THE ROLE OF ACCELERATION AND LOCALITY IN THE TWIN PARADOX

We study the role of acceleration in the twin paradox. From the coordinate transformation that relates an accelerated and an inertial observer we find that, from the point of view of the accelerated observer, the rate of the differential lapses of time depends not only on the relative velocity, but also on the product of the acceleration and the distance between the observers. However, this result does not have a direct operational interpretation because an observer at a certain position can measure only physical quantities that are defined at the same position. For local measurements, the asymmetry between the two observers can be attributed to the fact that noninertial coordinate systems, contrary to inertial coordinate systems, can be correctly interpreted only locally.     

Stochastic dynamics and Parrondo’s paradox

The Spanish physicist Juan Parrondo has provided two stochastic losing games such that for certain stochastic combinations one may obtain a winning game. If a large number of players are involved and if they try to play such that their gain in the next round is maximized one arrives at the problem of investigating a random walk on a certain space of measures.The appropriate abstract setting is as follows. There is given a compact metric space (M,d), and M is written as the union of certain closed subsets A₁,…,A_r. For every ρ=1,…,r there is prescribed a strict contraction Γ_ρ:A_ρ→M. A random walk (X_m)_m∈N0 on M is then defined as follows. The starting position is X₀=x₀, where x₀∈M is fixed, and if the walk at the m’th step is at position X_m∈M, then one chooses a ρ among the ρ with X_m∈A_ρ (with equal probability, say) and defines X_m+1 as Γ_ρ(X_m). Associated with the walk is a gainφ(X_m) in every round, where φ:M→R is a continuous function.The aim of the present investigations is the study of the expectation G_m of φ(X_m) as a function of m. Our main result states that the sequence (G_m) is “eventually approximately periodic” provided that all A_ρ are not only closed but also open in M: for every ε there is an l₀∈N such that (G_m) is l₀-periodic up to an error of at most ε for sufficiently large m. In fact it turns out that the behaviour of our process can be described well with a finite Markov chain.In the general case, however, the process might behave rather chaotically. We give an example where M is the unit interval. M is written as the union of two closed subsets A₁,A₂, the contractions Γ₁,Γ₂ are rather simple, but the expectations of the gains are not even Cesáro convergent.     

狭义相对论中的重力及"潜水艇佯谬"

在狭义相对论范畴内,如果考虑地球周围较小区域内的动力学问题,可以用均匀质量密度的无限大平面产生的重力场替代地球的史瓦西场,从而得到较为简单的重力表达式.在此基础上可以很方便地解释所谓的"潜水艇佯谬".     

A robotic model for Codman's paradox simulation and interpretation

A robotic approach based on Denavit–Hartenberg parametrization is proposed for simulating and interpreting Codman's paradox. A 3-degree-of-freedom robot model of the glenohumeral joint, driving the arm reduced to its long humerus, is considered for simulating the two-step rotational sequence of Codman's paradox. We propose to use the classical distinction made in robotics between the joint space, i.e. the inner space of joint angles, and the operational space, i.e. the outer physical space, for interpreting this historical version of the paradox, as there is some kind of confusion between these two spaces to be considered for arm movement definition. In its extended form, developed by MacConnail, the three-step rotational sequence of Codman's paradox would highlight the motor redundancy of the shoulder joint, necessitating for its simulation, according to our robotic approach, a 4-axis model of the shoulder spheroid joint. Our model provides a general prediction of the conjunct rotation angle in full accordance with clinical observation for a two-step or three-step version of Codman's paradox. The relation of the paradox with a possible general law of motion is finally discussed.     

Braess's paradox for the spectral gap in random graphs and delocalization of eigenvectors

We study how the spectral gap of the normalized Laplacian of a random graph changes when an edge is added to or removed from the graph. There are known examples of graphs where, perhaps counter‐intuitively, adding an edge can decrease the spectral gap, a phenomenon that is analogous to Braess's paradox in traffic networks. We show that this is often the case in random graphs in a strong sense. More precisely, we show that for typical instances of Erd?s‐Rényi random graphs G (n, p ) with constant edge density , the addition of a random edge will decrease the spectral gap with positive probability, strictly bounded away from zero. To do this, we prove a new delocalization result for eigenvectors of the Laplacian of G (n, p ), which might be of independent interest. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 584–611, 2017     

极坐标哈密顿体系约当型与弹性楔的佯谬解

讨论了极坐标弹性平面哈密顿体系的当型,并通过约当型的求解,直接给出了相关弹性楔体佯谬问题的解,从理论上阐明了经典弹性力学中某些佯谬问题的出现是由于其对应的是哈密顿体系中特殊的约当型解,同时也很自然地为该类问题提供了一个通用,有效的求解方法。     

双生子问题

采用爱因斯坦例子在狭义相对论范畴讨论双生子效应,然后利用直红运动常加速度内禀刚性加速系进一步严格讨论。     

简论近代物理学中的悖论

分析了近代物理学中的一些悖论,着重指出,悖论暴露了现有理论体系内在本质的矛盾。悖论的提出与解决对物理学的发展起着关键性的作用。     

Beyond Simpson's paradox: A descriptive approach

In considering the strength of association of particular variables, we cannot ignore the effects of confounding factors that cause Simpson's paradox. Many methods for adjusting these effects have been proposed, and a great deal of effort has been devoted to statistical tests. Apart from the statistical tests, the aim of the present study is to examine the strength of association of two categorical variables without reference to any explicit confounding factors. In other words, our aim is to specify the conditions under which Simpson's paradox does not occur, where the idea of classifying the original universe into groups is adopted. Let us begin by focusing our attention on a 2 × 2 contingency table (cross-classification table) and considering the association of X with Y, where X and Y denote dichotomous variables with classes A and B for X and classes + and − for Y. To examine the strength of association between these variables, the index k = q/p is used, where p denotes the proportion of A + in A and q denotes that of B + in B. Using the maximum and minimum values of the index k obtained by numerical calculation, the strength of association is examined. The results are discussed and examples given. © 1996 John Wiley & Sons, Ltd.