The symplectic approach proposed and developed by Zhong et al. in 1990s for elasticity problems is a rational analytical method, in which ample experience is not needed as in the conventional semi-inverse method. In t...The symplectic approach proposed and developed by Zhong et al. in 1990s for elasticity problems is a rational analytical method, in which ample experience is not needed as in the conventional semi-inverse method. In the symplectic space, elasticity problems can be solved using the method of separation of variables along with the eigenfunction expansion technique, as in traditional Fourier analysis. The eigensolutions include those corresponding to zero and nonzero eigenvalues. The latter group can be further divided into α-and β-sets. This paper reformulates the form of β-set eigensolutions to achieve the stability of numerical calculation, which is very important to obtain accurate results within the symplectic frame. An example is finally given and numerical results are compared and discussed.展开更多
Irreducible indeterminism is considered by most physicists as an ontological interpretation of quantum mechanics, which attributes inherent indeterminism to elementary paJcticles. This view was extrapolated by von Neu...Irreducible indeterminism is considered by most physicists as an ontological interpretation of quantum mechanics, which attributes inherent indeterminism to elementary paJcticles. This view was extrapolated by von Neumann from the atomocosm to the entire universe. Heisenberg proposed an epistemic interpretation, postulating that indeterminism stems from ambivalent detection systems, rather than being a characteristic of elementary particles Transformative detection that inherently affects the measured phenomena is responsible for the indeterminism in the atomocosm. As the same does not generally hold true in the macrocosm, this discrepancy has led to the notion of the Heisenberg cut. As explained by Heisenberg＇s microscope example, high-energy light can displace electrons from their atomic shells in the atomocosm, but would not induce the same effect on objects in the macrocosm, thus rendering such detection neutral. Therefore, detection systems are ambivalent in that they can be transformative under the cut and neutral otherwise. Device variation is found under and above the cut and is the essential cause of outcome variability in the macrocosm. Thus, two completely different categories of indeterminism exist simultaneously under the Heisenberg cut, but only one is found above the cut, known as measurement variations of devices. Experimental exploration of elementary paJcticle behaviors is possible only with the help of detection systems. If these systems affect particle characteristics in any way, this would be sufficient to explain the irreducible quantum mechanical indeterminism. Consequently, the true behavior of elementary particles, whether indeterminist or determinist, would never be detectable. Above the cut, on the other hand, variations in device performance are inevitable, due to reducible perturbing factors, inducing measurement wJciation of devices Heisenberg discovered a general principle of ambivalent detection systems, which can also be found in the macrocosm. In the Wilson Cloud Chamber, vapor is an ambivalent detection system, since high-energy charged particles would produce straight tracks, whereas those of lower energy would leave an irregular trace. According to the epistemic interpretation, von Neumann＇s extrapolation of irreducible quantum mechanical indeterminism to the entire universe would not be necessary, thereby avoiding the uncomfortable conclusion that the entire universe is based on indeterminism展开更多
The judicious and timely use of silence within worship is becoming increasingly recognised as a crucially important aspect of its performance. This article suggests that Samuel Beckett＇s Waiting for Godot has much to...The judicious and timely use of silence within worship is becoming increasingly recognised as a crucially important aspect of its performance. This article suggests that Samuel Beckett＇s Waiting for Godot has much to offer liturgists about silence＇s dramatic potential and its ability to alert others to a contemplative mode of being. I refute the predominant way of seeing the play as an absurdist text and indicate that a more persuasive reading would situate it within a contemplative hermeneutics which gives due weight to silence as an ontological phenomenon. One key to appreciating this interpretation is to see the play against the backdrop of the Christian contemplative tradition. Thus, the article, besides encouraging liturgists to pay attention to dramatists also suggests that dramatists might draw from religion＇s insights and history.展开更多
The article suggests to replace the conventional unit of thermodynamic temperature with one based on the energy unit joule by including the gas constant into the temperature definition. The suggestion may be seen as a...The article suggests to replace the conventional unit of thermodynamic temperature with one based on the energy unit joule by including the gas constant into the temperature definition. The suggestion may be seen as a contribution to the ongoing efforts to redefine base units. The gas constant includes the Boltzmann constant which both will be abrogated and molar heat capacity and entropy will become dimensionless pure numbers. The suggestion has no impact on thermodynamic theory, but will make thermodynamic relations more translucent and easier to grab for students.展开更多
The authors establish the existence of a large class of mathematical entropies (the so-called weak entropies) associated with the Euler equations for an isentropic, compressible fluid governed by a general pressure la...The authors establish the existence of a large class of mathematical entropies (the so-called weak entropies) associated with the Euler equations for an isentropic, compressible fluid governed by a general pressure law. A mild assumption on the behavior of the pressure law near the vacuum is solely required. The analysis is based on an asymptotic expansion of the fundamental solution (called here the entropy kernel) of a highly singular Euler- Poisson-Darboux equation. The entropy kernel is only Holder continuous and its regularity is carefully inversti- gated. Relying on a notion introduced earlier by the authors, it is also proven that, for the Euler equations, the set of eatropy flux-splittings coincides with the set of entropies-entropy fluxes. There results imply the existence of a flux-splitting consistent with all of the entropy inequalities.展开更多
基金the National Natural Science Foundation of China (Nos. 10725210 and 10432030) the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20060335107)the Program for New Century Excellent Talents in University, MOE, China (No. NCET-05-05010)
文摘The symplectic approach proposed and developed by Zhong et al. in 1990s for elasticity problems is a rational analytical method, in which ample experience is not needed as in the conventional semi-inverse method. In the symplectic space, elasticity problems can be solved using the method of separation of variables along with the eigenfunction expansion technique, as in traditional Fourier analysis. The eigensolutions include those corresponding to zero and nonzero eigenvalues. The latter group can be further divided into α-and β-sets. This paper reformulates the form of β-set eigensolutions to achieve the stability of numerical calculation, which is very important to obtain accurate results within the symplectic frame. An example is finally given and numerical results are compared and discussed.
