This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The definition of quasi-linearity is dis...This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The definition of quasi-linearity is discussed, in addition to the examination of properties and classifications of linear ring spaces. Particularly, the ring of holomorphic functions on a region of the complex plane is examined, and the manner in which it generates an iterated linear ring space under the complex derivative operator. This notion is then generalized to all rings with nth order linear and surjective operators. Basic operator theory regarding the classifications of linear ring maps is also covered.展开更多
This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study ...This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.展开更多
The co-adsorption behaviors of SO2 and H2 O on face-centered cubic Cu（100） ideal surface were studied using the GGA-r PBE method of density functional theory（DFT） with slab models. The optimized structures of sing...The co-adsorption behaviors of SO2 and H2 O on face-centered cubic Cu（100） ideal surface were studied using the GGA-r PBE method of density functional theory（DFT） with slab models. The optimized structures of single H2 O and SO2 on Cu（100） surface were calculated at the coverage of 0.25 ML（molecular layer） and 0.5 ML. The results show that there was no obvious chemical adsorption of them on Cu（100） surface. The adsorbed structures, adsorption energy and electronic properties including difference charge density, valence charge density, Bader charge analysis and partial density of states（PDOS） of co-adsorbed structures of H2 O and SO2 were investigated to illustrate the interaction between adsorbates and surface. H2 O and SO2 can adsorb on surface of Cu atoms chemically via molecule form at the coverage of 0.25 ML, while H2 O dissociated into OH adsorbed on surface and H bonded with SO2 which keeps away from surface at the coverage of 0.5 ML.展开更多
Pipes inevitably encounter high ambient pressure and bending moment during the deepwater pipe-laying process,which can lead to elliptical buckling and even deterioration failure.For the safety of pipe-laying operation...Pipes inevitably encounter high ambient pressure and bending moment during the deepwater pipe-laying process,which can lead to elliptical buckling and even deterioration failure.For the safety of pipe-laying operation,available formulas for the pipe stability are established on the basis of the assumption of uniform deformation along the tube length and symmetrical buckling.This method can predict the nonlinear response of elliptical collapse of steel circular tubes for different ratios of diameter to thickness（D/t）under pure bending or combined bending and external pressure.In these formulas,the strain-displacement relationship is deduced from the nonlinear ring theory,and the Ramberg-Osgood constitutive model is applied to simulate the inelastic material behavior.Meanwhile,the principle of virtual work is adopted to derive the equilibrium equations.A set of equations is solved by the Newton-Raphson method,and the iterative scheme contains nested iteration for the constitutive relation.In order to check the effectiveness of this theoretical method,illustrative examples are presented in this paper.Besides,the numerical simulation is carried out by use of ANSYS.A comparison of the results shows that the theoretical method can provide reasonable prediction for engineering practice.展开更多
In this study, we developed a general method to analytically tackle a kind of movable boundary problem from the viewpoint of energy variation. Having grouped the adhesion of a micro-beam, droplet and carbon nanotube ...In this study, we developed a general method to analytically tackle a kind of movable boundary problem from the viewpoint of energy variation. Having grouped the adhesion of a micro-beam, droplet and carbon nanotube （CNT） ring on a substrate into one framework, we used the developed line of reasoning to investigate the adhesion behaviors of these systems. Based upon the derived governing equations and transversality conditions, explicit solutions involving the critical parameters and morphologies for the three systems are successfully obtained, and then the parameter analogies and common characteristics of them are thor- oughly investigated. The presented method has been verified via the concept of energy release rate in fracture mechanics. Our analyses provide a new approach for exploring the mechanism of different systems with similarities as well as for understanding the unity of nature. The analysis results may be beneficial for the design of nano-structured materi- als, and hold potential for enhancing their mechanical, chemical, optical and electronic properties.展开更多
