A map of the average atomic number of lunar rock and soil can be used to differentiate lithology and soil type on the lunar surface.This paper establishes a linear relationship between the average atomic number of lun...A map of the average atomic number of lunar rock and soil can be used to differentiate lithology and soil type on the lunar surface.This paper establishes a linear relationship between the average atomic number of lunar rock or soil and the flux of position annihilation radiation(0.512-Me V gamma-ray) from the lunar surface.The relationship is confirmed by Monte Carlo simulation with data from lunar rock or soil samples collected by Luna(Russia) and Apollo(USA) missions.A map of the average atomic number of the lunar rock and soil on the lunar surface has been derived from the Gamma-Ray Spectrometer data collected by Chang'e-1,an unmanned Chinese lunar-orbiting spacecraft.In the map,the higher average atomic numbers(ZA > 12.5),which are related to different types of basalt,are in the maria region;the highest ZA(13.2) readings are associated with Sinus Aestuum.The middle ZA(~12.1) regions,in the shape of irregular oval rings,are in West Oceanus Procellarum and Mare Frigoris,which seems to be consistent with the distribution of potassium,rare earth elements,and phosphorus as a unique feature on the lunar surface.The lower average atomic numbers(ZA < 11.5)are found to be correlated with the anorthosite on the far side of the Moon.展开更多
The average aggregate number(N)of electrostatically stabilized aggregate(ESAg)composed of oppositely-charged long-chain molecules,i.e., sodium ω-[α-(nathphyl)ethoxyl]undecanoate(FP^-)and cetyltrimethyl ammonium chlo...The average aggregate number(N)of electrostatically stabilized aggregate(ESAg)composed of oppositely-charged long-chain molecules,i.e., sodium ω-[α-(nathphyl)ethoxyl]undecanoate(FP^-)and cetyltrimethyl ammonium chloride(CTAC),in aqueous solution at 25℃ has been measured to be 11 to 16 in the CTAC-concentration range of 11×10^(-5) M to 30×10^(-5) M at a fixed FP- concentration of 1.0×10^(-5)M by the photon counting method.展开更多
Measurement of the average aggregate number of coaggregates(N_co)and evaluation Of the number of coaggregates([CoAg])in the region of increasing degree of aggregation shows that only N_co increases linearly with the c...Measurement of the average aggregate number of coaggregates(N_co)and evaluation Of the number of coaggregates([CoAg])in the region of increasing degree of aggregation shows that only N_co increases linearly with the concentration of the target molecules CE-In and BL-ol.展开更多
Average aggregate number of coaggregates(N_co)of CE-n or BL-n and the fluoresc- ence probe(Np-16)have been determined by using time-resolved fluorescence spectroscopy. Chain-length,hydroxy-group and chain-foldability ...Average aggregate number of coaggregates(N_co)of CE-n or BL-n and the fluoresc- ence probe(Np-16)have been determined by using time-resolved fluorescence spectroscopy. Chain-length,hydroxy-group and chain-foldability effects on the N_co have been discussed.展开更多
In this paper, we study optimal recovery （reconstruction） of functions on the sphere in the average case setting. We obtain the asymptotic orders of average sampling numbers of a Sobolev space on the sphere with a G...In this paper, we study optimal recovery （reconstruction） of functions on the sphere in the average case setting. We obtain the asymptotic orders of average sampling numbers of a Sobolev space on the sphere with a Gaussian measure in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞.展开更多
This paper proposes a multi-criteria decision-making (MCGDM) method based on the improved single-valued neutrosophic Hamacher weighted averaging (ISNHWA) operator and grey relational analysis (GRA) to overcome the lim...This paper proposes a multi-criteria decision-making (MCGDM) method based on the improved single-valued neutrosophic Hamacher weighted averaging (ISNHWA) operator and grey relational analysis (GRA) to overcome the limitations of present methods based on aggregation operators. First, the limitations of several existing single-valued neutrosophic weighted averaging aggregation operators (i.e. , the single-valued neutrosophic weighted averaging, single-valued neutrosophic weighted algebraic averaging, single-valued neutrosophic weighted Einstein averaging, single-valued neutrosophic Frank weighted averaging, and single-valued neutrosophic Hamacher weighted averaging operators), which can produce some indeterminate terms in the aggregation process, are discussed. Second, an ISNHWA operator was developed to overcome the limitations of existing operators. Third, the properties of the proposed operator, including idempotency, boundedness, monotonicity, and commutativity, were analyzed. Application examples confirmed that the ISNHWA operator and the proposed MCGDM method are rational and effective. The proposed improved ISNHWA operator and MCGDM method can overcome the indeterminate results in some special cases in existing single-valued neutrosophic weighted averaging aggregation operators and MCGDM methods.展开更多
