This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An...This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.展开更多
Characterizing the gap eigenmode of shear Alfv′en waves(SAWs) and its interaction with energetic ions is important to the success of magnetically confined fusion. Previous studies have reported an experimental observ...Characterizing the gap eigenmode of shear Alfv′en waves(SAWs) and its interaction with energetic ions is important to the success of magnetically confined fusion. Previous studies have reported an experimental observation of the spectral gap of SAW on the on Large Plasma Device(LAPD)(Zhang et al. 2008 Phys. Plasmas 15 012103), a linear large plasma device(Gekelman et al. 1991 Rev. Sci. Instrum. 62 2875) possessing easier diagnostic access and lower cost compared with traditional fusion devices, and analytical theory and numerical gap eigenmode using ideal conditions(Chang 2014 Ph.D Thesis at Australian National University). To guide experimental implementation, the present work models the gap eigenmode of SAWs using exact LAPD parameters. A full picture of the wave field for previous experiment reveals that the previously observed spectral gap is not global but an axially local result. To form a global spectral gap, the number of magnetic mirrors has to be increased and stronger static magnetic field makes it clearer. Such a spectral gap is obtained for the magnetic field of B0(z) = 1.2 + 0.6 cos[2π(z-33.68)/3.63] with 7.74-m magnetic beach. By introducing two types of local defects(corresponding to Eθ(z0) = 0 and E’θ(z0) = 0 respectively), odd-parity and even-parity discrete eigenmodes are formed clearly inside the gap. The strength of these gap eigenmodes decreases significantly with collision frequency, which is consistent with previous studies. Parameter scans show that these gap eigenmodes can be even formed successfully for the field strength of B0(z) = 0.2 + 0.1 cos[2π(z-33.68)/3.63] and with only four magnetic mirrors, which are achievable by the LAPD at its present status. This work can serve as a strong motivation and direct reference for the experimental implementation of the gap eigenmode of SAWs on the LAPD and other linear plasma devices.展开更多
A novel soluble π-conjugated polymer, poly [（3-acetylpyrrole-2, 5-diyl） p-（N, N-dimethylamino） azobenzylidene] （PAPDMAABE）, was synthesized by condensation of 3-acetylpyrrole with 4-aldehyde-4＇-dimethylaminoaz...A novel soluble π-conjugated polymer, poly [（3-acetylpyrrole-2, 5-diyl） p-（N, N-dimethylamino） azobenzylidene] （PAPDMAABE）, was synthesized by condensation of 3-acetylpyrrole with 4-aldehyde-4＇-dimethylaminoazobenzene （ADMAA）. The chemical structure of PAPDMAABE was characterized by Fourier transform infrared spectroscopy （FTIR）, ^1H-NMR, and UV-Vis-NIR spectra. Transmission electron microscope （TEM） analysis for PAPDMAABE indicates that part of PAPDMAABE is in crystal state, due to the short-range order of the polymer. Thermogravimetric analysis （TGA） curve shows that the polymer has good thermal stability and its decomposition temperature is 248℃. The optical band gap of PAPDMAABE obtained from the optical absorption spectrum is about 1.73 eV. The resonant third-order nonlinear optical property of PAPDMAABE at 532 nm was studied using degenerate four-wave mixing （DFWM） technique. The resonant third-order nonlinear optical susceptibility of the polymer is about 7.48×10^-8 esu.展开更多
A novel soluble π-conjugated polymer, poly[(3-octanoylpyrrole-2,5-diyl)-p-(N,N-dimethylamino)benzylidene](POPDMABE), was synthesized firstly by the condensation of 3-octanoylpyrrole with para-dimethylaminobenzaldehyd...A novel soluble π-conjugated polymer, poly[(3-octanoylpyrrole-2,5-diyl)-p-(N,N-dimethylamino)benzylidene](POPDMABE), was synthesized firstly by the condensation of 3-octanoylpyrrole with para-dimethylaminobenzaldehyde. The chemical structure of the polymer was characterized by FTIR and 1H NMR spectrometries. The polymer is a potential nonlinear optical(NLO) material. According to the function of optical forbidden band gap(E_g) and photon energy(hν), the optical forbidden band gaps of the polymer before and after ion implantation were calculated. The resonant third-order nonlinear optical properties of POPDMABE before and after ion implantation were also studied by using the degenerate four-wave mixing(DFWM) technique at 532 nm. When the energy is 25 keV and the dose is 2.2×10 17 ions/cm 2, the {polymer′s} optical forbidden band gap is about 1.63 eV which is smaller than that of the non-implanted sample(1.98 eV) and the resonant third-order NLO susceptibility of POPDMABE is about 4.3×10 -7 esu, 1 order of magnitude higher than that of the non-implanted sample(4.1×10 -8 esu). The results show that nitrogen ion implantation is an effective method to improve the resonant third-order NLO property of the polymer.展开更多
