The Sylvester equation and integrable equations: I. The Korteweg-de Vries system and sine-Gordon equation

The paper is to reveal the direct links between the well known Sylvester equation in matrix theory and some integrable systems. Using the Sylvester equation $\boldsymbol{K} \boldsymbol{M}+\boldsymbol{M} \boldsymbol{K}=\boldsymbol{r}\, \boldsymbol{s}^{T}$ we introduce a scalar function $S^{(i,j)}=\boldsymbol{s}^{T}\, \boldsymbol{K}^j(\boldsymbol{I}+\boldsymbol{M})^{-1}\boldsymbol{K}^i\boldsymbol{r}$ which is defined as same as in discrete case. $S^{(i,j)}$ satisfy some recurrence relations which can be viewed as discrete equations and play indispensable roles in deriving continuous integrable equations. By imposing dispersion relations on $\boldsymbol{r}$ and $\boldsymbol{s}$, we find the Korteweg-de Vries equation, modified Korteweg-de Vries equation, Schwarzian Korteweg-de Vries equation and sine-Gordon equation can be expressed by some discrete equations of $S^{(i,j)}$ defined on certain points. Some special matrices are used to solve the Sylvester equation and prove symmetry property $S^{(i,j)}=S^{(i,j)}$. The solution $\boldsymbol{M}$ provides $\tau$ function by $\tau=|\boldsymbol{I}+\boldsymbol{M}|$. We hope our results can not only unify the Cauchy matrix approach in both continuous and discrete cases, but also bring more links for integrable systems and variety of areas where the Sylvester equation appears frequently.Comment: 23 page

甘肃永登薛家湾邵句调查

International audienceShaoju is the language spoken by residents in Xuejiawan, District Yongdeng of Gansu, China. It is a kind of argot or jargon, but not a non-Han language. The previous literature treats it as a mysterious non-Han language, even a language of Gypsy who migrated to China. Our article shows with abundant proofs that many words have been derived from different gang languages. The earliest are dated from the Song Dynasty. Only a few words have come from Turkic languages. Many of the Shaoju words have been innovations based on existing words of different periods. Their phonology, morphology and syntax have to be classified into the Chinese language system

Reduplication in languages: A case study of languages of China

International audienceReduplication is widely attested in human languages, especially in the southern hemisphere. This distribution, often complementary with plural markings, is also found in languages spoken in China, which show a correlation between plural marking and reduplication/classifiers: if reduplication and clas-sifiers are found extensively, then plural marking is not developed, and is sensitive to the semantic feature [+human]. The more plural marking is developed, such as in Altaic languages, the less this semantic feature is required. The more a language possesses a developed plural-marking morphology, the less it needs reduplication and classifiers. Subjectivity plays a key role in reduplicated adjectives. Reduplication is iconically motivated. Positive degree constitutes its core meaning. Reduplication with negative meaning characterizes the grammaticali-zation process from icon to symbol

Visualization of Co-authorshipin DIT Arrow

With the popularization of information technology and the unprecedented development of online reading, the management and service of the library are facing severe challenges; the traditional library operation mode has been challenging to optimize the service. At the same time, there is also a fatal impact on library collection and systematic management, however, with the development of visualization techniques in management and service, the library can alleviate the effect of the current network information basically, which achieves the intellectual development of library field. This study empirically provides the evidence to indicate that the force directed layout has the statistically significant performance than the radial layout for visualization of co-authorship in DIT Arrow repository based on the results of surveys

The Impact of Hedging on Stock Return and Firm Value: New Evidence from Canadian Oil and Gas Companies

This paper analyzes the impact of hedging activities of large Canadian oil and gas companies on their stock returns and firm value. Differing from the existing literature this research finds that some of these relationships are nonlinear based on the framework of nonlinear generalized additive models. The research based on this more general methodology reveals some interesting findings on oil and gas hedging activities. The large Canadian oil and gas firms are able to use hedging to protect downside risk against the unfavorable oil and gas price changes. But oil hedging appears to be more effective in protecting stock returns than gas hedging is when downside risk presents. In addition, oil and gas reserves are more likely to play a positive (negative) role when the oil and gas prices are increasing (decreasing). Finally, hedging, in particular hedging on gas, together with profitability, investment and leverage, has certain impacts on firm value.oil; gas; hedging; return; firm value; general additive models ; Canada