Over a century and half has passed when Bernhard Riemann hypothesized that the non-trivial roots of the Riemann zeta function ζ(s) all lie on the half-line . In this paper the Zeta function is iterated as a power tow...Over a century and half has passed when Bernhard Riemann hypothesized that the non-trivial roots of the Riemann zeta function ζ(s) all lie on the half-line . In this paper the Zeta function is iterated as a power tower and its properties are applied as an approach to an indication that the Riemann hypothesis might be true. It is known that complex valued Power towers converge under certain conditions to exponential power towers of entire functions. These properties can be used to resolve the Riemann Hypothesis.展开更多
Kolmogorov's exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper est...Kolmogorov's exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper establishes the Kolmogorov type exponential inequalities of the partial sums of independent random variables as well as negatively dependent random variables under the sub-linear expectations. As applications of the exponential inequalities, the laws of the iterated logarithm in the sense of non-additive capacities are proved for independent or negatively dependent identically distributed random variables with finite second order moments.For deriving a lower bound of an exponential inequality, a central limit theorem is also proved under the sublinear expectation for random variables with only finite variances.展开更多
To mitigate inter-cell interference in 3G evolution systems, a novel inter-cell interference coordination scheme called soft fractional frequency reuse is proposed in this article, which enables to improve the data ra...To mitigate inter-cell interference in 3G evolution systems, a novel inter-cell interference coordination scheme called soft fractional frequency reuse is proposed in this article, which enables to improve the data rate in cell-edge. On this basis, an inter-cell power control is presented for the inter-cell interference coordination, and the inter-cell balanced signal to interference plus noise ratio （SINR） among users is established for power allocation, which enables mitigation of inter-cell interference. Especially, the power control is based on a novel exponential kernel arithmetic kernel equations. Numerical results show that the proposed rate compared to the existing power control algorithms. equation at higher convergence speed than the traditional scheme improves the throughput and reduces the blocking展开更多
文摘Over a century and half has passed when Bernhard Riemann hypothesized that the non-trivial roots of the Riemann zeta function ζ(s) all lie on the half-line . In this paper the Zeta function is iterated as a power tower and its properties are applied as an approach to an indication that the Riemann hypothesis might be true. It is known that complex valued Power towers converge under certain conditions to exponential power towers of entire functions. These properties can be used to resolve the Riemann Hypothesis.
基金supported by National Natural Science Foundation of China (Grant No. 11225104)the National Basic Research Program of China (Grant No. 2015CB352302)the Fundamental Research Funds for the Central Universities
文摘Kolmogorov's exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper establishes the Kolmogorov type exponential inequalities of the partial sums of independent random variables as well as negatively dependent random variables under the sub-linear expectations. As applications of the exponential inequalities, the laws of the iterated logarithm in the sense of non-additive capacities are proved for independent or negatively dependent identically distributed random variables with finite second order moments.For deriving a lower bound of an exponential inequality, a central limit theorem is also proved under the sublinear expectation for random variables with only finite variances.
基金supported by Sino-Swedish Project (2008DFA12110)Key Project of BMSTC (D08080100620802)+1 种基金the National Natural Science Foundation of China (60872048)National Science and Technology Special Project ‘Group Cell’ (2009ZX03003-011)
文摘To mitigate inter-cell interference in 3G evolution systems, a novel inter-cell interference coordination scheme called soft fractional frequency reuse is proposed in this article, which enables to improve the data rate in cell-edge. On this basis, an inter-cell power control is presented for the inter-cell interference coordination, and the inter-cell balanced signal to interference plus noise ratio （SINR） among users is established for power allocation, which enables mitigation of inter-cell interference. Especially, the power control is based on a novel exponential kernel arithmetic kernel equations. Numerical results show that the proposed rate compared to the existing power control algorithms. equation at higher convergence speed than the traditional scheme improves the throughput and reduces the blocking