Titanium dioxide with CoB amorphous alloys nanoparticles deposited on the surface is known to exhibit higher catalytic activity than the CoB amorphous.A study of the structure of such system is necessary to understand...Titanium dioxide with CoB amorphous alloys nanoparticles deposited on the surface is known to exhibit higher catalytic activity than the CoB amorphous.A study of the structure of such system is necessary to understand this effect.A quantum chemical study of Co2B2 on the TiO2（110） surface was studied using periodic slab model within the framework of density functional theory（DFT）.The results of geometry optimization indicated that the most stable model of adsorption was Co2B2 cluster adsorbed on the hollow site of TiO2 .The adsorption energy calculated for Co2B2 on the hollow site was 439.3 kJ/mol.The adsorption of CO and O2 was further studied and the results indicated that CO and O2 are preferred to adsorb on the Co2 site.Co-adsorption of CO and O2 shows that Co2B2 /TiO2 is a good catalyst for the oxidation of CO to carbon dioxide in the presence of oxygen.展开更多
Due to low carrying capacity and short life of current ring reducer,we proposed a new planetary gearing with internal gear ring,which consisted of two stages.One was an involute planetary drive and the other was an N-...Due to low carrying capacity and short life of current ring reducer,we proposed a new planetary gearing with internal gear ring,which consisted of two stages.One was an involute planetary drive and the other was an N-type planetary drive with small teeth difference.The kinematic calculation was conducted based on the analysis of structural composition and working principle.Formulas of backlash calculation for the new planetary gearing were derived by using probabilistic theory and the analytical model was created at the same time.Then,main factors that affect the systematic backlash were introduced and the effects of manufacture error,misaligments and roller bearing parameters on the distribution of backlash were presented.The influence of gear backlash on systematic return difference was performed based on the backlash mathematic model proposed.The results show that the backlash is a little large,of which the backlash of bearing takes a greater part than two gearing stages.So we presented some practical methods to reduce the systematic backlash.展开更多
6H-SiC is an important semiconductor material. The 6H-SiC wafer is always exposed to a high-humidity environment and the effect from the absorbed water molecule and some relative adsorbates is not negligible. Here, th...6H-SiC is an important semiconductor material. The 6H-SiC wafer is always exposed to a high-humidity environment and the effect from the absorbed water molecule and some relative adsorbates is not negligible. Here, the oxygen and water molecules absorbed on the 6H-SiC(0001) surface and the dissociation process were studied with density functional theory. On the 6H-SiC(0001) surface, absorbed O2 is spontaneously dissociated into O*, which is absorbed on a hollow site, and further transforms the 6H-SiC(0001) surface into SiO2. The absorbed H2O is spontaneously broken into OH*and H*, which are both absorbed on the top of the Si atom, and OH* is further reversibly transformed into O* and H*. The H* could saturate the dangling Si bond and change the absorption type of O*, which could stabilize the 6H-SiC(0001) surface and prevent it from transforming into SiO2.展开更多
Photosynthesis in nature has been deemed as the most significant biochemical reaction,which maintains a relatively stable content of O_(2) and CO_(2) in the atmosphere.Herein,for a deeper comprehension of natural phot...Photosynthesis in nature has been deemed as the most significant biochemical reaction,which maintains a relatively stable content of O_(2) and CO_(2) in the atmosphere.Herein,for a deeper comprehension of natural photosynthesis,an artificial photosynthesis model reaction of photochemical CO_(2) to CO conversion(CO_(2)+2 H^(+)+2e^(-)→CO+H_(2)O)catalyzed by a homogeneous hexanuclear ring cobalt complex{K_(2)[CoO_(3)PCH_(2)N(CH_(2)CO_(2))_(2)]}_(6)(Co6 complex)is developed.Using the[Ru(bpy)_(3)]^(2+)as a photosensitizer and TEOA as a sacrificial electron donor,an optimal turnover frequency of 503.3 h^(‒1) and an apparent quantum efficiency of 0.81%are obtained.The good photocatalytic CO_(2) reduction performance is attributed to the efficient electron transfer between Co6 complex and[Ru(bpy)_(3)]^(2+),which boosts the photogenerated carriers separation of the photosensitizer.It is confirmed by the j‐V curves,light‐assisted UV‐vis curves,steady‐state photoluminescence spectra and real‐time laser flash photolysis experiments.In addition,the proposed catalytic mechanism for CO_(2) reduction reaction catalyzed by the Co6 complex is explored by the potassium thiocyanate poison experiment,Pourbaix diagram and density functional theory calculations.展开更多
