In this paper,we study the blow-up of solutions to a semilinear double-wave equation with nonlinearity of derivative type.By using the iteration method and the differential inequality techniques,we can get the estimat...In this paper,we study the blow-up of solutions to a semilinear double-wave equation with nonlinearity of derivative type.By using the iteration method and the differential inequality techniques,we can get the estimates of the lifespan and the blow-up of solutions in the subcritical case under some assumptions.展开更多
p-Menthane type monoterpene derivatives were identified as bio-based compounds with high herbicidal activities. In order to search novel p-menthane type monoterpene derivatives in good performance, a series of novel c...p-Menthane type monoterpene derivatives were identified as bio-based compounds with high herbicidal activities. In order to search novel p-menthane type monoterpene derivatives in good performance, a series of novel cis-p-menthane type Schiff base derivatives were designed and synthesized. All target products were easily available novel compounds and characterized by FT-IR,^1H NMR,^13 C NMR and ESI＋-MS. Their pre-emergence herbicidal activities against annual ryegrass were evaluated. The bioassays indicated that most of the target compounds displayed excellent herbicidal activities in pre-emergence treatment.展开更多
In this paper,we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type.By using methods of an iteration argument and di erential inequalities,we obtain the blow-...In this paper,we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type.By using methods of an iteration argument and di erential inequalities,we obtain the blow-up result for the semi-linear wave equation when the exponent of p is under certain conditions.Meanwhile,we derive an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear wave equation.展开更多
Let A be a unital^(*)-algebra with the unit I and a nontrivial projection P∈A.Suppose that A satisfies XAP=0 implies X=0 and XA(I-P)=0 implies X=0.In this paper,we prove thatΦis a nonlinear A^(*)B+B^(*)A type deriva...Let A be a unital^(*)-algebra with the unit I and a nontrivial projection P∈A.Suppose that A satisfies XAP=0 implies X=0 and XA(I-P)=0 implies X=0.In this paper,we prove thatΦis a nonlinear A^(*)B+B^(*)A type derivation on A if and only ifΦis an additive^(*)-derivation.This is then applied to prime^(*)-algebra,von Neumann algebras with no central summands of type I1.factor von Neumann algebras and standard operator algebras.展开更多
Cadmium(II)-based metal–organic frameworks(MOFs)have been widely investigated for fluorescence sensing due to their chemical stability and tunable optical properties.However,how to precisely improve their selectivity...Cadmium(II)-based metal–organic frameworks(MOFs)have been widely investigated for fluorescence sensing due to their chemical stability and tunable optical properties.However,how to precisely improve their selectivity and sensitivity to the target analytes is a key issue to be addressed.In this work,a photoactive MOF(PMOF)exhibiting specific cation fluorescence sensing and photochromism was constructed using Cd2+and di-lophine based tetracarboxylic acid with D–A–D configuration.The effective combination of two components can form a stable porous framework with multiple electron transfer paths such as short-range electron transport in ligands and metal-to-ligand charge transfer(MLCT).The Cd-MOF exhibits strong absorption in the visible light range of 400–450 nm and strong fluorescence emission at 475 nm.Theoretical calculations show that the absorption and emission mainly originate from charge transfer between the metal and the ligand.In addition,due to the stable and anionic porous framework,the Cd-MOF demonstrated fluorescence quenching sensing to a variety of substrates,such as UO_(2)^(2+),Fe^(3+),Cr_(2)O_(7)^(2−),MnO_(4)^(−),nitrofuran antibiotics,TNP explosives,etc.In particular,the fluorescence detection constants(K_(sv))of the Cd-MOF for UO_(2)^(2+)could reach 2.0×10^(5)M^(−1),which mainly originated from strong electrostatic interaction.The adsorption of UO_(2)^(2+)ions could effectively lower the energy level of the LUMO,which promotes the charge transfer from the[Cd(COO)_(4)]−node to UO_(2)^(2+)ions,leading to the fluorescence quenching of the Cd-MOF.In addition,the Cd-MOF can be photochromically responsive to visible light,generating a new strong absorption characteristic peak at 670 nm and a color change from yellow to green.The sensitive photochromic behavior should be assigned to the generation of imidazole radicals stabilized by the spatial confinement effect of the Cd-MOF,which lowers the energy level ofπ^(*)→πtransition within the ligand.These findings suggest that the strategic synthesis of PMOFs utilizing D–A–D-type dilophine ligands can significantly modulate both the light absorption and fluorescence sensing capabilities,which paves a new way for the development of advanced,high-performance photoactive materials.展开更多