文摘Irreducible indeterminism is considered by most physicists as an ontological interpretation of quantum mechanics, which attributes inherent indeterminism to elementary paJcticles. This view was extrapolated by von Neumann from the atomocosm to the entire universe. Heisenberg proposed an epistemic interpretation, postulating that indeterminism stems from ambivalent detection systems, rather than being a characteristic of elementary particles Transformative detection that inherently affects the measured phenomena is responsible for the indeterminism in the atomocosm. As the same does not generally hold true in the macrocosm, this discrepancy has led to the notion of the Heisenberg cut. As explained by Heisenberg＇s microscope example, high-energy light can displace electrons from their atomic shells in the atomocosm, but would not induce the same effect on objects in the macrocosm, thus rendering such detection neutral. Therefore, detection systems are ambivalent in that they can be transformative under the cut and neutral otherwise. Device variation is found under and above the cut and is the essential cause of outcome variability in the macrocosm. Thus, two completely different categories of indeterminism exist simultaneously under the Heisenberg cut, but only one is found above the cut, known as measurement variations of devices. Experimental exploration of elementary paJcticle behaviors is possible only with the help of detection systems. If these systems affect particle characteristics in any way, this would be sufficient to explain the irreducible quantum mechanical indeterminism. Consequently, the true behavior of elementary particles, whether indeterminist or determinist, would never be detectable. Above the cut, on the other hand, variations in device performance are inevitable, due to reducible perturbing factors, inducing measurement wJciation of devices Heisenberg discovered a general principle of ambivalent detection systems, which can also be found in the macrocosm. In the Wilson Cloud Chamber, vapor is an ambivalent detection system, since high-energy charged particles would produce straight tracks, whereas those of lower energy would leave an irregular trace. According to the epistemic interpretation, von Neumann＇s extrapolation of irreducible quantum mechanical indeterminism to the entire universe would not be necessary, thereby avoiding the uncomfortable conclusion that the entire universe is based on indeterminism
文摘The judicious and timely use of silence within worship is becoming increasingly recognised as a crucially important aspect of its performance. This article suggests that Samuel Beckett＇s Waiting for Godot has much to offer liturgists about silence＇s dramatic potential and its ability to alert others to a contemplative mode of being. I refute the predominant way of seeing the play as an absurdist text and indicate that a more persuasive reading would situate it within a contemplative hermeneutics which gives due weight to silence as an ontological phenomenon. One key to appreciating this interpretation is to see the play against the backdrop of the Christian contemplative tradition. Thus, the article, besides encouraging liturgists to pay attention to dramatists also suggests that dramatists might draw from religion＇s insights and history.
文摘The article suggests to replace the conventional unit of thermodynamic temperature with one based on the energy unit joule by including the gas constant into the temperature definition. The suggestion may be seen as a contribution to the ongoing efforts to redefine base units. The gas constant includes the Boltzmann constant which both will be abrogated and molar heat capacity and entropy will become dimensionless pure numbers. The suggestion has no impact on thermodynamic theory, but will make thermodynamic relations more translucent and easier to grab for students.
文摘The authors establish the existence of a large class of mathematical entropies (the so-called weak entropies) associated with the Euler equations for an isentropic, compressible fluid governed by a general pressure law. A mild assumption on the behavior of the pressure law near the vacuum is solely required. The analysis is based on an asymptotic expansion of the fundamental solution (called here the entropy kernel) of a highly singular Euler- Poisson-Darboux equation. The entropy kernel is only Holder continuous and its regularity is carefully inversti- gated. Relying on a notion introduced earlier by the authors, it is also proven that, for the Euler equations, the set of eatropy flux-splittings coincides with the set of entropies-entropy fluxes. There results imply the existence of a flux-splitting consistent with all of the entropy inequalities.
