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9 Aug 2005: 67 "#. @"# "5 8 ,"#0.@% #=24! #"5 $ % "#'"#! 8 24! 5"#A % "5'?"# ,"# =24. @ '?24,%. "#6. % "#'"#!( %<'" #9 =":9- 2. ... le2 22,. z q! % ,>- %<'! "! "# %<' %<?'. "#< ,"# #"#$ % "#'" 7 %?'. '! '? %<' ,"#. ) %<' 6'1 A( ), -2 01 '9;! "# & (&), - 24! '!"#:

12 Nov 2005: Find a monic polynomial over Z of degree 4 whoseGalois group is V = {e, (12)(34), (13)(24), (14)(23)}.(ii) Let f Z[X] be monic and separable of degree

7 Feb 2005: Mathematical Tripos Part IILent 2005. Professor A. Iserles. Numerical Analysis – Lecture 121. Methods 3.25A generalν-stageRunge–Kutta methodis. kl = f. . tn clh, yn h. ν. j=1. al,j kj. .  where. ν. j=1. al,j = cl, l = 1, 2,. ,

5 Sep 2005: Phys. Commun. 162 24[20] Pask J E and Sterne P A 2005 Modelling Simul. ... Rev. Lett. 93 176403[24] Mostofi A A, Skylaris C-K, Haynes P D and Payne M C 2002 Comput.

4 Mar 2005: Implementation 5.24 It is quite usual to solvehyperbolic PDEs (advection equation, wave equation,Schr̈odinger equation, Euler equations of invicid compressibleflow. )

9 Aug 2005: 2 f > f 35350 J<?L t'g<] e ]25342 gn h' [ <h'h <k% l e%f s<?]lxgk e 24<0l. ... 35 n J<?gh'l>lL2q0@ ' [ < f t_<?00 f 2' >'g#e[[ 35 e 24<0Nt e e,f / / l. (&)

9 Aug 2005: " #$ %& '& ()!,&-&. 0/ 12436587:9 ;=<?>"@BAC361D4EGF!H 24@. I8JLKNMOKQPSRUTWVXNXZY-[YT]_'aOJ=KZbO[cYd. T]_'aOJ=KZbO[cY'eGMOKNfcYJ=gLKQPSRihMO[cKZMOY-YJ=KZMO[kj Ylm]J=Pn_,Y-MoP. ... D>WH 7 m;6D1 33 24; "5 @ 5 D>"@!;m;6>W@ 9G7 58< 7.

7 Feb 2005: y0, n = 0, 1, 2,. 24. The following four-stage Runge–Kutta method has order four,.

12 Apr 2005: 302k 9k+ 16.0 13.9 24.8 –MLE 415k 9k+ 16.0 13.5 24.3 –. 398k 12k+ 16.1 13.6 24.5 –. 302k 9k+ 13.2 11.2 ... dev04 eval03 dev04f. MLEMPron 16.0 13.6 24.5SPron 15.6 13.5 24.2. MPEMPron 12.9 11.1 19.1SPron 12.7 10.8 18.8.

26 Jul 2005: LT. 0.500E-01 CONF 1 E = 62.24 ( 0.044) replaces structure 31 Minimization converged; gradient = 0.360E-01. ... LT. 0.500E-01 CONF 1 E = 62.24 ( 0.032) replaces structure 31 Minimization converged; gradient = 0.439E-01.