Let H and its dual H* be finite dimensional semisimple Hopf algebras. In this paper, we firstly prove that the derived representation types of an algebra A and the crossed product algebra A#σH are coincident. This is...Let H and its dual H* be finite dimensional semisimple Hopf algebras. In this paper, we firstly prove that the derived representation types of an algebra A and the crossed product algebra A#σH are coincident. This is an improvement of the conclusion about representation type of an algebra in Li and Zhang [Sci China Ser A, 2006, 50: 1-13]. Secondly, we give the relationship between Gorenstein projective modules over A and that over A#σH. Then, using this result, it is proven that A is a finite dimensional CM-finite Gorenstein algebra if and only if so is A#σH.展开更多
Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation, which makes the parameters unable to be adjusted according to the data characteristics of the actual problem...Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation, which makes the parameters unable to be adjusted according to the data characteristics of the actual problems. The results about fractional derivative multivariable grey models are very few at present. In this paper, a multivariable Caputo fractional derivative grey model with convolution integral CFGMC(q, N) is proposed. First, the Caputo fractional difference is used to discretize the model, and the least square method is used to solve the parameters. The orders of accumulations and differential equations are determined by using particle swarm optimization(PSO). Then, the analytical solution of the model is obtained by using the Laplace transform, and the convergence and divergence of series in analytical solutions are also discussed. Finally, the CFGMC(q, N) model is used to predict the municipal solid waste(MSW). Compared with other competition models, the model has the best prediction effect. This study enriches the model form of the multivariable grey model, expands the scope of application, and provides a new idea for the development of fractional derivative grey model.展开更多
A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid-liquid crystalline （LC） polymers. A concept of anisotropic viscoelastic simple fluid is introduced....A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid-liquid crystalline （LC） polymers. A concept of anisotropic viscoelastic simple fluid is introduced. The stress tensor instead of the velocity gradient tensor D in the classic Leslie-Ericksen theory is described by the first Rivlin-Ericksen tensor A and a spin tensor W measured with respect to a co-rotational coordinate system. A model LCP-H on this theory is proposed and the characteristic unsymmetric behaviour of the shear stress is predicted for LC polymer liquids. Two shear stresses thereby in shear flow of LC polymer liquids lead to internal vortex flow and rotational flow. The conclusion could be of theoretical meaning for the modern liquid crystalline display technology. By using the equation, extrusion-extensional flows of the fluid are studied for fiber spinning of LC polymer melts, the elongational viscosity vs. extension rate with variation of shear rate is given in figures. A considerable increase of elongational viscosity and bifurcation behaviour are observed when the orientational motion of the director vector is considered. The contraction of extru- date of LC polymer melts is caused by the high elongational viscosity. For anisotropic viscoelastic fluids, an important advance has been made in the investigation on the constitutive equation on the basis of which a seriesof new anisotropic non-Newtonian fluid problems can be addressed.展开更多
This research aims to use fractional operators to analyze a fractional-order model of a coronavirus disease of 2019 (COVID-19). We use some basic results and definitions from fractional calculus and then, by using the...This research aims to use fractional operators to analyze a fractional-order model of a coronavirus disease of 2019 (COVID-19). We use some basic results and definitions from fractional calculus and then, by using them, investigate the effects of these operators in a better elucidation of the epidemic COVID-19. We showed the existence and uniqueness of the solution of the proposed model by applying the Picard–Lindelöf theorem and Banach contraction principle. We established the generalized Hyers–Ulam stability of the fractional model using Gronwall’s inequality. We developed effective numerical scheme to solve these fractional systems, which gives a perfect approximate solution to the fractional system. Finally, the numerical simulations were performed in each case to verify all theoretical result.展开更多
基金Supported by the Natural Science Foundation of China(Grant No.61907010)Innovation Team Project in Colleges and Universities of Guangdong Province(Grant No.2020WCXTD008)Science Foundation of Huashang College Guangdong University of Finance&Economics(Grant No.2020HSDS01)。
文摘In this paper,we study the blow-up of solutions to a semilinear double-wave equation with nonlinearity of derivative type.By using the iteration method and the differential inequality techniques,we can get the estimates of the lifespan and the blow-up of solutions in the subcritical case under some assumptions.
