This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–M...This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.展开更多
In the legal and philosophical study of torture,two major problems arise:Why is torture evil(Problem 1)?And is there a form of permissible torture(Problem 2)?The key issue in Problem 1 is demonstrating the uniqueness ...In the legal and philosophical study of torture,two major problems arise:Why is torture evil(Problem 1)?And is there a form of permissible torture(Problem 2)?The key issue in Problem 1 is demonstrating the uniqueness of the evils of torture,while Problem 2 aims to find a suitable theory to balance the“intuitive rejection”and“intuition of exceptional cases”in the ticking bomb scenario.Existing mainstream approaches have generally failed to resolve these issues.However,Matthew Kramer’s view of torture addresses both aspects of these problems.For Problem 1,Kramer adopts a perpetrator-centered viewpoint,arguing that torture undermines the moral integrity of the perpetrator.Regarding Problem 2,he suggests that the situation we face is a moral conflict in which the use of torture is morally wrong but might be the best action in a given context,granting it a weaker form of permissibility.However,in terms of the evils of torture,Kramer fails to explain its uniqueness.His theory cannot apply to all types of torture,and his perpetrator-centered argument contains logical flaws.Regarding the permissibility of torture,while Kramer’s overall approach is correct,he does not provide a reasonable explanation of the moral obligation to“forbid torture”or the prima facie surrounding it.A correct view of torture should adhere to an inmate-centered viewpoint,understanding the evils of torture in an additive manner in Problem 1,and acknowledging the existence of moral conflict in Problem 2.It should not only demonstrate that,in some situations,the use of torture may be the morally best option,but also show that the moral obligation to prohibit torture is simply outweighed under these circumstances.展开更多
为了更好地描述沥青混合料的时间和温度依赖性,优选表征动态力学性质的黏弹力学模型,推广黏弹性动态力学设计方法。基于线性黏弹性Kramers-Kronig近似解析式,通过对存储模量Sigmoidal函数解析式求导后,得到损失模量解析式,称为Sigmoida...为了更好地描述沥青混合料的时间和温度依赖性,优选表征动态力学性质的黏弹力学模型,推广黏弹性动态力学设计方法。基于线性黏弹性Kramers-Kronig近似解析式,通过对存储模量Sigmoidal函数解析式求导后,得到损失模量解析式,称为SigmoidalⅡ类模型。应用黏弹性材料时-温等效原理,通过构造不同目标函数,建立了上述模型黏弹函数主曲线,并与SigmoidalⅠ-Ⅰ模型、SigmoidalⅠ-Ⅱ模型进行了对比分析。结果表明:3个模型均能应用时-温等效原理建立黏弹函数(动态模量和相位角)的主曲线,与AASHTO R 62-131规范对比,3个模型均提出了相位角主曲线解析式,目标函数构造时,黏弹参数的选择影响Sigmoidal模型的拟合效果。对比另外2个模型,SigmoidalⅡ模型仅采用一个黏弹参数(动态模量)构造目标函数即可建立所有黏弹参数主曲线及Cole-Cole曲线,且黏弹函数测试值与预测值吻合较好,其中,动态模量和相位角曲线的拟合优度均在0.95以上,说明该模型能更好地描述沥青混合料的动态黏弹参数。SigmoidalⅡ模型存储模量和损失模量(动态模量和相位角)共用一套模型参数,黏弹参数之间满足线性黏弹性因果关系且符合力学模型的要求。SigmoidalⅡ模型可为沥青混合料设计和沥青路面层状黏弹动力学计算提供新的参考。展开更多
Spectra of absorption, luminescence, magnetic circular dichroism （MCD）, and magnetic circular polarization of lumines- cence （MCPL） in Gd3Ga5O12：Eu3＋ and Eu3Ga3O12 garnets were studied within the visible spectra...Spectra of absorption, luminescence, magnetic circular dichroism （MCD）, and magnetic circular polarization of lumines- cence （MCPL） in Gd3Ga5O12：Eu3＋ and Eu3Ga3O12 garnets were studied within the visible spectral range at 300 K. Analysis of the spectral and temperature dependences of the magnetooptical and optical spectra made it possible to identify the magneto-dipole （MD） and electro-dipole （ED） 4f→4f transitions occurring between Stark sublevels of the 7FJ （J=1, 2） and 5D0 multiplets in Eua＋-containing garnet structures. Quantum mechanical ＂mixing＂ had significant influence on quasi-degenerate states of the non-Kramers rare-earth Eu3＋ ion for Eu3GasOl2 in MCD due to forbidden MD transition 7F1→SD0 and for GdaGasOiE：EU3＋ in MCPL due to MD 4f→4f transition 5Do→7F1 and forced ED-transition 5Do→7F2. A parameterized Hamiltonian defined to operate within the entire 4f（6） ground electronic configuration of Eu3＋ ion was used to model the experimental Stark levels, including their irreducible rep- resentations and wavefunctions. The crystal-field parameters were determined through a Monte-Carlo method in which nine in- dependent crystal-field parameters, Bkq, were given random starting values and optimized using standard least-squares fitting between calculated and experimental levels. The final fitting standard deviation between 57 calculated-to-experimental levels was 0.73 meV.展开更多
基金supported by the PhD Research Startup Foundation of Hubei University of Economics(Grand No.XJ23BS42).
