As per Hawking and Bekenstein’s work on black holes, information resides on the surface and there is a limit on it amounting to a bit for every Planck area. It would seem therefore that extra dimensions would logical...As per Hawking and Bekenstein’s work on black holes, information resides on the surface and there is a limit on it amounting to a bit for every Planck area. It would seem therefore that extra dimensions would logically lead to a hyper-surface for a black hole and consequently a reduction of the corresponding information density due to the dilution effect of these additional dimensions. The present paper argues that the counterintuitive opposite of the above is what should be expected. This surprising result is a consequence of a well known theorem on measure concentration due to I. Dvoretzky.展开更多
A uniformly first-order convergent numerical method for the discrete-ordinate transport equation in the rectangle geometry is proposed in this paper. Firstly we approximate the scattering coefficients and source terms...A uniformly first-order convergent numerical method for the discrete-ordinate transport equation in the rectangle geometry is proposed in this paper. Firstly we approximate the scattering coefficients and source terms by piecewise constants determined by their cell averages. Then for each cell, following the work of De Barros and Larsen [1, 19], the solution at the cell edge is approximated by its average along the edge. As a result, the solution of the system of equations for the cell edge averages in each cell can be obtained analytically. Finally, we piece together the numerical solution with the neighboring cells using the interface conditions. When there is no interface or boundary layer, this method is asymptotic-preserving, which implies that coarse meshes （meshes that do not resolve the mean free path） can be used to obtain good numerical approximations. Moreover, the uniform first-order convergence with respect to the mean free path is shown numerically and the rigorous proof is provided.展开更多
Previous studies in different ethnic groups show changes in heart rate, respiratory rate, cortisol cycle, and sleep-wake cycle throughout life. Our purpose is to verify such changes by comparing the values of each var...Previous studies in different ethnic groups show changes in heart rate, respiratory rate, cortisol cycle, and sleep-wake cycle throughout life. Our purpose is to verify such changes by comparing the values of each variable before and after puberty. Puberty is associated with the end of growth and is an important point in our theoretical framework: when growth ends, changes occur in the geometry of the biological system. At the same time, this causes phase changes in the oscillatory variables, which are seen as chronodisruption. The results confirm the changes found by other authors in the evolution of the variables throughout life. Then, we can conclude that the variables studied present phase changes when growth ends, in accordance with the proposed theoretical framework.展开更多
For planar polynomial systems, a limit cycle is called an algebraic limit cycle(ALC, for abbreviation) if it is a real closed component of an algebraic solution. Inthis note we initiate the study on the number of ALCs...For planar polynomial systems, a limit cycle is called an algebraic limit cycle(ALC, for abbreviation) if it is a real closed component of an algebraic solution. Inthis note we initiate the study on the number of ALCs and obtain the following re-sult.展开更多
Symmetry of the underlying probability density plays an important role in statistical inference, since the sampling distribution of the sample mean for a given sample size is more likely to be approximately normal for...Symmetry of the underlying probability density plays an important role in statistical inference, since the sampling distribution of the sample mean for a given sample size is more likely to be approximately normal for a symmetric distribution than for an asymmetric one. In this article, two new measures of skewness are proposed and the confidence intervals for true skewness are obtained via Monte Carlo simulation experiments. One advantage of the two proposed skewness measures over the standard measures of skewness is that the proposed measures of skewness take values inside the range (-1, +1).展开更多
文摘As per Hawking and Bekenstein’s work on black holes, information resides on the surface and there is a limit on it amounting to a bit for every Planck area. It would seem therefore that extra dimensions would logically lead to a hyper-surface for a black hole and consequently a reduction of the corresponding information density due to the dilution effect of these additional dimensions. The present paper argues that the counterintuitive opposite of the above is what should be expected. This surprising result is a consequence of a well known theorem on measure concentration due to I. Dvoretzky.
文摘A uniformly first-order convergent numerical method for the discrete-ordinate transport equation in the rectangle geometry is proposed in this paper. Firstly we approximate the scattering coefficients and source terms by piecewise constants determined by their cell averages. Then for each cell, following the work of De Barros and Larsen [1, 19], the solution at the cell edge is approximated by its average along the edge. As a result, the solution of the system of equations for the cell edge averages in each cell can be obtained analytically. Finally, we piece together the numerical solution with the neighboring cells using the interface conditions. When there is no interface or boundary layer, this method is asymptotic-preserving, which implies that coarse meshes （meshes that do not resolve the mean free path） can be used to obtain good numerical approximations. Moreover, the uniform first-order convergence with respect to the mean free path is shown numerically and the rigorous proof is provided.
文摘Previous studies in different ethnic groups show changes in heart rate, respiratory rate, cortisol cycle, and sleep-wake cycle throughout life. Our purpose is to verify such changes by comparing the values of each variable before and after puberty. Puberty is associated with the end of growth and is an important point in our theoretical framework: when growth ends, changes occur in the geometry of the biological system. At the same time, this causes phase changes in the oscillatory variables, which are seen as chronodisruption. The results confirm the changes found by other authors in the evolution of the variables throughout life. Then, we can conclude that the variables studied present phase changes when growth ends, in accordance with the proposed theoretical framework.
文摘For planar polynomial systems, a limit cycle is called an algebraic limit cycle(ALC, for abbreviation) if it is a real closed component of an algebraic solution. Inthis note we initiate the study on the number of ALCs and obtain the following re-sult.
文摘Symmetry of the underlying probability density plays an important role in statistical inference, since the sampling distribution of the sample mean for a given sample size is more likely to be approximately normal for a symmetric distribution than for an asymmetric one. In this article, two new measures of skewness are proposed and the confidence intervals for true skewness are obtained via Monte Carlo simulation experiments. One advantage of the two proposed skewness measures over the standard measures of skewness is that the proposed measures of skewness take values inside the range (-1, +1).