基金funded by the Key Projects in the National Science&Technology Pillar Program during the Twelfth Five-year Plan Period(No.2015BAD15B04)the National Natural Science Foundation of China(No.31600466)the Fundamental Research Funds for Jiangsu Key Laboratory of Biomass Energy and Material(No.JSBEM-S-201605)
文摘p-Menthane type monoterpene derivatives were identified as bio-based compounds with high herbicidal activities. In order to search novel p-menthane type monoterpene derivatives in good performance, a series of novel cis-p-menthane type Schiff base derivatives were designed and synthesized. All target products were easily available novel compounds and characterized by FT-IR,^1H NMR,^13 C NMR and ESI＋-MS. Their pre-emergence herbicidal activities against annual ryegrass were evaluated. The bioassays indicated that most of the target compounds displayed excellent herbicidal activities in pre-emergence treatment.
基金Supported by the Natural Science Foundation of China(Grant No.11371175)Innovation Team Project in Colleges and Universities of Guangdong Province(Grant No.2020WCXTD008)+1 种基金Science Foundation of Huashang College Guangdong University of Finance&Economics(Grant No.2020HSDS01)Science Research Team Project in Guangzhou Huashang College(Grant No.2021HSKT01).
文摘In this paper,we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type.By using methods of an iteration argument and di erential inequalities,we obtain the blow-up result for the semi-linear wave equation when the exponent of p is under certain conditions.Meanwhile,we derive an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear wave equation.
基金Supported by the National Natural Science Foundation of China(11601420)the Natural Science Basic Research Plan in Shaanxi Province(2018JM1053)。
文摘Let A be a unital^(*)-algebra with the unit I and a nontrivial projection P∈A.Suppose that A satisfies XAP=0 implies X=0 and XA(I-P)=0 implies X=0.In this paper,we prove thatΦis a nonlinear A^(*)B+B^(*)A type derivation on A if and only ifΦis an additive^(*)-derivation.This is then applied to prime^(*)-algebra,von Neumann algebras with no central summands of type I1.factor von Neumann algebras and standard operator algebras.
基金the National Natural Science Foundation of China(Grants 92161123 and 21971078)the Jiangxi Provincial Key Laboratory of Functional Crystalline Materials Chemistry(2024SSY05161)the Open Project Program of Jiangxi Provincial Key Laboratory of Functional Molecular Materials Chemistry of Jiangxi University of Science and Technology(20212BCD42018)for financial support.
文摘Cadmium(II)-based metal–organic frameworks(MOFs)have been widely investigated for fluorescence sensing due to their chemical stability and tunable optical properties.However,how to precisely improve their selectivity and sensitivity to the target analytes is a key issue to be addressed.In this work,a photoactive MOF(PMOF)exhibiting specific cation fluorescence sensing and photochromism was constructed using Cd2+and di-lophine based tetracarboxylic acid with D–A–D configuration.The effective combination of two components can form a stable porous framework with multiple electron transfer paths such as short-range electron transport in ligands and metal-to-ligand charge transfer(MLCT).The Cd-MOF exhibits strong absorption in the visible light range of 400–450 nm and strong fluorescence emission at 475 nm.Theoretical calculations show that the absorption and emission mainly originate from charge transfer between the metal and the ligand.In addition,due to the stable and anionic porous framework,the Cd-MOF demonstrated fluorescence quenching sensing to a variety of substrates,such as UO_(2)^(2+),Fe^(3+),Cr_(2)O_(7)^(2−),MnO_(4)^(−),nitrofuran antibiotics,TNP explosives,etc.In particular,the fluorescence detection constants(K_(sv))of the Cd-MOF for UO_(2)^(2+)could reach 2.0×10^(5)M^(−1),which mainly originated from strong electrostatic interaction.The adsorption of UO_(2)^(2+)ions could effectively lower the energy level of the LUMO,which promotes the charge transfer from the[Cd(COO)_(4)]−node to UO_(2)^(2+)ions,leading to the fluorescence quenching of the Cd-MOF.In addition,the Cd-MOF can be photochromically responsive to visible light,generating a new strong absorption characteristic peak at 670 nm and a color change from yellow to green.The sensitive photochromic behavior should be assigned to the generation of imidazole radicals stabilized by the spatial confinement effect of the Cd-MOF,which lowers the energy level ofπ^(*)→πtransition within the ligand.These findings suggest that the strategic synthesis of PMOFs utilizing D–A–D-type dilophine ligands can significantly modulate both the light absorption and fluorescence sensing capabilities,which paves a new way for the development of advanced,high-performance photoactive materials.
