Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-pla...Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractional wave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation （ODE）. The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional dif- ferential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.展开更多
Isotopic fractionation is the basis of tracing the water cycle using hydrogen and oxygen isotopes. Isotopic fractionation factors in water evaporating from free water bodies are mainly affected by temperature and rela...Isotopic fractionation is the basis of tracing the water cycle using hydrogen and oxygen isotopes. Isotopic fractionation factors in water evaporating from free water bodies are mainly affected by temperature and relative humidity, and vary significantly with these atmospheric factors over the course of a day. The evaporation rate （E） can reveal the effects of atmospheric factors. Therefore, there should be a certain functional relationship between isotopic fractionation factors and E. An average isotopic fractionation factor （ t~＊ ） was defined to describe isotopic differences between vapor and liquid phases in evaporation with time intervals of days. The relationship between or＊ and E based on the isotopic mass balance was investigated through an evaporation pan experiment with no inflow. The experimental results showed that the isotopic compositions of residual water were more enriched with time; tr＊ was affected by air temperature, relative humidity, and other atmospheric factors, and had a strong functional relation with E. The values of 0~＊ can be easily calculated with the known values of E, the initial volume of water in the pan, and isotopic compositions of residual water.展开更多
Several important equilibrium Si isotope fractionation factors among minerals,organic molecules and the H_4SiO_4 solution are complemented to facilitate the explanation of the distributions of Si isotopes in Earth'...Several important equilibrium Si isotope fractionation factors among minerals,organic molecules and the H_4SiO_4 solution are complemented to facilitate the explanation of the distributions of Si isotopes in Earth's surface environments.The results reveal that,in comparison to aqueous H_4SiO_4,heavy Si isotopes will be significantly enriched in secondary silicate minerals.On the contrary,quadra-coordinated organosilicon complexes are enriched in light silicon isotope relative to the solution.The extent of ^(28)Si-enrichment in hyper-coordinated organosilicon complexes was found to be the largest.In addition,the large kinetic isotope effect associated with the polymerization of monosilicic acid and dimer was calculated,and the results support the previous statement that highly ^(28)Sienrichment in the formation of amorphous quartz precursor contributes to the discrepancy between theoretical calculations and field observations.With the equilibrium Si isotope fractionation factors provided here,Si isotope distributions in many of Earth's surface systems can be explained.For example,the change of bulk soil δ^(30)Si can be predicted as a concave pattern with respect to the weathering degree,with the minimum value where allophane completely dissolves and the total amount of sesquioxides and poorly crystalline minerals reaches their maximum.When,under equilibrium conditions,the well-crystallized clays start to precipitate from the pore solutions,the bulk soil δ^(30)Si will increase again and reach a constant value.Similarly,the precipitation of crystalline smectite and the dissolution of poorly crystalline kaolinite may explain the δ^(30)Si variations in the ground water profile.The equilibrium Si isotope fractionations among the quadracoordinated organosilicon complexes and the H_4SiO_4solution may also shed light on the Si isotope distributions in the Si-accumulating plants.展开更多
This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be i...This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced.展开更多
There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given...There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given for most frequently used ACFs.展开更多
Objective Despite the fact that the bioavailability of trace metals indicated by their speciation has been an indispensable parameter in the assessment and treatment of the environmental pollution of trace metals, ma...Objective Despite the fact that the bioavailability of trace metals indicated by their speciation has been an indispensable parameter in the assessment and treatment of the environmental pollution of trace metals, many studies have suggested that the bioavailability of trace metals may change according to the conditions of the environment, and the speciation of trace metals can also transform between some fractions. These transformations are related with these factors such as the compositions, microorganism, time, and other physical-chemical conditions of the system. Our work aims to systematically investigate and probe the factors to affect the transformation aside from analysis at certain time-place. The results of these understanding and investigations can be used for reasonably determining the allocation of financial and technical resources in natural and engineered processes, with bringing about inspirations from the evolution of the speciation of the trace metals on environmental impacts.展开更多
