Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal ...Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal triangle elements and pascal matrix formation, etc. This paper explains about its functions and properties of N-Summet-k. The result of variation between N and k is shown in tabulation.展开更多
Ionization of atoms in counter-rotating and co-rotating bicircular laser fields is studied using the S-matrix theory in both length and velocity gauges.We show that for both the bicircular fields,ionization rates are ...Ionization of atoms in counter-rotating and co-rotating bicircular laser fields is studied using the S-matrix theory in both length and velocity gauges.We show that for both the bicircular fields,ionization rates are enhanced when the two circularly polarized lights have comparable intensities.In addition,the curves of ionization rate versus the field amplitude ratio of the two colors for counter-rotating and co-rotating fields coincide with each other in the length gauge case at the total laser intensity 5×10^14 W/cm^2,which agrees with the experimental observation.Moreover,the degree of the coincidence between the ionization rate curves of the two bicircular fields decreases with the increasing field amplitude ratio and decreasing total laser intensity.With the help of the ADK theory,the above characteristics of the ionization rate curves can be well interpreted,which is related to the transition from the tunneling to multiphoton ionization mechanism.展开更多
Mixed matrix hollow fiber membranes（MMHFMs）filled with metal-organic frameworks（MOFs）have great potential for energy-efficient gas separation processes,but the major hurdle is polymer/MOFs interfacial defects and ...Mixed matrix hollow fiber membranes（MMHFMs）filled with metal-organic frameworks（MOFs）have great potential for energy-efficient gas separation processes,but the major hurdle is polymer/MOFs interfacial defects and membrane plasticization.Herein,lab-synthesized MIL-53 was post-functionalized by aminosilane grafting and subsequently incorporated into Ultem-1000 polymer matrix to fabricate high performance MMHFMs.SEM,DLS,XRD and TGA were performed to characterize silane-modified MIL-53（S-MIL-53）and prepared MMHFMs.Moreover,the effect of MOFs loading was systematically investigated first;then gas separation performance of MMHFMs for pure and mixed gas was evaluated under different pressures.MMHFMs containing post-functionalized S-MIL-53 achieved remarkable gas permeation properties which was better than model predictions.Compared to pure HFMs,CO2permeance of MMHFM loaded with 15%S-MIL-53 increased by 157%accompanying with 40%increase for CO2/N2selectivity,which outperformed the MMHFM filled with naked MIL-53.The pure and mixed gas permeation measurements with elevated feed pressure indicated that incorporation of S-MIL-53 also increased the resistance against CO2plasticization.This work reveals that post-modified MOFs embedded in MMHFMs facilitate the improvement of gas separation performance and suppression of membrane plasticization.展开更多
Two hundred years after James Parkinson first described the cardinal motor symptoms of the disorder that would later bear his name,there is still an irrefutable need for a therapy that targets the underlying pathophys...Two hundred years after James Parkinson first described the cardinal motor symptoms of the disorder that would later bear his name,there is still an irrefutable need for a therapy that targets the underlying pathophysiology of the disease and not solely its symptoms.展开更多
This paper deals with S-matrix, born first approximation, amplitude, and differential cross-section (DCS), using Volkov function and Taylor series expansion in laser field, scattering. Equation (30) copes-with DCS and...This paper deals with S-matrix, born first approximation, amplitude, and differential cross-section (DCS), using Volkov function and Taylor series expansion in laser field, scattering. Equation (30) copes-with DCS and Equation (36) deals with S-matrix, with different parameters, moreover, both equations contain real and imaginary parts. The DCS increases with increasing angle and polarizabilities, constant with dipole distance for both emission and absorption of single-photon. The DCS for both emission and absorption is responded to low incidence energy (30 eV - 60 eV) and photon energy (15 eV) while at high energy only emission and absorption are responded for DCS. The DCS between absorption and emission of a photon with angle variation, dipole distance, and atomic polarizabilities was found 1.098 a.u.<sup>2</sup> and at high incidence, energies were found 0.1 a.u.<sup>2</sup>.展开更多
In order to reduce the amount of volumetric shrinkage that occurs in dental composites as a result of curing,a new kind of dental matrix resin combining bisphenol-S-bis（3-meth acry late-2-hydroxy propyl）ether（BisS-...In order to reduce the amount of volumetric shrinkage that occurs in dental composites as a result of curing,a new kind of dental matrix resin combining bisphenol-S-bis（3-meth acry late-2-hydroxy propyl）ether（BisS-GMA） with the expanding monomer unsaturated spiro orthoesters 2-methylene-1,4,6-trispiro[4,4] nonane （SOE） was prepared,with triethylene glycol dimethacrylate （TEGDMA） as diluent.CQ （camphorquinone） of 1wt% and DMAEMA （2-（dimethylamino） ethyl meth acrylate） of 2wt% were used as photoinitiation system to initiate the copolymerization of the matrix resins.The performance including volumetric shrinkage,degree of conversion and condition of the ring-opening reaction of SOE,as well as curing time and the tensile bond strength were investigated respectively by the dilatometer,Fourier transfer infrared,the universal testing machine,and so on.The ring-opening polymerization of SOE occurred.Meanwhile,the obtain copolymers were crosslinked.The matrix resin containing BisS-GMA and SOE showed a reduced amount of volumetric shrinkage at 1.52%,which is a promising strategy for obtaining a polymer with a low amount of volumetric shrinkage.Furthermore,the other properties were not compromised.展开更多
文摘Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal triangle elements and pascal matrix formation, etc. This paper explains about its functions and properties of N-Summet-k. The result of variation between N and k is shown in tabulation.
