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

Point Estimation and Confidence Interval for Population Proportion Under Triple Sampling Scheme

This thesis will focus on both point and confidence interval estimations for population proportions under a triple sampling scheme when the population following a binomial distribution. On the basis of introducing and reviewing methodologies for both single and double sampling schemes, this paper will explore how a triple sampling machinery works for the estimating process under a binomial distribution. The later part of this paper renders algorithms and simulation results for both double and triple sampling estimations, to evaluate the performance of this newly developed methodology

Effect of size, shape, and surface modification on cytotoxicity of gold nanoparticles to human Hep-2 and canine MDCK cells

There have been increasing interests in applying gold nanoparticles in biological research, drug delivery, and therapy. As the interaction of gold nanoparticles with cells relies on properties of nanoparticles, the cytotoxicity is complex and still under debating. In this work, we investigate the cytotoxicity of gold nanoparticles of different encapsulations, surface charge states, sizes and shapes to both human HEp-2 and canine MDCK cells. We found that cetyltrimethylammonium-bromide- (CTAB-) encapsulated gold nanorods (GNRs) were relatively higher cytotoxic than GNRs undergone further polymer coating and citrate stabilized gold nanospheres (GNSs). The toxicity of CTAB-encapsulated GNRs was mainly caused by CTAB on GNRs’ surface but not free CTAB in the solution. No obvious difference was found among GNRs of different aspect ratios. Time-lapse study revealed that cell death caused by GNRs occurred predominately within one hour through apoptosis, whereas cell death by free CTAB was in a time- and dose-dependent manner. Both positively and negatively surface-charged polymer-coated GNRs (PSS-GNRs and PAH-PSS-GNRs) showed similar levels of cytotoxic, suggesting the significance of surface functionality rather than surface charge in this case

Effect of size, shape, and surface modification on cytotoxicity of gold nanoparticles to human Hep-2 and canine MDCK cells

There have been increasing interests in applying gold nanoparticles in biological research, drug delivery, and therapy. As the interaction of gold nanoparticles with cells relies on properties of nanoparticles, the cytotoxicity is complex and still under debating. In this work, we investigate the cytotoxicity of gold nanoparticles of different encapsulations, surface charge states, sizes and shapes to both human HEp-2 and canine MDCK cells. We found that cetyltrimethylammonium-bromide- (CTAB-) encapsulated gold nanorods (GNRs) were relatively higher cytotoxic than GNRs undergone further polymer coating and citrate stabilized gold nanospheres (GNSs). The toxicity of CTAB-encapsulated GNRs was mainly caused by CTAB on GNRs’ surface but not free CTAB in the solution. No obvious difference was found among GNRs of different aspect ratios. Time-lapse study revealed that cell death caused by GNRs occurred predominately within one hour through apoptosis, whereas cell death by free CTAB was in a time- and dose-dependent manner. Both positively and negatively surface-charged polymer-coated GNRs (PSS-GNRs and PAH-PSS-GNRs) showed similar levels of cytotoxic, suggesting the significance of surface functionality rather than surface charge in this case

Effect of size, shape, and surface modification on cytotoxicity of gold nanoparticles to human Hep-2 and canine MDCK cells

There have been increasing interests in applying gold nanoparticles in biological research, drug delivery, and therapy. As the interaction of gold nanoparticles with cells relies on properties of nanoparticles, the cytotoxicity is complex and still under debating. In this work, we investigate the cytotoxicity of gold nanoparticles of different encapsulations, surface charge states, sizes and shapes to both human HEp-2 and canine MDCK cells. We found that cetyltrimethylammonium-bromide- (CTAB-) encapsulated gold nanorods (GNRs) were relatively higher cytotoxic than GNRs undergone further polymer coating and citrate stabilized gold nanospheres (GNSs). The toxicity of CTAB-encapsulated GNRs was mainly caused by CTAB on GNRs’ surface but not free CTAB in the solution. No obvious difference was found among GNRs of different aspect ratios. Time-lapse study revealed that cell death caused by GNRs occurred predominately within one hour through apoptosis, whereas cell death by free CTAB was in a time- and dose-dependent manner. Both positively and negatively surface-charged polymer-coated GNRs (PSS-GNRs and PAH-PSS-GNRs) showed similar levels of cytotoxic, suggesting the significance of surface functionality rather than surface charge in this case

Regional economic status inference from information flow and talent mobility

Novel data has been leveraged to estimate socioeconomic status in a timely manner, however, direct comparison on the use of social relations and talent movements remains rare. In this letter, we estimate the regional economic status based on the structural features of the two networks. One is the online information flow network built on the following relations on social media, and the other is the offline talent mobility network built on the anonymized resume data of job seekers with higher education. We find that while the structural features of both networks are relevant to economic status, the talent mobility network in a relatively smaller size exhibits a stronger predictive power for the gross domestic product (GDP). In particular, a composite index of structural features can explain up to about 84% of the variance in GDP. The result suggests future socioeconomic studies to pay more attention to the cost-effective talent mobility data.Comment: 7 pages, 5 figures, 2 table

Dynamical generation of dark solitons in spin-orbit-coupled Bose-Einstein condensates

We numerically investigate the ground state, the Raman-driving dynamics and the nonlinear excitations of a realized spin-orbit-coupled Bose-Einstein condensate in a one-dimensional harmonic trap. Depending on the Raman coupling and the interatomic interactions, three ground-state phases are identified: stripe, plane wave and zero-momentum phases. A narrow parameter regime with coexistence of stripe and zero-momentum or plane wave phases in real space is found. Several sweep progresses across different phases by driving the Raman coupling linearly in time is simulated and the non-equilibrium dynamics of the system in these sweeps are studied. We find kinds of nonlinear excitations, with the particular dark solitons excited in the sweep from the stripe phase to the plane wave or zero-momentum phase within the trap. Moreover, the number and the stability of the dark solitons can be controlled in the driving, which provide a direct and easy way to generate dark solitons and study their dynamics and interaction properties.Comment: 10 pages, 9 figur

Disclosure and Cost of Equity Capital Revisited

We reexamine the relation between disclosure indices and cost of equity capital employing an empirical specification similar to that of Botosan (1997) for a substantially larger sample over an extended time frame made possible by textual analysis. Our results provide no support for a hypothesis of a negative relation between disclosure indices and implied cost of equity capital. Rather, consistent with a bias of implied cost of equity capital as a proxy for expected return depicted by Hughes, Liu, and Liu (2009), we find strong evidence of a positive relation