The idea of ＂worship elegance＂ in Zhu Xi＇ are ＂worship elegance＂ and ＂express aspiration＂ , namely thoughts s music thoughts has been commonly discussed by most theorists, but there ＂restrain feelings＂ and ＂...The idea of ＂worship elegance＂ in Zhu Xi＇ are ＂worship elegance＂ and ＂express aspiration＂ , namely thoughts s music thoughts has been commonly discussed by most theorists, but there ＂restrain feelings＂ and ＂express feelings＂ co-existing in Zhu xi＇ s music thoughts.展开更多
The idea of ＂worship elegance＂ in Zhu Xi＇ s music thoughts has been commonly discussed by most theorists, but there are ＂worship elegance＂ and ＂express aspiration＂ , namely ＂restrain feelings＂ and ＂express f...The idea of ＂worship elegance＂ in Zhu Xi＇ s music thoughts has been commonly discussed by most theorists, but there are ＂worship elegance＂ and ＂express aspiration＂ , namely ＂restrain feelings＂ and ＂express feelings＂ co-existing in Zhu xi＇ s music thoughts.展开更多
Riemann proved three results: analytically continue ζ(s) over the whole complex plane s =σ + it with a pole s =1;(Theorem A) functional equation ξ(t) = G(s<sub>0</sub>)ζ (s<sub>0</sub>), s&...Riemann proved three results: analytically continue ζ(s) over the whole complex plane s =σ + it with a pole s =1;(Theorem A) functional equation ξ(t) = G(s<sub>0</sub>)ζ (s<sub>0</sub>), s<sub>0</sub> =1/2 + it and (Theorem B) product expression ξ<sub>1</sub>(t) by all roots of ξ(t). He stated Riemann conjecture (RC): All roots of ξ (t) are real. We find a mistake of Riemann: he used the same notation ξ(t) in two theorems. Theorem B must contain complex roots;it conflicts with RC. Thus theorem B can only be used by contradiction. Our research can be completed on s<sub>0</sub> =1/2 + it. Using all real roots r<sub>k</sub><sub> </sub>and (true) complex roots z<sub>j</sub> = t<sub>j</sub> + ia<sub>j</sub> of ξ (z), define product expressions w(t), w(0) =ξ(0) and Q(t) > 0, Q(0) =1 respectively, so ξ<sub>1</sub>(t) = w(t)Q(t). Define infinite point-set L(ω) = {t : t ≥10 and |ζ(s<sub>0</sub>)| =ω} for small ω > 0. If ξ(t) has complex roots, then ω =ωQ(t) on L(ω). Finally in a large interval of the first module |z<sub>1</sub>|>>1, we can find many points t ∈ L(ω) to make Q(t) . This contraction proves RC. In addition, Riemann hypothesis (RH) ζ for also holds, but it cannot be proved by ζ.展开更多
Riemann (1859) had proved four theorems: analytic continuation ζ(s), functional equation ξ(z)=G(s)ζ(s)(s=1/2+iz, z=t−i(σ−1/2)), product expression ξ1(z)and Riemann-Siegel formula Z(z), and proposed Riemann conjec...Riemann (1859) had proved four theorems: analytic continuation ζ(s), functional equation ξ(z)=G(s)ζ(s)(s=1/2+iz, z=t−i(σ−1/2)), product expression ξ1(z)and Riemann-Siegel formula Z(z), and proposed Riemann conjecture (RC): All roots of ξ(z)are real. We have calculated ξand ζ, and found that ξ(z)is alternative oscillation, which intuitively implies RC, and the property of ζ(s)is not good. Therefore Riemann’s direction is correct, but he used the same notation ξ(t)=ξ1(t)to confuse two concepts. So the product expression only can be used in contraction. We find that if ξhas complex roots, then its structure is destroyed, so RC holds. In our proof, using Riemann’s four theorems is sufficient, needn’t cite other results. Hilbert (1900) proposed Riemann hypothesis (RH): The non-trivial roots of ζhave real part 1/2. Of course, RH also holds, but can not be proved directly by ζ(s).展开更多
文摘The idea of ＂worship elegance＂ in Zhu Xi＇ are ＂worship elegance＂ and ＂express aspiration＂ , namely thoughts s music thoughts has been commonly discussed by most theorists, but there ＂restrain feelings＂ and ＂express feelings＂ co-existing in Zhu xi＇ s music thoughts.
文摘The idea of ＂worship elegance＂ in Zhu Xi＇ s music thoughts has been commonly discussed by most theorists, but there are ＂worship elegance＂ and ＂express aspiration＂ , namely ＂restrain feelings＂ and ＂express feelings＂ co-existing in Zhu xi＇ s music thoughts.
文摘Riemann proved three results: analytically continue ζ(s) over the whole complex plane s =σ + it with a pole s =1;(Theorem A) functional equation ξ(t) = G(s<sub>0</sub>)ζ (s<sub>0</sub>), s<sub>0</sub> =1/2 + it and (Theorem B) product expression ξ<sub>1</sub>(t) by all roots of ξ(t). He stated Riemann conjecture (RC): All roots of ξ (t) are real. We find a mistake of Riemann: he used the same notation ξ(t) in two theorems. Theorem B must contain complex roots;it conflicts with RC. Thus theorem B can only be used by contradiction. Our research can be completed on s<sub>0</sub> =1/2 + it. Using all real roots r<sub>k</sub><sub> </sub>and (true) complex roots z<sub>j</sub> = t<sub>j</sub> + ia<sub>j</sub> of ξ (z), define product expressions w(t), w(0) =ξ(0) and Q(t) > 0, Q(0) =1 respectively, so ξ<sub>1</sub>(t) = w(t)Q(t). Define infinite point-set L(ω) = {t : t ≥10 and |ζ(s<sub>0</sub>)| =ω} for small ω > 0. If ξ(t) has complex roots, then ω =ωQ(t) on L(ω). Finally in a large interval of the first module |z<sub>1</sub>|>>1, we can find many points t ∈ L(ω) to make Q(t) . This contraction proves RC. In addition, Riemann hypothesis (RH) ζ for also holds, but it cannot be proved by ζ.
文摘Riemann (1859) had proved four theorems: analytic continuation ζ(s), functional equation ξ(z)=G(s)ζ(s)(s=1/2+iz, z=t−i(σ−1/2)), product expression ξ1(z)and Riemann-Siegel formula Z(z), and proposed Riemann conjecture (RC): All roots of ξ(z)are real. We have calculated ξand ζ, and found that ξ(z)is alternative oscillation, which intuitively implies RC, and the property of ζ(s)is not good. Therefore Riemann’s direction is correct, but he used the same notation ξ(t)=ξ1(t)to confuse two concepts. So the product expression only can be used in contraction. We find that if ξhas complex roots, then its structure is destroyed, so RC holds. In our proof, using Riemann’s four theorems is sufficient, needn’t cite other results. Hilbert (1900) proposed Riemann hypothesis (RH): The non-trivial roots of ζhave real part 1/2. Of course, RH also holds, but can not be proved directly by ζ(s).