Elastohydrodynamic lubrication characteristics of hydraulic reciprocating seals have significant effects on sealing and tribology performances of hydraulic actuators, especially in high parameter hydraulic systems. On...Elastohydrodynamic lubrication characteristics of hydraulic reciprocating seals have significant effects on sealing and tribology performances of hydraulic actuators, especially in high parameter hydraulic systems. Only elastic deformations of hydraulic reciprocating seals were discussed, and hydrodynamic effects were neglected in many studies. The physical process of the fluid-solid interaction effect did not be clearly presented in the existing fluid-solid interaction models for hydraulic reciprocating O-ring seals, and few of these models had been simultaneously validated through experiments. By exploring the physical process of the fluid-solid interaction effect of the hydraulic reciprocating O-ring seal, a numerical fluid-solid interaction model consisting of fluid lubrication, contact mechanics, asperity contact and elastic deformation analyses is constructed with an iterative procedure. With the SRV friction and wear tester, the experiments are performed to investigate the elastohydrodynamic lubrication characteristics of the O-ring seal. The regularity of the friction coefficient varying with the speed of reciprocating motion is obtained in the mixed lubrication condition. The experimental result is used to validate the fluid-solid interaction model. Based on the model, The elastohydrodynamic lubrication characteristics of the hydraulic reciprocating O-ring seal are presented respectively in the dry friction, mixed lubrication and full film lubrication conditions, including of the contact pressure, film thickness, friction coefficient, liquid film pressure and viscous shear stress in the sealing zone. The proposed numerical fluid-solid interaction model can be effectively used to analyze the operation characteristics of the hydraulic reciprocating O-ring seal, and can also be widely used to study other hydraulic reciprocating seals.展开更多
文摘This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The definition of quasi-linearity is discussed, in addition to the examination of properties and classifications of linear ring spaces. Particularly, the ring of holomorphic functions on a region of the complex plane is examined, and the manner in which it generates an iterated linear ring space under the complex derivative operator. This notion is then generalized to all rings with nth order linear and surjective operators. Basic operator theory regarding the classifications of linear ring maps is also covered.
文摘This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.
基金Project(51222106)supported by the National Natural Science Foundation of ChinaProject(230201306500002)supported by the Fundamental Research Funds for the Central Universities+1 种基金ChinaProject(2014CB643300)supported by National Basic Research Program of China
文摘The co-adsorption behaviors of SO2 and H2 O on face-centered cubic Cu（100） ideal surface were studied using the GGA-r PBE method of density functional theory（DFT） with slab models. The optimized structures of single H2 O and SO2 on Cu（100） surface were calculated at the coverage of 0.25 ML（molecular layer） and 0.5 ML. The results show that there was no obvious chemical adsorption of them on Cu（100） surface. The adsorbed structures, adsorption energy and electronic properties including difference charge density, valence charge density, Bader charge analysis and partial density of states（PDOS） of co-adsorbed structures of H2 O and SO2 were investigated to illustrate the interaction between adsorbates and surface. H2 O and SO2 can adsorb on surface of Cu atoms chemically via molecule form at the coverage of 0.25 ML, while H2 O dissociated into OH adsorbed on surface and H bonded with SO2 which keeps away from surface at the coverage of 0.5 ML.