The ordered weighted geometric averaging（OWGA） operator is extended to accommodate uncertain conditions where all input arguments take the forms of interval numbers. First, a possibility degree formula for the compa...The ordered weighted geometric averaging（OWGA） operator is extended to accommodate uncertain conditions where all input arguments take the forms of interval numbers. First, a possibility degree formula for the comparison between interval numbers is introduced. It is proved that the introduced formula is equivalent to the existing formulae, and also some desired properties of the possibility degree is presented. Secondly, the uncertain OWGA operator is investigated in which the associated weighting parameters cannot be specified, but value ranges can be obtained and the associated aggregated values of an uncertain OWGA operator are known. A linear objective-programming model is established; by solving this model, the associated weights vector of an uncertain OWGA operator can be determined, and also the estimated aggregated values of the alternatives can be obtained. Then the alternatives can be ranked by the comparison of the estimated aggregated values using the possibility degree formula. Finally, a numerical example is given to show the feasibility and effectiveness of the developed method.展开更多
In this paper, we deduce Wiener number of some connected subgraphs in tilings (4, 4, 4, 4) and (4, 6, 12), which are in Archimedean tilings. And compute their average distance.
The bounds are obtained for the average crosscap number. Let G be a graph which is not a tree. It is shown that the average crosscap number of G is not less than 2 β(G?1/2 β(G?1 β(G) and not larger than β(G). Furt...The bounds are obtained for the average crosscap number. Let G be a graph which is not a tree. It is shown that the average crosscap number of G is not less than 2 β(G?1/2 β(G?1 β(G) and not larger than β(G). Furthermore, we also describe the structure of the graphs which attain the bounds of the average crosscap number.展开更多
We study the behavior of some polynomial interior-point algorithms for solving random linear programming (LP) problems. We show that the average number of iterations of these algorithms, coupled with a finite terminat...We study the behavior of some polynomial interior-point algorithms for solving random linear programming (LP) problems. We show that the average number of iterations of these algorithms, coupled with a finite termination technique, is bounded above by O( n1.5). The random LP problem is Todd’s probabilistic model with the standard Gauss distribution.展开更多
基金supported by the National High-tech R&D Program(No.2017YFC0602100)the Natural Science Foundation of China(No.41374136)
文摘A map of the average atomic number of lunar rock and soil can be used to differentiate lithology and soil type on the lunar surface.This paper establishes a linear relationship between the average atomic number of lunar rock or soil and the flux of position annihilation radiation(0.512-Me V gamma-ray) from the lunar surface.The relationship is confirmed by Monte Carlo simulation with data from lunar rock or soil samples collected by Luna(Russia) and Apollo(USA) missions.A map of the average atomic number of the lunar rock and soil on the lunar surface has been derived from the Gamma-Ray Spectrometer data collected by Chang'e-1,an unmanned Chinese lunar-orbiting spacecraft.In the map,the higher average atomic numbers(ZA > 12.5),which are related to different types of basalt,are in the maria region;the highest ZA(13.2) readings are associated with Sinus Aestuum.The middle ZA(~12.1) regions,in the shape of irregular oval rings,are in West Oceanus Procellarum and Mare Frigoris,which seems to be consistent with the distribution of potassium,rare earth elements,and phosphorus as a unique feature on the lunar surface.The lower average atomic numbers(ZA < 11.5)are found to be correlated with the anorthosite on the far side of the Moon.
文摘The average aggregate number(N)of electrostatically stabilized aggregate(ESAg)composed of oppositely-charged long-chain molecules,i.e., sodium ω-[α-(nathphyl)ethoxyl]undecanoate(FP^-)and cetyltrimethyl ammonium chloride(CTAC),in aqueous solution at 25℃ has been measured to be 11 to 16 in the CTAC-concentration range of 11×10^(-5) M to 30×10^(-5) M at a fixed FP- concentration of 1.0×10^(-5)M by the photon counting method.
