In this paper,we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE).The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Rie...In this paper,we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE).The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of orderβ∈(1,2]. We propose an implicit finite difference approximation for RSFRDE.The stability and convergence of the finite difference approximations are analyzed.Numerical results are found in good agreement with the theoretical analysis.展开更多
Fractional calculus and special functions have contributed a lot to mathematical physics and its various branches. The great use of mathematical physics in distinguished astrophysical problems has attracted astronomer...Fractional calculus and special functions have contributed a lot to mathematical physics and its various branches. The great use of mathematical physics in distinguished astrophysical problems has attracted astronomers and physicists to pay more attention to available mathematical tools that can be widely used in solving several problems of astrophysics/physics. In view of the great importance and usefulness of kinetic equations in certain astrophysical problems, the authors derive a generalized fractional kinetic equation involving the Lorenzo-Hartley function, a generalized function for fractional calculus. The fractional kinetic equation discussed here can be used to investigate a wide class of known （and possibly also new） fractional kinetic equations, hitherto scattered in the literature. A compact and easily computable solution is established in terms of the Lorenzo-Hartley function. Special cases, involving the generalized Mittag-Leffler function and the R-function, are considered. The obtained results imply the known results more precisely.展开更多
The solid-phase reaction of sapphire (Al2O3) substrates and spin-coated copper nitrate films was studied. X-ray diffraction analysis revealed that a CuO fraction was observed by annealing at temperatures higher than ...The solid-phase reaction of sapphire (Al2O3) substrates and spin-coated copper nitrate films was studied. X-ray diffraction analysis revealed that a CuO fraction was observed by annealing at temperatures higher than 800℃. In addition, crystalline CuAlO2 was formed at annealing temperatures in the range of 900℃ – 1000℃ by solid-phase reaction of the spin-coated films and sapphire substrate. Crystalline CuAlO2 was formed by annealing at 1000℃ for 5 - 10 h, and CuAl2O4 was formed by annealing at 1000℃ for 15 h. When annealing under N2 flow, Cu2O was observed rather than CuAlO2. For a sample annealed in air at 1000℃ for 5 h, X-ray photoelectron spectroscopy measurements at various depths from surface revealed that Cu2+ ions are located around the surface, which suggests that the CuO fraction is present near the surface while the CuAlO2 fraction is located at greater depths from the surface of the samples. The depth profile of the sample suggests that there is no pure CuAlO2 layer in the sample, but that crystalline CuAlO2 is present in the sample as a mixture with CuO and Al2O3.展开更多
目的:探究30%超分子水杨酸联合小光斑点阵CO_(2)激光治疗轻中度寻常痤疮的有效性和安全性。方法:选取2022年11月-2023年6月就诊于吉林大学中日联谊医院30例面部轻、中度寻常痤疮患者,以患者面部矢状线为界,按照随机数表将患者的双侧面...目的:探究30%超分子水杨酸联合小光斑点阵CO_(2)激光治疗轻中度寻常痤疮的有效性和安全性。方法:选取2022年11月-2023年6月就诊于吉林大学中日联谊医院30例面部轻、中度寻常痤疮患者,以患者面部矢状线为界,按照随机数表将患者的双侧面部随机分为对照侧和观察侧。对照侧(n=30),给予30%超分子水杨酸治疗(每4周治疗1次);观察侧(n=30),给予小光斑点阵CO_(2)激光治疗后即刻30%超分子水杨酸治疗(每4周治疗1次)。通过拍照、皮肤检测仪、皮损计数和痤疮综合分级系统(The global acne grading system,GAGS)评分等评估治疗的有效性;通过皮损清除率判定临床疗效,同时观察不良反应以评估安全性。治疗结束后12周对患者进行随访,评估复发情况。结果:治疗12周后,患者观察侧的临床疗效优于对照侧(P<0.05);观察侧的皮损清除效果明显优于对照侧(P<0.001);观察侧的GAGS评分改善程度明显优于对照侧(P<0.001)。治疗期间两侧均未出现严重不良反应。结论:30%超分子水杨酸联合小光斑点阵CO_(2)激光疗法对清除轻中度痤疮皮损优于30%超分子水杨酸单一治疗,具有见效快、安全性高、操作简单、患者满意度高等优点,且不增加患者相关不良反应。展开更多
针对磁化焙烧冷却过程开展了研究,考察了磁铁矿氧化反应分数和反应速率的变化规律,并采用模型匹配法进行了氧化动力学分析.结果表明:磁化焙烧冷却过程中,氧化温度对反应分数和反应速率均有着显著的影响;相同氧化时间下,反应分数和反应...针对磁化焙烧冷却过程开展了研究,考察了磁铁矿氧化反应分数和反应速率的变化规律,并采用模型匹配法进行了氧化动力学分析.结果表明:磁化焙烧冷却过程中,氧化温度对反应分数和反应速率均有着显著的影响;相同氧化时间下,反应分数和反应速率随氧化温度的升高而增加;不同氧化温度下,反应分数和反应速率随反应时间变化呈现出相同的变化规律;磁铁矿氧化过程动力学机理函数为n=4的AvramiErofee方程,氧化反应的表观活化能为135. 2 k J·mol,指前因子为6. 19×1010min-1.展开更多
基金The authors gratefully acknowledge the support of the National Natural Science Foundation of China under Grant 10271098 the Australian Research Council grant LP0348653.