In this paper, we introduce a new definition of fractional derivative which contains a fractional factor, and its physical meanings are given. When studying the fractional Schrdinger equation(FSE) with this form of fr...In this paper, we introduce a new definition of fractional derivative which contains a fractional factor, and its physical meanings are given. When studying the fractional Schrdinger equation(FSE) with this form of fractional derivative, the result shows that under the description of time FSE with fractional factor, the probability of finding a particle in the whole space is still conserved. By using this new definition to construct space FSE, we achieve a continuous transition from standard Schrdinger equation to the fractional one. When applying this form of Schrdinger equation to a particle in an infinite symmetrical square potential well, we find that the probability density distribution loses spatial symmetry and shows a kind of attenuation property. For the situation of a one-dimensional infinite δ potential well,the first derivative of time-independent wave function Φ to space coordinate x can be continuous everywhere when the particle is at some special discrete energy levels, which is much different from the standard Schrdinger equation.展开更多
In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of ...In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained.展开更多
A key issue of applying remotely sensed data to estimate evapotranspiration （ET） for water management is extrapolating instantaneous latent heat flux （LE） at satellite over-passing time to daily ET total. At prese...A key issue of applying remotely sensed data to estimate evapotranspiration （ET） for water management is extrapolating instantaneous latent heat flux （LE） at satellite over-passing time to daily ET total. At present, the most commonly used extrapolation methods have the same assumption that evaporative fraction （EF） can be treated as constant during daytime （so-called EF self-preservation）. However, large errors are reported by many documents over various ecosystems with the same approach, which indicates that further analysis of the diurnal pattern of EF is still necessary. The aim of this study is to examine the diurnal pattern of EF under fair weather conditions, then to analyze the dependencies of EF to meteorological and plant factors. Long-term flux observations at four sites over semi-arid and semi-humid climate regions in the northern China are used to analyze the EF diumal pattern. Results show that the EF self-preservation assumption no longer holds over growing seasons of crops. However, the ratio of reference ET to available energy is almost constant during the daytime, which implies the climate factors do not have much effect on the variability of EF. The analysis of diurnal pattern of air temperature, vapor pressure deficiency （VPD）, and relative humidity （RH） confirms the assumption that ET diurnal pattern is mainly influenced by stomatal regulation.展开更多
AIM To quantify the preventive fraction of physical fitness on the risk factors in patients with cardiovascular diseases(CVDs).METHODS A total of 249 subjects(205 men and 44 women) suffering from CVD were categorized ...AIM To quantify the preventive fraction of physical fitness on the risk factors in patients with cardiovascular diseases(CVDs).METHODS A total of 249 subjects(205 men and 44 women) suffering from CVD were categorized into four groups, according to their percentage of physical fitness. We calculated the odds ratio to obtain the preventive fraction in order to evaluate the impact of the physical fitness level on the risk factors(i.e., abdominal obesity, depression, diabetes, dyslipidemia, hypertension, obesity, overweight and smoking).RESULTS It is observed that a normal physical fitness level is sufficient to induce a preventive action on abdominal obesity(38%), diabetes(12%), hypertension(33%), obesity(12%) and overweight(11%). Also, the preventive fraction increases with the level of physical fitness, in particular for hypertension(36%) and overweight(16%). A high physical fitness level does not necessarily induce a preventive action in most risk factors, excluding depression. CONCLUSION This is the first study which demonstrates that reaching a normal physical fitness level is enough to induce a protection for some risk factors, despite having a CVD.展开更多
In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It ...In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.展开更多
We consider plus-operators in Krein spaces and generated operator linear fractional relations of the following form: . We study some special type of factorization for plus-operators T, among them the following one: T ...We consider plus-operators in Krein spaces and generated operator linear fractional relations of the following form: . We study some special type of factorization for plus-operators T, among them the following one: T = BU, where B is a lower triangular plus-operator, U is a J-unitary operator. We apply the above factorization to the study of basical properties of relations (1), in particular, convexity and compactness of their images with respect to the weak operator topology. Obtained results we apply to the known Koenigs embedding problem, the Krein-Phillips problem of existing of invariant semidefinite subspaces for some families of plus-operators and to some other fields.展开更多
基金supported by the National Natural Science Foundation of China(11072060)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractional wave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation （ODE）. The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional dif- ferential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.