基金supported by the National High Technology Research and Development Programof China(863 Program,Grant No.2006AA09A105)
文摘Pipes inevitably encounter high ambient pressure and bending moment during the deepwater pipe-laying process,which can lead to elliptical buckling and even deterioration failure.For the safety of pipe-laying operation,available formulas for the pipe stability are established on the basis of the assumption of uniform deformation along the tube length and symmetrical buckling.This method can predict the nonlinear response of elliptical collapse of steel circular tubes for different ratios of diameter to thickness（D/t）under pure bending or combined bending and external pressure.In these formulas,the strain-displacement relationship is deduced from the nonlinear ring theory,and the Ramberg-Osgood constitutive model is applied to simulate the inelastic material behavior.Meanwhile,the principle of virtual work is adopted to derive the equilibrium equations.A set of equations is solved by the Newton-Raphson method,and the iterative scheme contains nested iteration for the constitutive relation.In order to check the effectiveness of this theoretical method,illustrative examples are presented in this paper.Besides,the numerical simulation is carried out by use of ANSYS.A comparison of the results shows that the theoretical method can provide reasonable prediction for engineering practice.
基金supported by the National Natural Science Foundation of China (11272357 and 11102140)Doctoral Fund of Ministry of Education of China (200804251520 and 20110141120024)Natural Science Foundation of Shandong Province (ZR2009AQ006)
文摘In this study, we developed a general method to analytically tackle a kind of movable boundary problem from the viewpoint of energy variation. Having grouped the adhesion of a micro-beam, droplet and carbon nanotube （CNT） ring on a substrate into one framework, we used the developed line of reasoning to investigate the adhesion behaviors of these systems. Based upon the derived governing equations and transversality conditions, explicit solutions involving the critical parameters and morphologies for the three systems are successfully obtained, and then the parameter analogies and common characteristics of them are thor- oughly investigated. The presented method has been verified via the concept of energy release rate in fracture mechanics. Our analyses provide a new approach for exploring the mechanism of different systems with similarities as well as for understanding the unity of nature. The analysis results may be beneficial for the design of nano-structured materi- als, and hold potential for enhancing their mechanical, chemical, optical and electronic properties.
基金supported by the program for the National Natural Science Foundation of China (90922022, 10676007, and 20773025)NCETFJ (No.HX2006-103)+1 种基金Science and Technology Foundation of Fujian Education Bureau (No. JA08019)Foundation of State Key Laboratory of Coal Combustion(No. FSKLCC0814)
文摘Titanium dioxide with CoB amorphous alloys nanoparticles deposited on the surface is known to exhibit higher catalytic activity than the CoB amorphous.A study of the structure of such system is necessary to understand this effect.A quantum chemical study of Co2B2 on the TiO2（110） surface was studied using periodic slab model within the framework of density functional theory（DFT）.The results of geometry optimization indicated that the most stable model of adsorption was Co2B2 cluster adsorbed on the hollow site of TiO2 .The adsorption energy calculated for Co2B2 on the hollow site was 439.3 kJ/mol.The adsorption of CO and O2 was further studied and the results indicated that CO and O2 are preferred to adsorb on the Co2 site.Co-adsorption of CO and O2 shows that Co2B2 /TiO2 is a good catalyst for the oxidation of CO to carbon dioxide in the presence of oxygen.
基金Funded by Key Technology R&D Program of Chongqing(No. 2008AC3087)Science & Technology Project of Chongqing Education Committee(No. KJ091414)
文摘Due to low carrying capacity and short life of current ring reducer,we proposed a new planetary gearing with internal gear ring,which consisted of two stages.One was an involute planetary drive and the other was an N-type planetary drive with small teeth difference.The kinematic calculation was conducted based on the analysis of structural composition and working principle.Formulas of backlash calculation for the new planetary gearing were derived by using probabilistic theory and the analytical model was created at the same time.Then,main factors that affect the systematic backlash were introduced and the effects of manufacture error,misaligments and roller bearing parameters on the distribution of backlash were presented.The influence of gear backlash on systematic return difference was performed based on the backlash mathematic model proposed.The results show that the backlash is a little large,of which the backlash of bearing takes a greater part than two gearing stages.So we presented some practical methods to reduce the systematic backlash.
