The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose...The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, originating, piece-wisely, from generalized logistic functions: they ensure <em>exact</em> (in the numerical sense) asymptotic values, besides to be quite practical to use, for example with fit to data algorithms;moreover they unveil a useful feature, that in fact, at least with very strict approximation, is also owned by the (numerical) solutions of the <em>exact</em> equations. The novelties in the work are: the way the approximate equations are obtained, using simple, analytic geometry considerations;the easy and practical formulation of the final approximate solutions;the mentioned useful feature, never disclosed before. The work’s method and result prove to be robust over a range of values of the well known non-dimensional parameter called <em>basic reproduction ratio</em>, that covers at least all the known epidemic cases, from influenza to measles: this is a point which doesn’t appear much discussed in analogous works.展开更多
Linearized equations of fluid dynamics of cell two phase flow for one dimensional case are proposed. Based on the equations, an analytic solution is derived, in which the frequency of wave is observed. The frequency f...Linearized equations of fluid dynamics of cell two phase flow for one dimensional case are proposed. Based on the equations, an analytic solution is derived, in which the frequency of wave is observed. The frequency formula consists of all important parameters of the fluid dynamics. In our observation, the group velocity and phase velocity of the motion of wave propagation are explicitly exhibited as well.展开更多
We describe the evolution of certain multiplicities and intersection numbers of plane curve singularities under the iterated action of an analytic morphism.
Indicators are the basis for judging the working performance of exhaust hood and capture performance are usually used as the only indicator.An evaluation index system including three factors of cooking oil fumes(COF)i...Indicators are the basis for judging the working performance of exhaust hood and capture performance are usually used as the only indicator.An evaluation index system including three factors of cooking oil fumes(COF)instantaneous capture,health risk impact and thermal comfort was proposed to assess the comprehensive performance of exhaust hood in the present study.The primary capture efficiency(PCE)of formaldehyde,the PCE of particulate matter with the diameter less than or equal to 2.5μm(PM_(2.5)),the incremental lifetime cancer risk(ILCR)of formaldehyde,the ILCR of PM_(2.5)and the predicted mean vote(PMV),which can all be quantified with the aid of computational fluid dynamics(CFD),were selected as the indicators.And the analytic hierarchy process(AHP)method was introduced to perform the comprehensive performance evaluation of exhaust hood.The performance of two exhaust hood structures(grille and orifice type)with three exhaust rates(3000,4000,and 5000 m^(3)/h)in two cooking zones of a university canteen kitchen were evaluated.The result showed that the reduction of ILCR of COF exposure is the most important to the performance of exhaust hood.The comprehensive performance of orifice exhaust hood with exhaust rate of 4000 and 5000 m^(3)/h are optimal;the orifice exhaust hood with exhaust of 3000 m^(3)/h and grille exhaust hood with exhaust rate of 5000 m^(3)/h are moderate;the grille exhaust hood with exhaust rate of 3000 and 4000 m^(3)/h are low.Decision-making priorities based on comprehensive and individual performance are not exactly the same in the two cooking zones.It is necessary to use the index system to evaluate the comprehensive performance of exhaust hood that considers the impact on human health and thermal comfort.展开更多
The point defects and their related physical properties in L10 FePt are investigated by molecular dynamics simulations based on an analytic bond-order potential. The calculated results agree well with the experimental...The point defects and their related physical properties in L10 FePt are investigated by molecular dynamics simulations based on an analytic bond-order potential. The calculated results agree well with the experimental value, indicating that the analytic bond-order potential is suitable to describe the structural properties and surface energies of the FePt alloy in the L10 phase. However, the calculated vacancy formation energy of an Fe atom is higher than that of a Pt atom, which disagrees with some other previously calculated results. This result indicates that the analytic bond-order potential is unable to describe the related point defect properties. The analytic bond-order potential needs to be modified in order to study these defect properties of an FePt alloy.展开更多
文摘The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, originating, piece-wisely, from generalized logistic functions: they ensure <em>exact</em> (in the numerical sense) asymptotic values, besides to be quite practical to use, for example with fit to data algorithms;moreover they unveil a useful feature, that in fact, at least with very strict approximation, is also owned by the (numerical) solutions of the <em>exact</em> equations. The novelties in the work are: the way the approximate equations are obtained, using simple, analytic geometry considerations;the easy and practical formulation of the final approximate solutions;the mentioned useful feature, never disclosed before. The work’s method and result prove to be robust over a range of values of the well known non-dimensional parameter called <em>basic reproduction ratio</em>, that covers at least all the known epidemic cases, from influenza to measles: this is a point which doesn’t appear much discussed in analogous works.
基金Supported by the National Natural Science Foundation of China(10672022)
文摘Linearized equations of fluid dynamics of cell two phase flow for one dimensional case are proposed. Based on the equations, an analytic solution is derived, in which the frequency of wave is observed. The frequency formula consists of all important parameters of the fluid dynamics. In our observation, the group velocity and phase velocity of the motion of wave propagation are explicitly exhibited as well.
文摘We describe the evolution of certain multiplicities and intersection numbers of plane curve singularities under the iterated action of an analytic morphism.
基金supported by the National Key R&D Program of China(No.2017YFC0211502).
文摘Indicators are the basis for judging the working performance of exhaust hood and capture performance are usually used as the only indicator.An evaluation index system including three factors of cooking oil fumes(COF)instantaneous capture,health risk impact and thermal comfort was proposed to assess the comprehensive performance of exhaust hood in the present study.The primary capture efficiency(PCE)of formaldehyde,the PCE of particulate matter with the diameter less than or equal to 2.5μm(PM_(2.5)),the incremental lifetime cancer risk(ILCR)of formaldehyde,the ILCR of PM_(2.5)and the predicted mean vote(PMV),which can all be quantified with the aid of computational fluid dynamics(CFD),were selected as the indicators.And the analytic hierarchy process(AHP)method was introduced to perform the comprehensive performance evaluation of exhaust hood.The performance of two exhaust hood structures(grille and orifice type)with three exhaust rates(3000,4000,and 5000 m^(3)/h)in two cooking zones of a university canteen kitchen were evaluated.The result showed that the reduction of ILCR of COF exposure is the most important to the performance of exhaust hood.The comprehensive performance of orifice exhaust hood with exhaust rate of 4000 and 5000 m^(3)/h are optimal;the orifice exhaust hood with exhaust of 3000 m^(3)/h and grille exhaust hood with exhaust rate of 5000 m^(3)/h are moderate;the grille exhaust hood with exhaust rate of 3000 and 4000 m^(3)/h are low.Decision-making priorities based on comprehensive and individual performance are not exactly the same in the two cooking zones.It is necessary to use the index system to evaluate the comprehensive performance of exhaust hood that considers the impact on human health and thermal comfort.
基金supported by the National Natural Science Foundation of China (Grant No. 50971011)the Beijing Natural Science Foundation (Grant No. 1102025)the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20091102110038)
文摘The point defects and their related physical properties in L10 FePt are investigated by molecular dynamics simulations based on an analytic bond-order potential. The calculated results agree well with the experimental value, indicating that the analytic bond-order potential is suitable to describe the structural properties and surface energies of the FePt alloy in the L10 phase. However, the calculated vacancy formation energy of an Fe atom is higher than that of a Pt atom, which disagrees with some other previously calculated results. This result indicates that the analytic bond-order potential is unable to describe the related point defect properties. The analytic bond-order potential needs to be modified in order to study these defect properties of an FePt alloy.