基金supported by National Natural Science Foundation of China (Grant No.11171296)the Zhejiang Provincial Natural Science Foundation of China (Grant No. D7080064)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110101110010)
文摘Let H and its dual H* be finite dimensional semisimple Hopf algebras. In this paper, we firstly prove that the derived representation types of an algebra A and the crossed product algebra A#σH are coincident. This is an improvement of the conclusion about representation type of an algebra in Li and Zhang [Sci China Ser A, 2006, 50: 1-13]. Secondly, we give the relationship between Gorenstein projective modules over A and that over A#σH. Then, using this result, it is proven that A is a finite dimensional CM-finite Gorenstein algebra if and only if so is A#σH.
基金supported by the National Natural Science Foundation of China (51479151,61403288)。
文摘Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation, which makes the parameters unable to be adjusted according to the data characteristics of the actual problems. The results about fractional derivative multivariable grey models are very few at present. In this paper, a multivariable Caputo fractional derivative grey model with convolution integral CFGMC(q, N) is proposed. First, the Caputo fractional difference is used to discretize the model, and the least square method is used to solve the parameters. The orders of accumulations and differential equations are determined by using particle swarm optimization(PSO). Then, the analytical solution of the model is obtained by using the Laplace transform, and the convergence and divergence of series in analytical solutions are also discussed. Finally, the CFGMC(q, N) model is used to predict the municipal solid waste(MSW). Compared with other competition models, the model has the best prediction effect. This study enriches the model form of the multivariable grey model, expands the scope of application, and provides a new idea for the development of fractional derivative grey model.
基金the National Natural Science Foundation of China(10372100,19832050)(Key project).
文摘A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid-liquid crystalline （LC） polymers. A concept of anisotropic viscoelastic simple fluid is introduced. The stress tensor instead of the velocity gradient tensor D in the classic Leslie-Ericksen theory is described by the first Rivlin-Ericksen tensor A and a spin tensor W measured with respect to a co-rotational coordinate system. A model LCP-H on this theory is proposed and the characteristic unsymmetric behaviour of the shear stress is predicted for LC polymer liquids. Two shear stresses thereby in shear flow of LC polymer liquids lead to internal vortex flow and rotational flow. The conclusion could be of theoretical meaning for the modern liquid crystalline display technology. By using the equation, extrusion-extensional flows of the fluid are studied for fiber spinning of LC polymer melts, the elongational viscosity vs. extension rate with variation of shear rate is given in figures. A considerable increase of elongational viscosity and bifurcation behaviour are observed when the orientational motion of the director vector is considered. The contraction of extru- date of LC polymer melts is caused by the high elongational viscosity. For anisotropic viscoelastic fluids, an important advance has been made in the investigation on the constitutive equation on the basis of which a seriesof new anisotropic non-Newtonian fluid problems can be addressed.
文摘This research aims to use fractional operators to analyze a fractional-order model of a coronavirus disease of 2019 (COVID-19). We use some basic results and definitions from fractional calculus and then, by using them, investigate the effects of these operators in a better elucidation of the epidemic COVID-19. We showed the existence and uniqueness of the solution of the proposed model by applying the Picard–Lindelöf theorem and Banach contraction principle. We established the generalized Hyers–Ulam stability of the fractional model using Gronwall’s inequality. We developed effective numerical scheme to solve these fractional systems, which gives a perfect approximate solution to the fractional system. Finally, the numerical simulations were performed in each case to verify all theoretical result.