文摘This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.
基金This text represents a periodic outcome of the Beijing Social Science Fund Youth Project(Project Approval Number 22FXC018).
文摘In the legal and philosophical study of torture,two major problems arise:Why is torture evil(Problem 1)?And is there a form of permissible torture(Problem 2)?The key issue in Problem 1 is demonstrating the uniqueness of the evils of torture,while Problem 2 aims to find a suitable theory to balance the“intuitive rejection”and“intuition of exceptional cases”in the ticking bomb scenario.Existing mainstream approaches have generally failed to resolve these issues.However,Matthew Kramer’s view of torture addresses both aspects of these problems.For Problem 1,Kramer adopts a perpetrator-centered viewpoint,arguing that torture undermines the moral integrity of the perpetrator.Regarding Problem 2,he suggests that the situation we face is a moral conflict in which the use of torture is morally wrong but might be the best action in a given context,granting it a weaker form of permissibility.However,in terms of the evils of torture,Kramer fails to explain its uniqueness.His theory cannot apply to all types of torture,and his perpetrator-centered argument contains logical flaws.Regarding the permissibility of torture,while Kramer’s overall approach is correct,he does not provide a reasonable explanation of the moral obligation to“forbid torture”or the prima facie surrounding it.A correct view of torture should adhere to an inmate-centered viewpoint,understanding the evils of torture in an additive manner in Problem 1,and acknowledging the existence of moral conflict in Problem 2.It should not only demonstrate that,in some situations,the use of torture may be the morally best option,but also show that the moral obligation to prohibit torture is simply outweighed under these circumstances.
文摘为了更好地描述沥青混合料的时间和温度依赖性,优选表征动态力学性质的黏弹力学模型,推广黏弹性动态力学设计方法。基于线性黏弹性Kramers-Kronig近似解析式,通过对存储模量Sigmoidal函数解析式求导后,得到损失模量解析式,称为SigmoidalⅡ类模型。应用黏弹性材料时-温等效原理,通过构造不同目标函数,建立了上述模型黏弹函数主曲线,并与SigmoidalⅠ-Ⅰ模型、SigmoidalⅠ-Ⅱ模型进行了对比分析。结果表明:3个模型均能应用时-温等效原理建立黏弹函数(动态模量和相位角)的主曲线,与AASHTO R 62-131规范对比,3个模型均提出了相位角主曲线解析式,目标函数构造时,黏弹参数的选择影响Sigmoidal模型的拟合效果。对比另外2个模型,SigmoidalⅡ模型仅采用一个黏弹参数(动态模量)构造目标函数即可建立所有黏弹参数主曲线及Cole-Cole曲线,且黏弹函数测试值与预测值吻合较好,其中,动态模量和相位角曲线的拟合优度均在0.95以上,说明该模型能更好地描述沥青混合料的动态黏弹参数。SigmoidalⅡ模型存储模量和损失模量(动态模量和相位角)共用一套模型参数,黏弹参数之间满足线性黏弹性因果关系且符合力学模型的要求。SigmoidalⅡ模型可为沥青混合料设计和沥青路面层状黏弹动力学计算提供新的参考。
基金Project supported by National Natural Science Foundation of China(11205116)International Cooperation Program of the Ministry of Science and Technology of China(2011DFR50580)
文摘Spectra of absorption, luminescence, magnetic circular dichroism （MCD）, and magnetic circular polarization of lumines- cence （MCPL） in Gd3Ga5O12：Eu3＋ and Eu3Ga3O12 garnets were studied within the visible spectral range at 300 K. Analysis of the spectral and temperature dependences of the magnetooptical and optical spectra made it possible to identify the magneto-dipole （MD） and electro-dipole （ED） 4f→4f transitions occurring between Stark sublevels of the 7FJ （J=1, 2） and 5D0 multiplets in Eua＋-containing garnet structures. Quantum mechanical ＂mixing＂ had significant influence on quasi-degenerate states of the non-Kramers rare-earth Eu3＋ ion for Eu3GasOl2 in MCD due to forbidden MD transition 7F1→SD0 and for GdaGasOiE：EU3＋ in MCPL due to MD 4f→4f transition 5Do→7F1 and forced ED-transition 5Do→7F2. A parameterized Hamiltonian defined to operate within the entire 4f（6） ground electronic configuration of Eu3＋ ion was used to model the experimental Stark levels, including their irreducible rep- resentations and wavefunctions. The crystal-field parameters were determined through a Monte-Carlo method in which nine in- dependent crystal-field parameters, Bkq, were given random starting values and optimized using standard least-squares fitting between calculated and experimental levels. The final fitting standard deviation between 57 calculated-to-experimental levels was 0.73 meV.