基金supported by the Fundamental Research Project of Qinghai Province (2017-ZJ-795)
文摘6H-SiC is an important semiconductor material. The 6H-SiC wafer is always exposed to a high-humidity environment and the effect from the absorbed water molecule and some relative adsorbates is not negligible. Here, the oxygen and water molecules absorbed on the 6H-SiC(0001) surface and the dissociation process were studied with density functional theory. On the 6H-SiC(0001) surface, absorbed O2 is spontaneously dissociated into O*, which is absorbed on a hollow site, and further transforms the 6H-SiC(0001) surface into SiO2. The absorbed H2O is spontaneously broken into OH*and H*, which are both absorbed on the top of the Si atom, and OH* is further reversibly transformed into O* and H*. The H* could saturate the dangling Si bond and change the absorption type of O*, which could stabilize the 6H-SiC(0001) surface and prevent it from transforming into SiO2.
文摘Photosynthesis in nature has been deemed as the most significant biochemical reaction,which maintains a relatively stable content of O_(2) and CO_(2) in the atmosphere.Herein,for a deeper comprehension of natural photosynthesis,an artificial photosynthesis model reaction of photochemical CO_(2) to CO conversion(CO_(2)+2 H^(+)+2e^(-)→CO+H_(2)O)catalyzed by a homogeneous hexanuclear ring cobalt complex{K_(2)[CoO_(3)PCH_(2)N(CH_(2)CO_(2))_(2)]}_(6)(Co6 complex)is developed.Using the[Ru(bpy)_(3)]^(2+)as a photosensitizer and TEOA as a sacrificial electron donor,an optimal turnover frequency of 503.3 h^(‒1) and an apparent quantum efficiency of 0.81%are obtained.The good photocatalytic CO_(2) reduction performance is attributed to the efficient electron transfer between Co6 complex and[Ru(bpy)_(3)]^(2+),which boosts the photogenerated carriers separation of the photosensitizer.It is confirmed by the j‐V curves,light‐assisted UV‐vis curves,steady‐state photoluminescence spectra and real‐time laser flash photolysis experiments.In addition,the proposed catalytic mechanism for CO_(2) reduction reaction catalyzed by the Co6 complex is explored by the potassium thiocyanate poison experiment,Pourbaix diagram and density functional theory calculations.
基金supported by National Basic Research Program of China(973 Program,Grant No. 2009CB724304)Key Research Program of the State Key Laboratory of Tribology of Tsinghua University,China (Grant No. SKLT08A06)National Natural Science Foundation of China(Grant No. 50975157)
文摘Elastohydrodynamic lubrication characteristics of hydraulic reciprocating seals have significant effects on sealing and tribology performances of hydraulic actuators, especially in high parameter hydraulic systems. Only elastic deformations of hydraulic reciprocating seals were discussed, and hydrodynamic effects were neglected in many studies. The physical process of the fluid-solid interaction effect did not be clearly presented in the existing fluid-solid interaction models for hydraulic reciprocating O-ring seals, and few of these models had been simultaneously validated through experiments. By exploring the physical process of the fluid-solid interaction effect of the hydraulic reciprocating O-ring seal, a numerical fluid-solid interaction model consisting of fluid lubrication, contact mechanics, asperity contact and elastic deformation analyses is constructed with an iterative procedure. With the SRV friction and wear tester, the experiments are performed to investigate the elastohydrodynamic lubrication characteristics of the O-ring seal. The regularity of the friction coefficient varying with the speed of reciprocating motion is obtained in the mixed lubrication condition. The experimental result is used to validate the fluid-solid interaction model. Based on the model, The elastohydrodynamic lubrication characteristics of the hydraulic reciprocating O-ring seal are presented respectively in the dry friction, mixed lubrication and full film lubrication conditions, including of the contact pressure, film thickness, friction coefficient, liquid film pressure and viscous shear stress in the sealing zone. The proposed numerical fluid-solid interaction model can be effectively used to analyze the operation characteristics of the hydraulic reciprocating O-ring seal, and can also be widely used to study other hydraulic reciprocating seals.