基金Project supported by the Key Laboratory Project of Computational Physics of National Defense Science and Technology of China(Grant No.6142A05180401)the National Key Program for S&T Research and Development of China(Grant Nos.2019YFA0307700 and 2016YFA0401100)the National Natural Science Foundation of China(Grant Nos.11847307,11425414,11504215,11774361,and 11874246).
文摘Ionization of atoms in counter-rotating and co-rotating bicircular laser fields is studied using the S-matrix theory in both length and velocity gauges.We show that for both the bicircular fields,ionization rates are enhanced when the two circularly polarized lights have comparable intensities.In addition,the curves of ionization rate versus the field amplitude ratio of the two colors for counter-rotating and co-rotating fields coincide with each other in the length gauge case at the total laser intensity 5×10^14 W/cm^2,which agrees with the experimental observation.Moreover,the degree of the coincidence between the ionization rate curves of the two bicircular fields decreases with the increasing field amplitude ratio and decreasing total laser intensity.With the help of the ADK theory,the above characteristics of the ionization rate curves can be well interpreted,which is related to the transition from the tunneling to multiphoton ionization mechanism.
基金the financial support from the National Natural Science Foundation of China(No.21436009)
文摘Mixed matrix hollow fiber membranes（MMHFMs）filled with metal-organic frameworks（MOFs）have great potential for energy-efficient gas separation processes,but the major hurdle is polymer/MOFs interfacial defects and membrane plasticization.Herein,lab-synthesized MIL-53 was post-functionalized by aminosilane grafting and subsequently incorporated into Ultem-1000 polymer matrix to fabricate high performance MMHFMs.SEM,DLS,XRD and TGA were performed to characterize silane-modified MIL-53（S-MIL-53）and prepared MMHFMs.Moreover,the effect of MOFs loading was systematically investigated first;then gas separation performance of MMHFMs for pure and mixed gas was evaluated under different pressures.MMHFMs containing post-functionalized S-MIL-53 achieved remarkable gas permeation properties which was better than model predictions.Compared to pure HFMs,CO2permeance of MMHFM loaded with 15%S-MIL-53 increased by 157%accompanying with 40%increase for CO2/N2selectivity,which outperformed the MMHFM filled with naked MIL-53.The pure and mixed gas permeation measurements with elevated feed pressure indicated that incorporation of S-MIL-53 also increased the resistance against CO2plasticization.This work reveals that post-modified MOFs embedded in MMHFMs facilitate the improvement of gas separation performance and suppression of membrane plasticization.
基金supported by the European Union Horizon 2020 Programme(H2020-MSCA-ITN-2015) under the Marie Sklodowska-Curie Innovative Training NetworksGrant Agreement No.676408,Science Foundation Ireland(11/RFP/NES/3183)through a postgraduate scholarship from the Irish Research Council to Niamh Moriarty
文摘Two hundred years after James Parkinson first described the cardinal motor symptoms of the disorder that would later bear his name,there is still an irrefutable need for a therapy that targets the underlying pathophysiology of the disease and not solely its symptoms.
文摘This paper deals with S-matrix, born first approximation, amplitude, and differential cross-section (DCS), using Volkov function and Taylor series expansion in laser field, scattering. Equation (30) copes-with DCS and Equation (36) deals with S-matrix, with different parameters, moreover, both equations contain real and imaginary parts. The DCS increases with increasing angle and polarizabilities, constant with dipole distance for both emission and absorption of single-photon. The DCS for both emission and absorption is responded to low incidence energy (30 eV - 60 eV) and photon energy (15 eV) while at high energy only emission and absorption are responded for DCS. The DCS between absorption and emission of a photon with angle variation, dipole distance, and atomic polarizabilities was found 1.098 a.u.<sup>2</sup> and at high incidence, energies were found 0.1 a.u.<sup>2</sup>.
基金Supported by the National Natural Science Foundation of China (31600299)the Youth Science and Technology Nova Program of Shaanxi Province,China (2022KJXX-01)the Scientific Research Program Funded by Yunnan Provincial Education Department,China (2022J0949)。
基金Funded by the National Natural Science Foundation of China(No.50673065)
文摘In order to reduce the amount of volumetric shrinkage that occurs in dental composites as a result of curing,a new kind of dental matrix resin combining bisphenol-S-bis（3-meth acry late-2-hydroxy propyl）ether（BisS-GMA） with the expanding monomer unsaturated spiro orthoesters 2-methylene-1,4,6-trispiro[4,4] nonane （SOE） was prepared,with triethylene glycol dimethacrylate （TEGDMA） as diluent.CQ （camphorquinone） of 1wt% and DMAEMA （2-（dimethylamino） ethyl meth acrylate） of 2wt% were used as photoinitiation system to initiate the copolymerization of the matrix resins.The performance including volumetric shrinkage,degree of conversion and condition of the ring-opening reaction of SOE,as well as curing time and the tensile bond strength were investigated respectively by the dilatometer,Fourier transfer infrared,the universal testing machine,and so on.The ring-opening polymerization of SOE occurred.Meanwhile,the obtain copolymers were crosslinked.The matrix resin containing BisS-GMA and SOE showed a reduced amount of volumetric shrinkage at 1.52%,which is a promising strategy for obtaining a polymer with a low amount of volumetric shrinkage.Furthermore,the other properties were not compromised.
