[分析] 高微
不好意思小弟又來尋求大家的協助QQ
sin(x^a)
1. Assume a>0 and b>0. Find all (a,b) such that --------- is continuous
1+x^b
uniformly on {x|x>0}.
其實我對這類型的題目都蠻不知從何下手的
不管是均勻連續還是均勻收斂等等
可以請教大家這類型的題目要怎麼下手或思考比較好
感恩
2.Assume that g(x,y)<g(x,z) for all y<z and g(x,y)<g(t,y) for all x<t
Can this assumtion imple that g is Riemann integrable on[0,1]x[0,1]?
這題是跟一維的比較的題目
因為單變數函數單調的話則黎曼可積
所以我想這題應該不是吧，但也想不出好的反例
3.Let N={1,2,3,..} and E be defined as follow: A is contained in E iff A is
a subset of N. Show that there is a bijective mapping from E to an open
interval (0,1).
原本嘗試了許多的函數 像是0.a_1a_2...
結果這類函數都會在切割的地方不同導致不是1-1
a_11(x) a_12(x)
4. Suppose A=[ ] is a 2*2 matrix of complex-valued functions.
a_21(x) a_22(x)
x∈|R, a_ij(x) is C^1 in a nhb of x_0∈|R. Assume that λ_1(x_0) and λ_2(x_0)
are eigenvalues of A(x_0), λ_1(x_0)≠λ_2(x_0). Show that near x_0, there
esists a matrix of function P(x) with C^1 element and two scalar C^1 function
λ_1(x) and λ_2(x) such that
-1 λ_1(x) 0
P (x)A(x)P(x)=[ ]
0 λ_2(x)
And given an expamle to show that this is not true of λ_1(x_0)=λ_2(x_0)
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◆ From: 111.251.153.196
※ 編輯: jacky7987 來自: 111.251.153.196 (09/16 11:55)
※ 編輯: jacky7987 來自: 111.251.153.196 (09/16 15:02)
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