文摘In this paper,we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE).The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of orderβ∈(1,2]. We propose an implicit finite difference approximation for RSFRDE.The stability and convergence of the finite difference approximations are analyzed.Numerical results are found in good agreement with the theoretical analysis.
文摘Fractional calculus and special functions have contributed a lot to mathematical physics and its various branches. The great use of mathematical physics in distinguished astrophysical problems has attracted astronomers and physicists to pay more attention to available mathematical tools that can be widely used in solving several problems of astrophysics/physics. In view of the great importance and usefulness of kinetic equations in certain astrophysical problems, the authors derive a generalized fractional kinetic equation involving the Lorenzo-Hartley function, a generalized function for fractional calculus. The fractional kinetic equation discussed here can be used to investigate a wide class of known （and possibly also new） fractional kinetic equations, hitherto scattered in the literature. A compact and easily computable solution is established in terms of the Lorenzo-Hartley function. Special cases, involving the generalized Mittag-Leffler function and the R-function, are considered. The obtained results imply the known results more precisely.
文摘The solid-phase reaction of sapphire (Al2O3) substrates and spin-coated copper nitrate films was studied. X-ray diffraction analysis revealed that a CuO fraction was observed by annealing at temperatures higher than 800℃. In addition, crystalline CuAlO2 was formed at annealing temperatures in the range of 900℃ – 1000℃ by solid-phase reaction of the spin-coated films and sapphire substrate. Crystalline CuAlO2 was formed by annealing at 1000℃ for 5 - 10 h, and CuAl2O4 was formed by annealing at 1000℃ for 15 h. When annealing under N2 flow, Cu2O was observed rather than CuAlO2. For a sample annealed in air at 1000℃ for 5 h, X-ray photoelectron spectroscopy measurements at various depths from surface revealed that Cu2+ ions are located around the surface, which suggests that the CuO fraction is present near the surface while the CuAlO2 fraction is located at greater depths from the surface of the samples. The depth profile of the sample suggests that there is no pure CuAlO2 layer in the sample, but that crystalline CuAlO2 is present in the sample as a mixture with CuO and Al2O3.
文摘目的:探究30%超分子水杨酸联合小光斑点阵CO_(2)激光治疗轻中度寻常痤疮的有效性和安全性。方法:选取2022年11月-2023年6月就诊于吉林大学中日联谊医院30例面部轻、中度寻常痤疮患者,以患者面部矢状线为界,按照随机数表将患者的双侧面部随机分为对照侧和观察侧。对照侧(n=30),给予30%超分子水杨酸治疗(每4周治疗1次);观察侧(n=30),给予小光斑点阵CO_(2)激光治疗后即刻30%超分子水杨酸治疗(每4周治疗1次)。通过拍照、皮肤检测仪、皮损计数和痤疮综合分级系统(The global acne grading system,GAGS)评分等评估治疗的有效性;通过皮损清除率判定临床疗效,同时观察不良反应以评估安全性。治疗结束后12周对患者进行随访,评估复发情况。结果:治疗12周后,患者观察侧的临床疗效优于对照侧(P<0.05);观察侧的皮损清除效果明显优于对照侧(P<0.001);观察侧的GAGS评分改善程度明显优于对照侧(P<0.001)。治疗期间两侧均未出现严重不良反应。结论:30%超分子水杨酸联合小光斑点阵CO_(2)激光疗法对清除轻中度痤疮皮损优于30%超分子水杨酸单一治疗,具有见效快、安全性高、操作简单、患者满意度高等优点,且不增加患者相关不良反应。
文摘针对磁化焙烧冷却过程开展了研究,考察了磁铁矿氧化反应分数和反应速率的变化规律,并采用模型匹配法进行了氧化动力学分析.结果表明:磁化焙烧冷却过程中,氧化温度对反应分数和反应速率均有着显著的影响;相同氧化时间下,反应分数和反应速率随氧化温度的升高而增加;不同氧化温度下,反应分数和反应速率随反应时间变化呈现出相同的变化规律;磁铁矿氧化过程动力学机理函数为n=4的AvramiErofee方程,氧化反应的表观活化能为135. 2 k J·mol,指前因子为6. 19×1010min-1.
