Three-dimensional Curve Motions Induced by the Modified Korteweg-de Vries Equation

We have constructed one-phase quasi-periodic solutions of the curve equation induced by the mKdV equation. The solution is expressed in terms of the elliptic functions of Weierstrass. This solution can describe curve dynamics such as a vortex filament with axial velocity embedded in an incompressible inviscid fluid. There exist two types of curves (type-A, type-B) according to the form of the main spectra of the finite-band integrated solution. Our solution includes various filament shapes such as the Kelvin-type wave, the rigid vortex, plane curves, closed curves, and the Hasimoto one-solitonic filament.Comment: 26 pages, 4 figure

Sine-Gordon Soliton on a Cnoidal Wave Background

The method of Darboux transformation, which is applied on cnoidal wave solutions of the sine-Gordon equation, gives solitons moving on a cnoidal wave background. Interesting characteristics of the solution, i.e., the velocity of solitons and the shift of crests of cnoidal waves along a soliton, are calculated. Solutions are classified into three types (Type-1A, Type-1B, Type-2) according to their apparent distinct properties.Comment: 11 pages, 5 figures, Contents change

Fair value accounting and financial stability.

Market prices give timely signals that can aid decision making. However, in the presence of distorted incentives and illiquid markets, there are other less benign effects that inject artifi cial volatility to prices that distorts real decisions. In a world of marking-to-market, asset price changes show up immediately on the balance sheets of financial intermediaries and elicit responses from them. Banks and other intermediaries have always responded to changes in economic environment, but marking-to-market sharpens and synchronises their responses, adding impetus to the feedback effects in financial markets. For junior assets trading in liquid markets (such as traded stocks), marking-to-market is superior to historical cost in terms of the trade-offs. But for senior, long-lived and illiquid assets and liabilities (such as bank loans and insurance liabilities), the harm caused by distortions can outweigh the benefi ts. We review the competing effects and weigh the arguments.