基金supported by the National Natural Science Foundation of China (Grants No.50679024,40901015,and 41001011)the Fundamental Research Funds for the Central Universities (Grants No.B1020072 and B1020062)+2 种基金the Ph. D. Programs Foundation of the Ministry of Education of China (Grant No.20090094120008)the Special Fund of the State Key Laboratory of China (Grant No.2009586412)the Science Foundation of the HydroChina Chengdu Engineering Corporation (Grant No.P058)
文摘Isotopic fractionation is the basis of tracing the water cycle using hydrogen and oxygen isotopes. Isotopic fractionation factors in water evaporating from free water bodies are mainly affected by temperature and relative humidity, and vary significantly with these atmospheric factors over the course of a day. The evaporation rate （E） can reveal the effects of atmospheric factors. Therefore, there should be a certain functional relationship between isotopic fractionation factors and E. An average isotopic fractionation factor （ t~＊ ） was defined to describe isotopic differences between vapor and liquid phases in evaporation with time intervals of days. The relationship between or＊ and E based on the isotopic mass balance was investigated through an evaporation pan experiment with no inflow. The experimental results showed that the isotopic compositions of residual water were more enriched with time; tr＊ was affected by air temperature, relative humidity, and other atmospheric factors, and had a strong functional relation with E. The values of 0~＊ can be easily calculated with the known values of E, the initial volume of water in the pan, and isotopic compositions of residual water.
基金the funding support from the 973 Program(2014CB440904)CAS/SAFEA International Partnership Program for Creative Research Teams(Intraplate Mineralization Research Team,KZZD-EW-TZ-20)Chinese NSF projects(41173023,41225012,41490635,41530210)
文摘Several important equilibrium Si isotope fractionation factors among minerals,organic molecules and the H_4SiO_4 solution are complemented to facilitate the explanation of the distributions of Si isotopes in Earth's surface environments.The results reveal that,in comparison to aqueous H_4SiO_4,heavy Si isotopes will be significantly enriched in secondary silicate minerals.On the contrary,quadra-coordinated organosilicon complexes are enriched in light silicon isotope relative to the solution.The extent of ^(28)Si-enrichment in hyper-coordinated organosilicon complexes was found to be the largest.In addition,the large kinetic isotope effect associated with the polymerization of monosilicic acid and dimer was calculated,and the results support the previous statement that highly ^(28)Sienrichment in the formation of amorphous quartz precursor contributes to the discrepancy between theoretical calculations and field observations.With the equilibrium Si isotope fractionation factors provided here,Si isotope distributions in many of Earth's surface systems can be explained.For example,the change of bulk soil δ^(30)Si can be predicted as a concave pattern with respect to the weathering degree,with the minimum value where allophane completely dissolves and the total amount of sesquioxides and poorly crystalline minerals reaches their maximum.When,under equilibrium conditions,the well-crystallized clays start to precipitate from the pore solutions,the bulk soil δ^(30)Si will increase again and reach a constant value.Similarly,the precipitation of crystalline smectite and the dissolution of poorly crystalline kaolinite may explain the δ^(30)Si variations in the ground water profile.The equilibrium Si isotope fractionations among the quadracoordinated organosilicon complexes and the H_4SiO_4solution may also shed light on the Si isotope distributions in the Si-accumulating plants.
基金This work is supported by NNSF of ChinaRFDP of Higher Education
文摘This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced.
基金Supported by the National Natural Science Foundation of china
文摘There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given for most frequently used ACFs.
基金funded by the National Natural Science Foundation of China(grant No.41572329)
文摘Objective Despite the fact that the bioavailability of trace metals indicated by their speciation has been an indispensable parameter in the assessment and treatment of the environmental pollution of trace metals, many studies have suggested that the bioavailability of trace metals may change according to the conditions of the environment, and the speciation of trace metals can also transform between some fractions. These transformations are related with these factors such as the compositions, microorganism, time, and other physical-chemical conditions of the system. Our work aims to systematically investigate and probe the factors to affect the transformation aside from analysis at certain time-place. The results of these understanding and investigations can be used for reasonably determining the allocation of financial and technical resources in natural and engineered processes, with bringing about inspirations from the evolution of the speciation of the trace metals on environmental impacts.