文摘Measurement of the average aggregate number of coaggregates(N_co)and evaluation Of the number of coaggregates([CoAg])in the region of increasing degree of aggregation shows that only N_co increases linearly with the concentration of the target molecules CE-In and BL-ol.
文摘Average aggregate number of coaggregates(N_co)of CE-n or BL-n and the fluoresc- ence probe(Np-16)have been determined by using time-resolved fluorescence spectroscopy. Chain-length,hydroxy-group and chain-foldability effects on the N_co have been discussed.
基金supported by the National Natural Science Foundation of China(No.11426179)the National Natural Science Foundation of China(Nos.10871132,11271263)+4 种基金the Key Scientific Research Fund of Xihua University(No.z1312624)the Foundation of Sichuan Educational Committee(No.14ZA0112)the Preeminent Youth Fund for School of Science in Xihua Universitythe Beijing Natural Science Foundation(No.1132001)BCMIIS
文摘In this paper, we study optimal recovery （reconstruction） of functions on the sphere in the average case setting. We obtain the asymptotic orders of average sampling numbers of a Sobolev space on the sphere with a Gaussian measure in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞.
文摘This paper proposes a multi-criteria decision-making (MCGDM) method based on the improved single-valued neutrosophic Hamacher weighted averaging (ISNHWA) operator and grey relational analysis (GRA) to overcome the limitations of present methods based on aggregation operators. First, the limitations of several existing single-valued neutrosophic weighted averaging aggregation operators (i.e. , the single-valued neutrosophic weighted averaging, single-valued neutrosophic weighted algebraic averaging, single-valued neutrosophic weighted Einstein averaging, single-valued neutrosophic Frank weighted averaging, and single-valued neutrosophic Hamacher weighted averaging operators), which can produce some indeterminate terms in the aggregation process, are discussed. Second, an ISNHWA operator was developed to overcome the limitations of existing operators. Third, the properties of the proposed operator, including idempotency, boundedness, monotonicity, and commutativity, were analyzed. Application examples confirmed that the ISNHWA operator and the proposed MCGDM method are rational and effective. The proposed improved ISNHWA operator and MCGDM method can overcome the indeterminate results in some special cases in existing single-valued neutrosophic weighted averaging aggregation operators and MCGDM methods.
基金The Technological Innovation Foundation of NanjingForestry University(No.163060033).
文摘The ordered weighted geometric averaging（OWGA） operator is extended to accommodate uncertain conditions where all input arguments take the forms of interval numbers. First, a possibility degree formula for the comparison between interval numbers is introduced. It is proved that the introduced formula is equivalent to the existing formulae, and also some desired properties of the possibility degree is presented. Secondly, the uncertain OWGA operator is investigated in which the associated weighting parameters cannot be specified, but value ranges can be obtained and the associated aggregated values of an uncertain OWGA operator are known. A linear objective-programming model is established; by solving this model, the associated weights vector of an uncertain OWGA operator can be determined, and also the estimated aggregated values of the alternatives can be obtained. Then the alternatives can be ranked by the comparison of the estimated aggregated values using the possibility degree formula. Finally, a numerical example is given to show the feasibility and effectiveness of the developed method.
文摘In this paper, we deduce Wiener number of some connected subgraphs in tilings (4, 4, 4, 4) and (4, 6, 12), which are in Archimedean tilings. And compute their average distance.
基金This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 60373030,10751013)
文摘The bounds are obtained for the average crosscap number. Let G be a graph which is not a tree. It is shown that the average crosscap number of G is not less than 2 β(G?1/2 β(G?1 β(G) and not larger than β(G). Furthermore, we also describe the structure of the graphs which attain the bounds of the average crosscap number.
文摘We study the behavior of some polynomial interior-point algorithms for solving random linear programming (LP) problems. We show that the average number of iterations of these algorithms, coupled with a finite termination technique, is bounded above by O( n1.5). The random LP problem is Todd’s probabilistic model with the standard Gauss distribution.
