The main aim of the article is to investigate the irrational and transcendental properties of certain real numbers by means of the factorial series and the factorial number system. The difference between the factorial...The main aim of the article is to investigate the irrational and transcendental properties of certain real numbers by means of the factorial series and the factorial number system. The difference between the factorial series and the factorial system is that the factorial series does not set an upper bound at a given place after the radix point, while in the factorial system (i – 1) is the maximal possible value for r<sub>i</sub> after the radix point. I give an extended definition of periodic numbers, and show the relationship between periodic and irrational numbers. I prove the transcendence of e by means of the factorial series and the factorial number system.展开更多
In this paper, we consider <i>r</i>-generalization of the central factorial numbers with odd arguments of the first and second kind. Mainly, we obtain various identities and properties related to these num...In this paper, we consider <i>r</i>-generalization of the central factorial numbers with odd arguments of the first and second kind. Mainly, we obtain various identities and properties related to these numbers. Matrix representation and the relation between these numbers and Pascal matrix are given. Furthermore, the distributions of the signless r-central factorial numbers are derived. In addition, connections between these numbers and the Legendre-Stirling numbers are given.展开更多
The Baotou iron-Steel and Rare Earth Co. is located in Baotou of the AutonomousRegion of Inner Mongolia, where China has her largest mineral reserves of rare earths, par-ticularly that at Baiyunebo. The rare earth res...The Baotou iron-Steel and Rare Earth Co. is located in Baotou of the AutonomousRegion of Inner Mongolia, where China has her largest mineral reserves of rare earths, par-ticularly that at Baiyunebo. The rare earth reserves in this region amount to as high as 80%of that of the whole Nation. The No. 3 Rare Earth Factory was established in 196l and itwas then a pilot plant of the Baotou Steel Works. In 1970 it was reconstructed as a formalplant. Now, it becomes one of the biggest rare earth production bases in China.展开更多
The authors establish an explicit formula for the generalized Euler NumbersE2n^（x）, and obtain some identities and congruences involving the higher＇order Euler numbers, Stirling numbers, the central factorial numbe...The authors establish an explicit formula for the generalized Euler NumbersE2n^（x）, and obtain some identities and congruences involving the higher＇order Euler numbers, Stirling numbers, the central factorial numbers and the values of the Riemann zeta-function.展开更多
The present study attempts to investigate the effect of moisture conditioning on the in- direct tensile strength （ITS） of cold recycled mixture with bitumen emulsion. Firstly, samples were prepared using a Superpave...The present study attempts to investigate the effect of moisture conditioning on the in- direct tensile strength （ITS） of cold recycled mixture with bitumen emulsion. Firstly, samples were prepared using a Superpave gyratory compactor. They were hence condi- tioned using moisture induced sensitivity tester （MIST） device. Factorial design was carried out considering four factors each at two different levels. These factors were specimen thickness, air voids content, pressure and number of cycles. In the MIST device, samples are cyclically subjected to water pressure through the sample pores. The MIST conditioned samples were tested for indirect tensile strength. The analysis of two-level full-factorial designed experiments revealed that all four factors have a negative effect on tensile strength of cold recycled mixture with bitumen emulsion. Specimen thickness was the most significant factor affecting the tensile strength followed by air voids content. In two- factor interaction, specimen thickness-number of cycles, air voids content-pressure, and pressure-number of cycles were significant. The most significant three-factor interaction was specimen thickness-pressure-number of cycles. The results from the study suggest that in measuring tensile strength, the appropriate specimen thickness and air voids content should be selected to quantify the representative tensile strength for in-situ conditions.展开更多
文摘The main aim of the article is to investigate the irrational and transcendental properties of certain real numbers by means of the factorial series and the factorial number system. The difference between the factorial series and the factorial system is that the factorial series does not set an upper bound at a given place after the radix point, while in the factorial system (i – 1) is the maximal possible value for r<sub>i</sub> after the radix point. I give an extended definition of periodic numbers, and show the relationship between periodic and irrational numbers. I prove the transcendence of e by means of the factorial series and the factorial number system.
文摘In this paper, we consider <i>r</i>-generalization of the central factorial numbers with odd arguments of the first and second kind. Mainly, we obtain various identities and properties related to these numbers. Matrix representation and the relation between these numbers and Pascal matrix are given. Furthermore, the distributions of the signless r-central factorial numbers are derived. In addition, connections between these numbers and the Legendre-Stirling numbers are given.
文摘The Baotou iron-Steel and Rare Earth Co. is located in Baotou of the AutonomousRegion of Inner Mongolia, where China has her largest mineral reserves of rare earths, par-ticularly that at Baiyunebo. The rare earth reserves in this region amount to as high as 80%of that of the whole Nation. The No. 3 Rare Earth Factory was established in 196l and itwas then a pilot plant of the Baotou Steel Works. In 1970 it was reconstructed as a formalplant. Now, it becomes one of the biggest rare earth production bases in China.
基金the Guangdong Provincial Natural Science Foundation (No.05005928)the National Natural Science Foundation (No.10671155) of P.R.China
文摘The authors establish an explicit formula for the generalized Euler NumbersE2n^（x）, and obtain some identities and congruences involving the higher＇order Euler numbers, Stirling numbers, the central factorial numbers and the values of the Riemann zeta-function.
基金supported by the National Natural Science Foundation of China(grant No.51308477)
文摘The present study attempts to investigate the effect of moisture conditioning on the in- direct tensile strength （ITS） of cold recycled mixture with bitumen emulsion. Firstly, samples were prepared using a Superpave gyratory compactor. They were hence condi- tioned using moisture induced sensitivity tester （MIST） device. Factorial design was carried out considering four factors each at two different levels. These factors were specimen thickness, air voids content, pressure and number of cycles. In the MIST device, samples are cyclically subjected to water pressure through the sample pores. The MIST conditioned samples were tested for indirect tensile strength. The analysis of two-level full-factorial designed experiments revealed that all four factors have a negative effect on tensile strength of cold recycled mixture with bitumen emulsion. Specimen thickness was the most significant factor affecting the tensile strength followed by air voids content. In two- factor interaction, specimen thickness-number of cycles, air voids content-pressure, and pressure-number of cycles were significant. The most significant three-factor interaction was specimen thickness-pressure-number of cycles. The results from the study suggest that in measuring tensile strength, the appropriate specimen thickness and air voids content should be selected to quantify the representative tensile strength for in-situ conditions.
