Series of exponential equations in the form of were solved graphically, numerically and analytically. The analytical solution was derived in terms of Lambert-W function. A general numerical solution for any y is found...Series of exponential equations in the form of were solved graphically, numerically and analytically. The analytical solution was derived in terms of Lambert-W function. A general numerical solution for any y is found in terms of n or in base y. A solution is close to the fine structure constant. The equation which provided the solution as the fine structure constant was derived in terms of the fundamental constants.展开更多
Conventional analysis of enzyme-catalyzed reactions uses a set of initial rates of product formation or substrate decay at a variety of substrate concentrations. Alternatively to the conventional methods, attempts hav...Conventional analysis of enzyme-catalyzed reactions uses a set of initial rates of product formation or substrate decay at a variety of substrate concentrations. Alternatively to the conventional methods, attempts have been made to use an integrated Michaelis-Menten equation to assess the values of the Michaelis-Menten KM and turnover kcat constants directly from a single time course of an enzymatic reaction. However, because of weak convergence, previous fits of the integrated Michaelis-Menten equation to a single trace of the reaction have no proven records of success. Here we propose a reliable method with fast convergence based on an explicit solution of the Michaelis-Menten equation in terms of the Lambert-W function with transformed variables. Tests of the method with stopped-flow measurements of the catalytic reaction of cytochrome c oxidase, as well as with simulated data, demonstrate applicability of the approach to de termine KM and kcat constants free of any systematic errors. This study indicates that the approach could be an alternative solution for the characterization of enzymatic reactions, saving time, sample and efforts. The single trace method can greatly assist the real time monitoring of enzymatic activity, in particular when a fast control is mandatory. It may be the only alternative when conventional analysis does not apply, e.g. because of limited amount of sample.展开更多
Planck’s radiation law provides an equation for the intensity of the electromagnetic radiation from a physical body as a function of frequency and temperature. The frequency that corresponds to the maximum intensity ...Planck’s radiation law provides an equation for the intensity of the electromagnetic radiation from a physical body as a function of frequency and temperature. The frequency that corresponds to the maximum intensity is a function of temperature. At a specific temperature, for the frequencies correspond to much less than the maximum intensity, an equation was derived in the form of the Lambert <em>W</em> function. Numerical calculations validate the equation. A new form of solution for the Euler’s transcendental equation was derived in the form of the Lambert <em>W</em> function with logarithmic argument. Numerical solutions to the Euler’s equation were determined iteratively and iterative convergences were investigated. Numerical coincidences with physical constants were explored.展开更多
Manganese-based materials are influenced by the Jahn-Teller effect,causing the spontaneous dismutation of Mn^(3+)(2Mn^(3+)→Mn^(2+)+Mn^(4+))and the dissolution of Mn^(2+),which often results in diminished activity.Thi...Manganese-based materials are influenced by the Jahn-Teller effect,causing the spontaneous dismutation of Mn^(3+)(2Mn^(3+)→Mn^(2+)+Mn^(4+))and the dissolution of Mn^(2+),which often results in diminished activity.This study uniquely employs a W doping strategy to suppress this effect.Externally,a simple template-free method was initially used to prepare cobalt-and manganese-based precursors,followed by a W doping process during the synthesis of transition bimetallic phosphides.Ultimately,W-doped bimetallic phosphides(W-CoMnP)were obtained.The W-CoMnP material demonstrates excellent HER and OER performance with low overpotentials of 95 mV(η_(₁₀)HER)and 225 mV(η_(₅₀)OER),and can achieve overall water splitting at a voltage of 1.52 V while maintaining stable cycling for 24 h.To enable commercial application,W-CoMnP was incorporated into an anion exchange membrane(AEM)electrolysis water device,demonstrating continuous and stable hydrogen production under ambient temperature conditions.This study offers a promising strategy for the future development of catalysts for AEM electrolysis water devices.展开更多