Porous Si3N4–Si3N4 composite ceramics were fabricated by 3D printing combined with low-pressure chemical vapor infiltration(CVI).This technique could effectively improve the designability of porous Si3N4 ceramics and...Porous Si3N4–Si3N4 composite ceramics were fabricated by 3D printing combined with low-pressure chemical vapor infiltration(CVI).This technique could effectively improve the designability of porous Si3N4 ceramics and optimize the mechanical and dielectric properties.The effects of process parameters including the deposition time and heat treatment on the microstructure and properties of porous Si3N4–Si3N4 composite ceramics were studied.The study highlights following:When CVI processing time was increased from 0 to 12 h,the porosity decreased from68.65%to 26.07%and the density increased from 0.99 to 2.02 g/cm3.At the same time,the dielectric constant gradually increased from 1.72 to 3.60;however,the dielectric loss always remained less than0.01,indicating the excellent electromagnetic(EM)wave-transparent performance of porous Si3N4–Si3N4 composite ceramics.The maximum flexural strength of 47±2 MPa was achieved when the deposition time attained 6 h.After heat treatment,the porosity increased from 26.07%to 36.02%and the dielectric constant got a slight increase from 3.60 to 3.70 with the dielectric loss still maintaining lower than 0.01.It has been demonstrated that the porous Si3N4–Si3N4 composite ceramics are a promising structural and EM wave-transparent material suitable for high temperature service.展开更多
Background Fish oil, rich in long-chain n-3 PUFAs, EPA and DHA, are known to reduce various risk factors for CAD1-3. However, conclusive regarding the benefits of n-3 PUFAs on arterial stiffness, a risk factor for CAD...Background Fish oil, rich in long-chain n-3 PUFAs, EPA and DHA, are known to reduce various risk factors for CAD1-3. However, conclusive regarding the benefits of n-3 PUFAs on arterial stiffness, a risk factor for CAD, has not yet been established. Methods In the placebo-controlled, single-blind, prospective study, 60 subjects were randomly allocated to consume daily nutritional supplement of 3 gram capsules containing either placebo （soybean oil） or fish oil, EPA （540 mg） ＋ DHA （360 mg） for 12 weeks. Anthropometry, pulse wave velocity （PWV） and polyunsaturated fatty acid were measured and compared before and after study therapy. Results After study therapy, PWV reduced significantly in the fish oil group compared with the placebo group （-8 ± 18 cm/s vs 39 ± 19 cm/s, P 〈 0.05）. Conclusions Fish oil shows beneficial effect on improving arterial stiffness in patients with coronary disease.展开更多
文摘This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.
基金Project supported by the National Natural Science Foundation of China(Grant No.11405271)the China Postdoctoral Science Foundation(Grant No.2017M612901)+4 种基金the Fund from Chongqing Science and Technology Commission(Grant No.cstc2017jcyjAX0047)Chongqing Postdoctoral Special Foundation(Grant No.Xm2017109)the Fundamental Research Funds for Central Universities,China(Grant No.YJ201796)the Pre-research Key Laboratory Fund for Equipment(Grant No.61422070306)the Fund from the Laboratory of Advanced Space Propulsion(Grant No.LabASP-2017-10)
文摘Characterizing the gap eigenmode of shear Alfv′en waves(SAWs) and its interaction with energetic ions is important to the success of magnetically confined fusion. Previous studies have reported an experimental observation of the spectral gap of SAW on the on Large Plasma Device(LAPD)(Zhang et al. 2008 Phys. Plasmas 15 012103), a linear large plasma device(Gekelman et al. 1991 Rev. Sci. Instrum. 62 2875) possessing easier diagnostic access and lower cost compared with traditional fusion devices, and analytical theory and numerical gap eigenmode using ideal conditions(Chang 2014 Ph.D Thesis at Australian National University). To guide experimental implementation, the present work models the gap eigenmode of SAWs using exact LAPD parameters. A full picture of the wave field for previous experiment reveals that the previously observed spectral gap is not global but an axially local result. To form a global spectral gap, the number of magnetic mirrors has to be increased and stronger static magnetic field makes it clearer. Such a spectral gap is obtained for the magnetic field of B0(z) = 1.2 + 0.6 cos[2π(z-33.68)/3.63] with 7.74-m magnetic beach. By introducing two types of local defects(corresponding to Eθ(z0) = 0 and E’θ(z0) = 0 respectively), odd-parity and even-parity discrete eigenmodes are formed clearly inside the gap. The strength of these gap eigenmodes decreases significantly with collision frequency, which is consistent with previous studies. Parameter scans show that these gap eigenmodes can be even formed successfully for the field strength of B0(z) = 0.2 + 0.1 cos[2π(z-33.68)/3.63] and with only four magnetic mirrors, which are achievable by the LAPD at its present status. This work can serve as a strong motivation and direct reference for the experimental implementation of the gap eigenmode of SAWs on the LAPD and other linear plasma devices.
