In Riemann’s prime distribution formula, there is a key Riemann ladder function. This is the basis for Riemann to study the distribution of prime numbers. But the calculation of Riemann’s ladder function is very com...In Riemann’s prime distribution formula, there is a key Riemann ladder function. This is the basis for Riemann to study the distribution of prime numbers. But the calculation of Riemann’s ladder function is very complicated. According to the definition of Riemannian ladder function, we greatly improve the Riemannian ladder function, obtain new ladder function and improved Riemannian prime distribution formula, and prove the improved Riemannian prime distribution formula. We use the improved Riemannian prime distribution formula and merdens theorem to obtain a strong prime theorem.展开更多
Ladder-like polysilsesquioxanes （LPSQs） with different amino contents have been synthesized by controlling of the dosage of Pd/C catalyst. The concentration and activity of amino groups were investigated by Fourier ...Ladder-like polysilsesquioxanes （LPSQs） with different amino contents have been synthesized by controlling of the dosage of Pd/C catalyst. The concentration and activity of amino groups were investigated by Fourier transform infrared spectroscopy. Polyimide （PI）/LPSQ hybrid films have been prepared by incorporating of the obtained LPSQs with different amino contents into PI matrix, respectively. The interfacial interactions between PI matrix and LPSQ were studied with scanning electron microscopy and X-ray photoelectron spectroscopy, meanwhile the thermal and mechanical properties of the hybrid films were studied using dynamic mechanical analysis and tensile tests. The results indicate that the functionality of LPSQ has great effects on the interfacial interactions and the properties of hybrid films. With the increase of amino content, both the interracial interactions and the cross-linking density of hybrids enhanced, which results in the decline of surface silicon concentration, increase of Young＇s modulus and drop of elongation at break. Excessive amino content makes the hybrid films brittle and leads to incomplete imidization.展开更多
The genus distribution of a graph is a polynomial whose coefficients are the partition of the number of embeddings with respect to the genera. In this paper, the genus distribution of Mobius ladders is provided which ...The genus distribution of a graph is a polynomial whose coefficients are the partition of the number of embeddings with respect to the genera. In this paper, the genus distribution of Mobius ladders is provided which is an infinite class of 3-connected simple graphs.展开更多
The theory of RC uniform ladder networks based upon the recurrence of voltage and cur-rent functions is extended as a vehicle to analyse the dynamic characteristics of reg lines. Meth-ods for computing the time consta...The theory of RC uniform ladder networks based upon the recurrence of voltage and cur-rent functions is extended as a vehicle to analyse the dynamic characteristics of reg lines. Meth-ods for computing the time constants and simplifying the transfer functions for reg lines are alsopresented.展开更多
文摘In Riemann’s prime distribution formula, there is a key Riemann ladder function. This is the basis for Riemann to study the distribution of prime numbers. But the calculation of Riemann’s ladder function is very complicated. According to the definition of Riemannian ladder function, we greatly improve the Riemannian ladder function, obtain new ladder function and improved Riemannian prime distribution formula, and prove the improved Riemannian prime distribution formula. We use the improved Riemannian prime distribution formula and merdens theorem to obtain a strong prime theorem.
基金financially supported by the National Natural Science Foundation of China (No.51073020)
文摘Ladder-like polysilsesquioxanes （LPSQs） with different amino contents have been synthesized by controlling of the dosage of Pd/C catalyst. The concentration and activity of amino groups were investigated by Fourier transform infrared spectroscopy. Polyimide （PI）/LPSQ hybrid films have been prepared by incorporating of the obtained LPSQs with different amino contents into PI matrix, respectively. The interfacial interactions between PI matrix and LPSQ were studied with scanning electron microscopy and X-ray photoelectron spectroscopy, meanwhile the thermal and mechanical properties of the hybrid films were studied using dynamic mechanical analysis and tensile tests. The results indicate that the functionality of LPSQ has great effects on the interfacial interactions and the properties of hybrid films. With the increase of amino content, both the interracial interactions and the cross-linking density of hybrids enhanced, which results in the decline of surface silicon concentration, increase of Young＇s modulus and drop of elongation at break. Excessive amino content makes the hybrid films brittle and leads to incomplete imidization.
基金The NSF (10201022) of China NSF (1012003) of Beijing City.
文摘The genus distribution of a graph is a polynomial whose coefficients are the partition of the number of embeddings with respect to the genera. In this paper, the genus distribution of Mobius ladders is provided which is an infinite class of 3-connected simple graphs.
文摘The theory of RC uniform ladder networks based upon the recurrence of voltage and cur-rent functions is extended as a vehicle to analyse the dynamic characteristics of reg lines. Meth-ods for computing the time constants and simplifying the transfer functions for reg lines are alsopresented.