The three-layered(W-60 vol%Cu/W-40 vol%Cu/W-20 vol%Cu)W/Cu functionally graded material(FGM)containing a Cu network structure was fabricated at different temperatures by hot-pressed sintering produced from copper-coat...The three-layered(W-60 vol%Cu/W-40 vol%Cu/W-20 vol%Cu)W/Cu functionally graded material(FGM)containing a Cu network structure was fabricated at different temperatures by hot-pressed sintering produced from copper-coated tungsten powders.The effects of various sintering temperatures on relative density,microstructure,thermal conductivity,hardness and flexural strength were investigated.Scanning electron microscopy(SEM)and X-ray diffraction(XRD)analysis show that a Cu network extends throughout the W/Cu FGM specimens sintered at 1065℃and the graded structure can be retained perfectly,and W particles are distributed homogeneously.The low-temperature sintering densification of W/Cu FGM arises because the sintering mode of the copper-coated tungsten particles includes just sintering Cu to Cu,rather than Cu to W,Cu to Cu and W to W,as required for conventional powder particles.The relative density of W/Cu FGM sintered at 1065℃for 3 h under a load of25 MPa is 96.1%.The thermal conductivity is up to204 W·m^-1·K^-1 at normal temperature and 150 W·m^-1·K^-1at 800℃.And the Vickers hardness varies with the gradient of different layers from 3.34 to 4.05 GPa.展开更多
Objective:This study was designed to observe the effect of electroacupuncture at Hégǔ(合谷L14),or Hòuxī(后溪SI3) or Wàiguān(外关TE5) acupoints on the function of the brain regions of a healthy human,...Objective:This study was designed to observe the effect of electroacupuncture at Hégǔ(合谷L14),or Hòuxī(后溪SI3) or Wàiguān(外关TE5) acupoints on the function of the brain regions of a healthy human,and to explore the neural information mechanism of a specific connection between LI4 and the facialoral area from the point of view of the brain function connection network.A further objective was to enrich knowledge of the specific connection between the body surface and the meridian route,and the specificity of acupoint effects.Methods:A total of 30 healthy volunteers were randomly assigned to LI4,SI3,and TE5 groups.The members of each group were stimulated with electroacupuncture,and their heads were scanned using fMRI.DPARSFA 2.4 and REST 1.8 software were used for data preprocessing and statistical analysis.The paired t-test was used within group and the double sample t-test was used for two-group comparisons.Results:In healthy people,left LI4 with electroacupuncture mainly caused a decrease of the functional connection of the right orofacial motor area of the brain,which remained decreased after removing the needle.When LI4 was compared with SI3 and TE5,LI4 caused a more significant decline in the functional connection of the right side of the brain during acupuncture.Conclusions:Acupuncture at LI4 has a significant effect on the function of the face-and mouth-related areas in the brain,and there is a continuous effect.It is suggested that LI4 and the face and mouth have a specific relationship in the brain,which is most obvious during acupuncture.展开更多
In this paper, we get W 1,p(Rn)-boundedness for tangential maximal func- tion and nontangential maximal function , which improves J.Kinnunen, P.Lindqvist and Tananka’s results.
The Whitney immersion theorem asserts that every smooth n-dimensional manifold can be immersed in R2n-1, in particular, smooth surfaces can be immersed in R3, and for embeddings the ambient dimension needs to go up by...The Whitney immersion theorem asserts that every smooth n-dimensional manifold can be immersed in R2n-1, in particular, smooth surfaces can be immersed in R3, and for embeddings the ambient dimension needs to go up by 1. Immersions or embeddings carry both intrinsic and extrinsic information of manifolds, and the latter determines how the manifold fits into the Euclidean space. The key geometric quantity to capture the extrinsic geometry is the second fundamental form.展开更多
This study proposes a new flexible family of distributions called the Lambert-G family.The Lambert family is very flexible and exhibits desirable properties.Its three-parameter special sub-models provide all significa...This study proposes a new flexible family of distributions called the Lambert-G family.The Lambert family is very flexible and exhibits desirable properties.Its three-parameter special sub-models provide all significantmonotonic and non-monotonic failure rates.A special sub-model of the Lambert family called the Lambert-Lomax(LL)distribution is investigated.General expressions for the LL statistical properties are established.Characterizations of the LL distribution are addressed mathematically based on its hazard function.The estimation of the LL parameters is discussed using six estimation methods.The performance of this estimation method is explored through simulation experiments.The usefulness and flexibility of the LL distribution are demonstrated empirically using two real-life data sets.The LL model better fits the exponentiated Lomax,inverse power Lomax,Lomax-Rayleigh,power Lomax,and Lomax distributions.展开更多
文摘Series of exponential equations in the form of were solved graphically, numerically and analytically. The analytical solution was derived in terms of Lambert-W function. A general numerical solution for any y is found in terms of n or in base y. A solution is close to the fine structure constant. The equation which provided the solution as the fine structure constant was derived in terms of the fundamental constants.