基金the National Natural Science Foundation of China for financial support of this work(No.60277002).
文摘A novel soluble π-conjugated polymer, poly [（3-acetylpyrrole-2, 5-diyl） p-（N, N-dimethylamino） azobenzylidene] （PAPDMAABE）, was synthesized by condensation of 3-acetylpyrrole with 4-aldehyde-4＇-dimethylaminoazobenzene （ADMAA）. The chemical structure of PAPDMAABE was characterized by Fourier transform infrared spectroscopy （FTIR）, ^1H-NMR, and UV-Vis-NIR spectra. Transmission electron microscope （TEM） analysis for PAPDMAABE indicates that part of PAPDMAABE is in crystal state, due to the short-range order of the polymer. Thermogravimetric analysis （TGA） curve shows that the polymer has good thermal stability and its decomposition temperature is 248℃. The optical band gap of PAPDMAABE obtained from the optical absorption spectrum is about 1.73 eV. The resonant third-order nonlinear optical property of PAPDMAABE at 532 nm was studied using degenerate four-wave mixing （DFWM） technique. The resonant third-order nonlinear optical susceptibility of the polymer is about 7.48×10^-8 esu.
文摘A novel soluble π-conjugated polymer, poly[(3-octanoylpyrrole-2,5-diyl)-p-(N,N-dimethylamino)benzylidene](POPDMABE), was synthesized firstly by the condensation of 3-octanoylpyrrole with para-dimethylaminobenzaldehyde. The chemical structure of the polymer was characterized by FTIR and 1H NMR spectrometries. The polymer is a potential nonlinear optical(NLO) material. According to the function of optical forbidden band gap(E_g) and photon energy(hν), the optical forbidden band gaps of the polymer before and after ion implantation were calculated. The resonant third-order nonlinear optical properties of POPDMABE before and after ion implantation were also studied by using the degenerate four-wave mixing(DFWM) technique at 532 nm. When the energy is 25 keV and the dose is 2.2×10 17 ions/cm 2, the {polymer′s} optical forbidden band gap is about 1.63 eV which is smaller than that of the non-implanted sample(1.98 eV) and the resonant third-order NLO susceptibility of POPDMABE is about 4.3×10 -7 esu, 1 order of magnitude higher than that of the non-implanted sample(4.1×10 -8 esu). The results show that nitrogen ion implantation is an effective method to improve the resonant third-order NLO property of the polymer.
基金supported by the Chinese National Foundation for Natural Sciences under Contract (Nos. 51602258 and 51672217)111 Project of China (B08040)
文摘Porous Si3N4–Si3N4 composite ceramics were fabricated by 3D printing combined with low-pressure chemical vapor infiltration(CVI).This technique could effectively improve the designability of porous Si3N4 ceramics and optimize the mechanical and dielectric properties.The effects of process parameters including the deposition time and heat treatment on the microstructure and properties of porous Si3N4–Si3N4 composite ceramics were studied.The study highlights following:When CVI processing time was increased from 0 to 12 h,the porosity decreased from68.65%to 26.07%and the density increased from 0.99 to 2.02 g/cm3.At the same time,the dielectric constant gradually increased from 1.72 to 3.60;however,the dielectric loss always remained less than0.01,indicating the excellent electromagnetic(EM)wave-transparent performance of porous Si3N4–Si3N4 composite ceramics.The maximum flexural strength of 47±2 MPa was achieved when the deposition time attained 6 h.After heat treatment,the porosity increased from 26.07%to 36.02%and the dielectric constant got a slight increase from 3.60 to 3.70 with the dielectric loss still maintaining lower than 0.01.It has been demonstrated that the porous Si3N4–Si3N4 composite ceramics are a promising structural and EM wave-transparent material suitable for high temperature service.
文摘Background Fish oil, rich in long-chain n-3 PUFAs, EPA and DHA, are known to reduce various risk factors for CAD1-3. However, conclusive regarding the benefits of n-3 PUFAs on arterial stiffness, a risk factor for CAD, has not yet been established. Methods In the placebo-controlled, single-blind, prospective study, 60 subjects were randomly allocated to consume daily nutritional supplement of 3 gram capsules containing either placebo （soybean oil） or fish oil, EPA （540 mg） ＋ DHA （360 mg） for 12 weeks. Anthropometry, pulse wave velocity （PWV） and polyunsaturated fatty acid were measured and compared before and after study therapy. Results After study therapy, PWV reduced significantly in the fish oil group compared with the placebo group （-8 ± 18 cm/s vs 39 ± 19 cm/s, P 〈 0.05）. Conclusions Fish oil shows beneficial effect on improving arterial stiffness in patients with coronary disease.
