

... of order ѓї−1 and the ith component of u −u Ѓ‡ decays at infinity at least ... If
the second component of the boundary condition decays slower than |y| −3/2 ...
www.iop.org/EJ/article/0951-7715/15/2/306/no2206.pdf

--------------------------------------------------
Note added at 42 mins (2003-10-17 19:59:27 GMT)
--------------------------------------------------

... Gamma t (jOE. 0. j. 2. \\Lambda U)(x). j. : (3.39) Since U decays at infinity slower
than any Gaussian, Lemma 3.5 (i) implies. lim jxj!1. ln. \\Gamma. jOE. 0. j. 2. \\Lambda
U. ...
www.theorie1.physik.uni-erlangen.de/ leschke/papers/DiscrDec.ps

--------------------------------------------------
Note added at 44 mins (2003-10-17 20:00:35 GMT)
--------------------------------------------------

... the positive part W + (x) = max{0, W (x)} of W decayed slower than the ... stabilizes
to const Ў¤|x| −m . 1.3 We suppose that W ЎК L ЎЮ decays at infinity as |x ...

www.eco.utexas.edu/~sboyarch/wchang3.pdf

--------------------------------------------------
Note added at 58 mins (2003-10-17 20:15:02 GMT)
--------------------------------------------------

... where ϕ is a smooth function which decays at infinity and satisfies ... while ϕ 0 decays
at the slower rate |x ... as analogues of (1.1) for Haar-function and wavelet ...

www.iumj.indiana.edu/iumj/PDF/wheed953.pdf

Olga Demiryurek
Türkiye
Local time: 05:57
Native speaker of: Russian
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1 hr   confidence: Answerer confidence 5/5 peer agreement (net): +2
убывать не слабее, чем
to decrease at least exponentially (fast /quickly) / as fast as an exponential function / as exp ()


Explanation:
Повторяю варианты:

Если известно какая именно экспонента, то:
to decrease/decay at least as fast as exp ().
to decrease/decay at least exponentially as exp ()


Если просто сказано "не слабее экспоненты", то:

to decrease/decay at least exponentially (fast /quickly)
to decrease/decay at least as fast as an exponential function


Убывать на бесконечности = to descrease at infinity

Убывать на бесконечности не слабее чем экспонента = to decrease at least exponentially at infinity
А также все возможные перефразировки - см. варианты выше.


Примеры:



--------------------------------------------------
Note added at 1 hr 19 mins (2003-10-17 20:35:47 GMT)
--------------------------------------------------

... We simply quote the first one from Ref. [11]: Poincare lemma. Let ?(x) be a p-form that decreases at least exponentially at infinity. ...
http://arxiv.org/pdf/hep-lat/9906015

IF the parent has an unbounded tail that decreases at least as fast as an exponential function, and has finite moments (as does the normal, for example). http://www.statisticalengineering.com/extreme_value.htm

ss=(0.2*(exp(5.)-exp(-5.))) Interval ... quadrature scheme --
albeit a simple one -- whose fractional error decreases at least as fast as N. ...
http://www.ma.utexas.edu/documentation/nr/bookf/f7-6.ps

... if the probability of finding it outside a ball B r of radius r around the origin, ie in IR 3 \\B r , decreases at least as exp{-Kr} for large r ...
http://arxiv.org/pdf/quant-ph/9809030

. In opposite case coupling energy decreases exponentially as exp - 8 T DL . ...
http://arxiv.org/pdf/cond-mat/0209084

The Boltzmann factor decreases exponentially with increasing energy: exp (-Я E ) ...
ariadne.mse.uiuc.edu/390/lecture09a.pdf

... unstable unless the density of large spheres decreases at least exponentially as their ... ...
http://arxiv.org/pdf/cond-mat/9811150

... ref{T:main} shows that the spectral gap decreases at least exponentially fast in $N ... condition decays exponentially to 0 as the boundary recedes to infinity. ...
http://mpej.unige.ch/mp_arc/papers/00-230

... be reached from which there is a positive probability of escape to infinity. ... c0||x||. Hence g(x) <= exp{-hc0||x||}decreases at least exponentially quickly with ...
http://www.math.leidenuniv.nl/~spieksma/papers/Lyapunov.ps


... for some s ? 0. This means that the tail of G decreases at least exponentially fast ... It relates the behaviour of regularly varying functions at infinity to the ...
http://www.math.ethz.ch/~hjfurrer/mydiss.ps


    Reference: http://www.statisticalengineering.com/extreme_value.htm
    Reference: http://arxiv.org/pdf/hep-lat/9906015
Vera Fluhr (X)
Local time: 04:57
Native speaker of: Native in RussianRussian, Native in FrenchFrench
PRO pts in category: 53
Grading comment
Спасибо!

Peer comments on this answer (and responses from the answerer)
agree  olganet
4 hrs
  -> спасибо

agree  Arsen (X): decreases (at infinity) at least exponentially
1 day 3 hrs
  -> Cпасибо. Именно так.
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