文摘Conventional analysis of enzyme-catalyzed reactions uses a set of initial rates of product formation or substrate decay at a variety of substrate concentrations. Alternatively to the conventional methods, attempts have been made to use an integrated Michaelis-Menten equation to assess the values of the Michaelis-Menten KM and turnover kcat constants directly from a single time course of an enzymatic reaction. However, because of weak convergence, previous fits of the integrated Michaelis-Menten equation to a single trace of the reaction have no proven records of success. Here we propose a reliable method with fast convergence based on an explicit solution of the Michaelis-Menten equation in terms of the Lambert-W function with transformed variables. Tests of the method with stopped-flow measurements of the catalytic reaction of cytochrome c oxidase, as well as with simulated data, demonstrate applicability of the approach to de termine KM and kcat constants free of any systematic errors. This study indicates that the approach could be an alternative solution for the characterization of enzymatic reactions, saving time, sample and efforts. The single trace method can greatly assist the real time monitoring of enzymatic activity, in particular when a fast control is mandatory. It may be the only alternative when conventional analysis does not apply, e.g. because of limited amount of sample.
文摘Planck’s radiation law provides an equation for the intensity of the electromagnetic radiation from a physical body as a function of frequency and temperature. The frequency that corresponds to the maximum intensity is a function of temperature. At a specific temperature, for the frequencies correspond to much less than the maximum intensity, an equation was derived in the form of the Lambert <em>W</em> function. Numerical calculations validate the equation. A new form of solution for the Euler’s transcendental equation was derived in the form of the Lambert <em>W</em> function with logarithmic argument. Numerical solutions to the Euler’s equation were determined iteratively and iterative convergences were investigated. Numerical coincidences with physical constants were explored.
文摘Manganese-based materials are influenced by the Jahn-Teller effect,causing the spontaneous dismutation of Mn^(3+)(2Mn^(3+)→Mn^(2+)+Mn^(4+))and the dissolution of Mn^(2+),which often results in diminished activity.This study uniquely employs a W doping strategy to suppress this effect.Externally,a simple template-free method was initially used to prepare cobalt-and manganese-based precursors,followed by a W doping process during the synthesis of transition bimetallic phosphides.Ultimately,W-doped bimetallic phosphides(W-CoMnP)were obtained.The W-CoMnP material demonstrates excellent HER and OER performance with low overpotentials of 95 mV(η_(₁₀)HER)and 225 mV(η_(₅₀)OER),and can achieve overall water splitting at a voltage of 1.52 V while maintaining stable cycling for 24 h.To enable commercial application,W-CoMnP was incorporated into an anion exchange membrane(AEM)electrolysis water device,demonstrating continuous and stable hydrogen production under ambient temperature conditions.This study offers a promising strategy for the future development of catalysts for AEM electrolysis water devices.