基金Supported by National Natural Science Foundation of China under Grant Nos.11472247 and 11872335
文摘In this paper, we introduce a new definition of fractional derivative which contains a fractional factor, and its physical meanings are given. When studying the fractional Schrdinger equation(FSE) with this form of fractional derivative, the result shows that under the description of time FSE with fractional factor, the probability of finding a particle in the whole space is still conserved. By using this new definition to construct space FSE, we achieve a continuous transition from standard Schrdinger equation to the fractional one. When applying this form of Schrdinger equation to a particle in an infinite symmetrical square potential well, we find that the probability density distribution loses spatial symmetry and shows a kind of attenuation property. For the situation of a one-dimensional infinite δ potential well,the first derivative of time-independent wave function Φ to space coordinate x can be continuous everywhere when the particle is at some special discrete energy levels, which is much different from the standard Schrdinger equation.
基金This work is supported by NSFC (10471078.10201019)RSDP (20040422004) of China
文摘In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained.
基金supported by the the National Natural Science Funds for Distinguished Yong Scholar,China(51025931)the National Natural Science Foundation of China(50939004)
文摘A key issue of applying remotely sensed data to estimate evapotranspiration （ET） for water management is extrapolating instantaneous latent heat flux （LE） at satellite over-passing time to daily ET total. At present, the most commonly used extrapolation methods have the same assumption that evaporative fraction （EF） can be treated as constant during daytime （so-called EF self-preservation）. However, large errors are reported by many documents over various ecosystems with the same approach, which indicates that further analysis of the diurnal pattern of EF is still necessary. The aim of this study is to examine the diurnal pattern of EF under fair weather conditions, then to analyze the dependencies of EF to meteorological and plant factors. Long-term flux observations at four sites over semi-arid and semi-humid climate regions in the northern China are used to analyze the EF diumal pattern. Results show that the EF self-preservation assumption no longer holds over growing seasons of crops. However, the ratio of reference ET to available energy is almost constant during the daytime, which implies the climate factors do not have much effect on the variability of EF. The analysis of diurnal pattern of air temperature, vapor pressure deficiency （VPD）, and relative humidity （RH） confirms the assumption that ET diurnal pattern is mainly influenced by stomatal regulation.
文摘AIM To quantify the preventive fraction of physical fitness on the risk factors in patients with cardiovascular diseases(CVDs).METHODS A total of 249 subjects(205 men and 44 women) suffering from CVD were categorized into four groups, according to their percentage of physical fitness. We calculated the odds ratio to obtain the preventive fraction in order to evaluate the impact of the physical fitness level on the risk factors(i.e., abdominal obesity, depression, diabetes, dyslipidemia, hypertension, obesity, overweight and smoking).RESULTS It is observed that a normal physical fitness level is sufficient to induce a preventive action on abdominal obesity(38%), diabetes(12%), hypertension(33%), obesity(12%) and overweight(11%). Also, the preventive fraction increases with the level of physical fitness, in particular for hypertension(36%) and overweight(16%). A high physical fitness level does not necessarily induce a preventive action in most risk factors, excluding depression. CONCLUSION This is the first study which demonstrates that reaching a normal physical fitness level is enough to induce a protection for some risk factors, despite having a CVD.
文摘In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.
文摘We consider plus-operators in Krein spaces and generated operator linear fractional relations of the following form: . We study some special type of factorization for plus-operators T, among them the following one: T = BU, where B is a lower triangular plus-operator, U is a J-unitary operator. We apply the above factorization to the study of basical properties of relations (1), in particular, convexity and compactness of their images with respect to the weak operator topology. Obtained results we apply to the known Koenigs embedding problem, the Krein-Phillips problem of existing of invariant semidefinite subspaces for some families of plus-operators and to some other fields.
