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。     

On the mechanism by which nose bluntness suppresses second-mode instability

A physical mechanism by which nose bluntness suppresses second-mode instability is proposed.Considered are 7 degree half-angle straight cones with nose bluntness radii of 0.15 mm, 3.556 mm,5 mm, 9.525 mm, 12.7 mm and 25.4 mm at tunnel conditions relevant to the AFOSR-Notre Dame Large Mach 6 Quiet Tunnel. It is shown that second-mode suppression is achieved via entropy layer modulation of the basic state density gradient. A weakening of the density gradient disrupts the acoustic resonance necessary to sustain second-mode growth. These results are consistent with the thermoacoustic interpretation which posits that second-mode instability can be modeled as thermoacoustic resonance of acoustic energy trapped within an acoustic impedance well.Furthermore, the generalized inflection point criterion of Lees and Lin is applied to develop a criterion for the existence of second-mode instability based on the strength of the basic state density gradient.     

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     

Synthesis and properties of cationic surfactants with tuned hydrophylicity

A series of pyridinium-based cationic surfactants has been synthesised and their amphiphilic properties have been studied by conductivity and surface tension measurements. The modification of the substitution pattern on the pyridinium ring by hydrophobic moieties (methyl vs. hydrogen and presence or not of condensed benzene ring) gave the opportunity to investigate structure–activity relationships. Characterization by conductivity and surface tension measurements shed light on the behaviour at the air/water interface and in the micellar environment. In particular, the tendency to form ion pairs at very low concentration was evidenced for all the surfactants substituted on the ring, but not for the simple pyridinium ones. The formation of ion pairs affects both the conductivity and the surface tension plots, showing that a series of steps is involved during the adsorption to the air/water surface. An attempt was made to qualify the single steps in the adsorption at the surface layer. Those steps were attributed to different chemical species (free surfactant ions or ion pairs) and to different arrangements of the surfactant. This work also represents a contribution of investigation at very low surfactant concentrations and high surface tension values.     

The Dimension Paradox in Parameter Space of Cosine Family.

It is proved in this paper that the union of escaping parameter rays without endpoints for the cosine family S_κ(z) = e~κ(e~z+ e~(-z)), where κ∈ C is a parameter, has Hausdorff dimension 1, which implies that the ray endpoints alone have Hausdorff dimension 2. This shows that Karpińska's dimension paradox occurs also in the parameter plane of the cosine family.     

Strategy-indifferent games of best choice

The game of best choice (or “secretary problem”) is a model for making an irrevocable decision among a fixed number of candidate choices that are presented sequentially in random order, one at a time. Because the classically optimal solution is known to reject an initial sequence of candidates, a paradox emerges from the fact that candidates have an incentive to position themselves immediately after this cutoff which challenges the assumption that candidates arrive in uniformly random order.One way to resolve this is to consider games for which every (reasonable) strategy results in the same probability of success. In this work, we classify these “strategy-indifferent” games of best choice. It turns out that the probability of winning such a game is essentially the reciprocal of the expected number of left-to-right maxima in the full collection of candidate rank orderings. We present some examples of these games based on avoiding permutation patterns of size 3, which involves computing the distribution of left-to-right maxima in each of these pattern classes.     

Proposal for preparing entangled coherent states using atom-cavity-mode Raman interaction

A scheme for preparing entangled coherent states is presented. It is based on the atom-cavity-mode Raman interaction. We also generalize this method for generating multi-mode entangled coherent states. Finally, our experimental feasibility is discussed. Received 15 September 2001 and Received in final form 15 November 2001     

奥伯斯佯谬浅析

给出满足宇宙学原理的宇宙模型中计算星体视光度的一般公式，作为特例，导出“稳恒态”和“大爆炸”模型中星体视光度的表达式，结果表明这些模型是可以避免奥伯斯佯谬的。     

On collapsibilities of Yule’s measure

Simpson’s paradox reminds people that the statistical inference in a low-dimensional space probably distorts the reality in a high one seriously.To study the paradox with respect to Yule’s measure, this paper discusses simple collapsibility, strong collapsibility and consecutive collapsibility, and presents necessary and sufficient conditions of them.In fact, these conditions are of great importance for observational and experimental designs, eliminating confounding bias, categorizing discrete variables and so on.     

Destabilization paradox due to breaking the Hamiltonian and reversible symmetry

Stability of a linear autonomous non-conservative system in the presence of potential, gyroscopic, dissipative, and non-conservative positional forces is studied. The cases when the non-conservative system is close to a gyroscopic system or to a circulatory one are examined. It is known that marginal stability of gyroscopic and circulatory systems can be destroyed or improved up to asymptotic stability due to action of small non-conservative positional and velocity-dependent forces. The present paper shows that in both cases the boundary of the asymptotic stability domain of the perturbed system possesses singularities such as “Dihedral angle” and “Whitney umbrella” that govern stabilization and destabilization. In case of two degrees of freedom, approximations of the stability boundary near the singularities are found in terms of the invariants of matrices of the system. As an example, the asymptotic stability domain of the modified Maxwell-Bloch equations is investigated with an application to the stability problems of gyroscopic systems with stationary and rotating damping.