基金financially supported by the Wenzhou Public Welfare Technology Research Industry Project(No.G20140042)。
文摘The three-layered(W-60 vol%Cu/W-40 vol%Cu/W-20 vol%Cu)W/Cu functionally graded material(FGM)containing a Cu network structure was fabricated at different temperatures by hot-pressed sintering produced from copper-coated tungsten powders.The effects of various sintering temperatures on relative density,microstructure,thermal conductivity,hardness and flexural strength were investigated.Scanning electron microscopy(SEM)and X-ray diffraction(XRD)analysis show that a Cu network extends throughout the W/Cu FGM specimens sintered at 1065℃and the graded structure can be retained perfectly,and W particles are distributed homogeneously.The low-temperature sintering densification of W/Cu FGM arises because the sintering mode of the copper-coated tungsten particles includes just sintering Cu to Cu,rather than Cu to W,Cu to Cu and W to W,as required for conventional powder particles.The relative density of W/Cu FGM sintered at 1065℃for 3 h under a load of25 MPa is 96.1%.The thermal conductivity is up to204 W·m^-1·K^-1 at normal temperature and 150 W·m^-1·K^-1at 800℃.And the Vickers hardness varies with the gradient of different layers from 3.34 to 4.05 GPa.
基金Supported by grants from National Key R&D Program of China:2019YFC1709001the National Natural Science Foundation of China:81973959+4 种基金8177443581674068the Foundation of Sichuan Provincial Administration of Traditional Chinese Medicine:2018JC007the Foundation of Chengdu University of Traditional Chinese Medicine:QNXZ2018034the National Program on Key Basic Research Project of China:2010CB530501.
文摘Objective:This study was designed to observe the effect of electroacupuncture at Hégǔ(合谷L14),or Hòuxī(后溪SI3) or Wàiguān(外关TE5) acupoints on the function of the brain regions of a healthy human,and to explore the neural information mechanism of a specific connection between LI4 and the facialoral area from the point of view of the brain function connection network.A further objective was to enrich knowledge of the specific connection between the body surface and the meridian route,and the specificity of acupoint effects.Methods:A total of 30 healthy volunteers were randomly assigned to LI4,SI3,and TE5 groups.The members of each group were stimulated with electroacupuncture,and their heads were scanned using fMRI.DPARSFA 2.4 and REST 1.8 software were used for data preprocessing and statistical analysis.The paired t-test was used within group and the double sample t-test was used for two-group comparisons.Results:In healthy people,left LI4 with electroacupuncture mainly caused a decrease of the functional connection of the right orofacial motor area of the brain,which remained decreased after removing the needle.When LI4 was compared with SI3 and TE5,LI4 caused a more significant decline in the functional connection of the right side of the brain during acupuncture.Conclusions:Acupuncture at LI4 has a significant effect on the function of the face-and mouth-related areas in the brain,and there is a continuous effect.It is suggested that LI4 and the face and mouth have a specific relationship in the brain,which is most obvious during acupuncture.
基金Supported by the key Academic Discipline of Zhejiang Province of China under Grant No.2005the Zhejiang Provincial Natural Science Foundation of China
文摘In this paper, we get W 1,p(Rn)-boundedness for tangential maximal func- tion and nontangential maximal function , which improves J.Kinnunen, P.Lindqvist and Tananka’s results.
文摘The Whitney immersion theorem asserts that every smooth n-dimensional manifold can be immersed in R2n-1, in particular, smooth surfaces can be immersed in R3, and for embeddings the ambient dimension needs to go up by 1. Immersions or embeddings carry both intrinsic and extrinsic information of manifolds, and the latter determines how the manifold fits into the Euclidean space. The key geometric quantity to capture the extrinsic geometry is the second fundamental form.
文摘This study proposes a new flexible family of distributions called the Lambert-G family.The Lambert family is very flexible and exhibits desirable properties.Its three-parameter special sub-models provide all significantmonotonic and non-monotonic failure rates.A special sub-model of the Lambert family called the Lambert-Lomax(LL)distribution is investigated.General expressions for the LL statistical properties are established.Characterizations of the LL distribution are addressed mathematically based on its hazard function.The estimation of the LL parameters is discussed using six estimation methods.The performance of this estimation method is explored through simulation experiments.The usefulness and flexibility of the LL distribution are demonstrated empirically using two real-life data sets.The LL model better fits the exponentiated Lomax,inverse power Lomax,Lomax-Rayleigh,power Lomax,and Lomax distributions.
