1、III?2020cccaaa )KKK888;nnn)LLL:1. ?150?moO1802. kY7L?3K?3Kv?Ko540E!“!A!VK?O90)I3KKK?LLL150?K(IXJ?KL?UK?KSg?K8L?K8?cK?K?SNEEE1. (10) ?N?/N?2. (10) z4 5z + 1 = 0 3 ?S9? z C : 1 |z| 0).4. (20) ? f(z) ?limr+M(r)rn. M = S1 D ?. D = S1? S1?N?o-iii) m M/M ?u=m4. (15) x T = S1 S1, ?T-?+I)?5. (15) ?m?d?y?d?m
2、k?N+6. (15) y Brouwer :nu n 4N Dn?YgN? f : Dn Dn, f(x) = x, x Dn, 3)1. (20) b? X ?, f : X 0, ?,RXf d = c, 0 c , . y:limnZXnlog1 + (f/n)d =e 0 1,ce = 1,0e 1 0, , r , kfkr . y: ? p ,kfkp kfk.3. (15) y: 3F?Am H , z48 E ?k?.4.(15) b? f : I R1 AC ?, I = a,b, F(x) = supNXi=1|f(ti) f(ti1)|(a x b),8;n12?5,
3、(.?Hk? N 9kva = t0 t1 0, y:Z+0sinaxZ+0f(y)exydydx = aZ+0f(y)a2+ y2dy.“1. (15) ? k = Fq q ?k V 4 k-5mK V ? k-fmk?2. (15) ? G ?N?fNC+ (=k?N?mfN$|?+)y G=S4o?+?T+3?N? 3 L?A?I3. (20 ) (1) o? (splitting field)(2) ? p q p ? k = FpK L k Xq X ?=? L q ?kAO/k q ?k?4. (20 ) y?“ ZX ?n (1) (0) (2) (p) (p ) (3)(f(
4、X) (f(X) ZX ?) (4) (p,f(X) ( p f(X) ? p ? FpX?)5. (20 )? p G k+ P G ? Sylow p-f+ N = NG(P)pNG(H) = g G | gHg1= HK N = NG(N)AAA1. (15) (1) ? r = r(u,v) = (acosucosv, acosusinv, asinu), /2 u /2, 0 v 0,b 6= 0 ?-r = r(u,v) = (acosu, asinu, bv),0 u 2, v +,?-(t) = (acost, asint, bt), 0 t 2.(1) - ?-L(2) ?t
5、0 (0,2). -3 (t0) ? 0(t0) ?-(3) ?- -?/nd8;n13?53. (20)3 r = r(u,v) = (acosucosv, acosusinv, asinu), /2 u /2, 0 v 2 ? C(v) := r(u0,v), 0 v 2 , p u0 (0,/2). O- C /- kg?HCkgds .4. (30) ? M E3?K-z r = r(u,v). K ru,rv,n g,Ie|p n |?: p MPW : TpM TpMWeingarten C(1) ?C W vW rurv!= A rurv!.?A.1!1?/?XL(2) yeDd
6、vDduruDduDdvru= K |ru rv| R2(ru),pDdu,Ddv?C? K pd-R2(ru) ru_?=2?=R2(ru) = |ru| (rv)|(rv)|,(rv):= rv?rv,ru|ru|?ru|ru|.VVV1. (10) ,kN Wzk|l?l?/?3gm;:8ez?r|l?k?gC?l?V.2. (10) ? = r Q : r 0,1 0,1 ?kn8, A “, z8kp?Xe/?8A ?:r : a r b, r : a r b, r : a r b, r : a r b,0 a b 1, XJB =nPi=1AiX/8Ai?k?KP(B) =nPi=
7、1(bi ai), ai,biO8Ai?m:, y8P(A),A A A ?k8?.3. (15) -(x) =12ex22, x ,g(x) =cos(x),|x| 0,|x| ,p(x,y) = (x)(y) +12e2g(x)g(y), x,y S?, (3)X0, (4)S, (5)?.8;n14?54. (15) e1,2, ,n?C, l, p(x), Ok n :E?1+ 2+ + k1+ 2+ + n?.5. (15) ?kk ? , zg8?1i ?Vpi,kPi=1pi= 1, zg8mp?. e?8?n , o ?a?(=8?n ?, ?1? a?)6. (15) LNt,t R+r?PoissonL(;?mY), eP(N0= 0) = 1, Nt,t R+OL, s t, Nt Nsl(t s)?Poisson. WrP1r a?u)?, =Wr t u)L1r a?y?u?ut, l?Wr t = Nt r. CWr?F(t) = P(Wr t) 9Vp(t).7. (10) ?,?( :U)C,:f(x) = 2x,0 x 1.?”?, =#?O.XiL1i ?, Sn=nPi=1XiL1n ?”?, ”?r Xe:r = limnnSn.b?CXi,i 1 p, ”?r.8;n15?5
