We investigate dynamical properties of bright solitons with a finite background in the F = 1 spinor Bose-Einstein condensate (BEC), based on an integrable spinor model which is equivalent to the matrix nonlinear Schrödinger equation with a self-focusing nonlineality.We apply the inverse scattering method formulated for nonvanishing boundary conditions.The resulting soliton solutions can be regarded as a generalization of those under vanishing boundary conditions. One-soliton solutions are derived in an explicit manner. According to the behaviors at the infinity, they are classified into two kinds, domain-wall (DW) type and phase-shift (PS) type. The DW-type implies the ferromagnetic state with nonzero total spin and the PS-type implies the polar state, where the total spin amounts to zero. We also discuss two-soliton collisions. In particular, the spin-mixing phenomenon is confirmed in a collision involving the DW-type. The results are consistent with those of the previous studies for bright solitons under vanishing boundary conditions and dark solitons. As a result, we establish the robustness and the usefulness of the multiple matter-wave solitons in the spinor BECs.
Highlights
We study the relationship between oil and the US stock market.
We compare the relationship before and after the onset of the Covid-19 crisis.
To do so, we compute upside and downside correlations between the two markets.
We find that both upside and downside correlations increased after the crisis.
We reinvestigate the classic portfolio optimization problem where the notion of portfolio risk is captured by the "Foster-Hart risk"-a new, bankruptcy-proof, reserve based measure of risk, extremely sensitive to left tail events (Foster and Hart, 2009). To include financial market frictions induced by market microstructure, we employ a general, ex-ante transaction cost function with fixed, linear and quadratic penalty terms in the objective function. We represent the US equity market by the Dow Jones Industrial Average (DJIA) index and study the performance of the Foster-Hart optimal DJIA portfolio. In order to capture the skewed and leptokurtotic nature of real life stock returns, we model the returns of the DJIA constituents as an ARMA-GARCH process with multivariate "normal tempered stable" innovations. We demonstrate that the Foster-Hart optimal portfolio's performance is superior to those obtained under several techniques currently in use in academia and industry.
We reinvestigate the classic portfolio optimization problem where the notion of portfolio risk is captured by the "Foster-Hart risk"-a new, bankruptcy-proof, reserve based measure of risk, extremely sensitive to left tail events (Foster and Hart, 2009). To include financial market frictions induced by market microstructure, we employ a general, ex-ante transaction cost function with fixed, linear and quadratic penalty terms in the objective function. We represent the US equity market by the Dow Jones Industrial Average (DJIA) index and study the performance of the Foster-Hart optimal DJIA portfolio. In order to capture the skewed and leptokurtotic nature of real life stock returns, we model the returns of the DJIA constituents as an ARMA-GARCH process with multivariate "normal tempered stable" innovations. We demonstrate that the Foster-Hart optimal portfolio's performance is superior to those obtained under several techniques currently in use in academia and industry.
We examine the effectiveness of Foster-Hart optimization for currency portfolios. Compared to stock trading, short selling is quite common in currency trading. Combining long and short positions leads to maintaining positive expected portfolio returns. Foster-Hart optimization is more applicable to currency portfolios than to stock portfolios because the Foster-Hart risk measure is not defined for the gamble whose expected returns are negative. Our sample portfolio consists of ten European currencies. For time series analysis, we employ a generalized autoregressive conditional heteroscedasticity (GARCH) model with multivariate normal tempered stable (MNTS) distributed residuals in order to capture fat-tailedness, skewness, and asymmetric interdependence of exchange rate dynamics. Statistical tests indicate that the model is recommendable among the candidate models. We establish that Foster-Hart optimization is more profitable than standard techniques in this context.
We propose a new ternary infinite (even full-infinite) square-free sequence.
The sequence is defined both by an iterative method and by a direct definition.
Both definitions are analogous to those of the Thue-Morse sequence. The direct
definition is given by a deterministic finite automaton with output. In short,
the sequence is automatic.Comment: 9 pages, 1 figures, to appear in Information Processing Letter
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