搜索结果: 1-9 共查到“数理逻辑与数学基础 function”相关记录9条 . 查询时间(0.184 秒)
Recursion Relations and Functional Equations for the Riemann Zeta Function
Riemann zeta function zeros of zeta function recursion relation of zeta function functional equation of zeta function
2011/9/14
Abstract: New recursion relations for the Riemann zeta function are introduced. Their derivation started from the standard functional equation. The new functional equations have both real and imaginar...
Constructive Proof of Global Lyapunov Function as Potential Function
Constructive Proof Global Lyapunov Function Potential Function
2011/3/2
We provide a constructive proof on the equivalence of two fundamental concepts: the global
Lyapunov function in engineering and the potential function in physics, establishing a bridge be-tween these...
The Padé iterations for the matrix sign function and their reciprocals are optimal
The Padé iterations the matrix sign function reciprocals
2010/11/12
It is proved that among the rational iterations locally converging with order s>1 to the sign function, the Pad\'e iterations and their reciprocals are the unique rationals with the lowest sum of the ...
Bernoulli Operator and Riemann's Zeta Function
Bernoulli Operator Riemann's Zeta Function
2010/11/19
We introduce a Bernoulli operator,let "B" denote the operator symbol,for n=0,1,2,3,... let ${B^n}: = {B_n}$ (where ${B_n}$ are Bernoulli numbers,${B_0} = 1,B{}_1 = 1/2,{B_2} = 1/6,{B_3} = 0$...).We o...
On Karatsuba's Problem Concerning the Divisor Function $\tau(n)$
On Karatsuba's Problem the Divisor Function $\tau(n)$
2010/11/11
We study an asymptotic behavior of the sum $\sum\limits_{n\le x}\frac{\D \tau(n)}{\D \tau(n+a)}$. Here $\tau(n)$ denotes the number of divisors of $n$ and $a\ge 1$ is a fixed integer.
Riemann hypothesis and some new asymptotically multiplicative integrals which contain the remainder of the prime-counting function $\pi(x)$
Riemann hypothesis asymptotically multiplicative integrals
2010/11/9
A new parametric integral is obtained as a consequence of the Riemann hypothesis. An asymptotic multiplicability is the main property of this integral
Let $\Psi(n):=n\prod_{p | n}(1+\frac{1}{p})$ denote the Dedekind $\Psi$ function. Define, for $n\ge 3,$ the ratio $R(n):=\frac{\Psi(n)}{n\log\log n}.$ We prove unconditionally that $R(n)\le e^\gamma$...
We examine Bourbaki's function, an easily-constructed continu-ous but nowhere-di erentiable function, and explore properties including func-tional identities, the antiderivative, and the box dimension...
On the Consistency of the Deterministic Local Volatility Function Model ('implied tree')
the Deterministic Local Volatility Function Model math
2010/11/2
We show that the frequent claim that the implied tree prices exotic options consistently with the market is untrue if the local volatilities are subject to change and the market is arbitrage-free. In...