Asymptotics for a censored generalized linear model with unknown link function

For censored response variable against projected co-variable, a generalized linear model with an unknown link function can cover almost all existing models under censorship. Its special cases include the accelerated failure time model with censored data. Such a model in the uncensored case is called the single-index model in econometrics. In this paper, we systematically study the asymptotic properties. We derive the central limit theorem and the law of the iterated logarithm for an estimator of the direction parameter. We also obtain the optimal convergence rate of an estimator of the unknown link function in the model.      

Beliefs and Attitudes Toward Mathematics Among Third- and Fifth-Grade Students: A Descriptive Study

A survey on attitudes toward mathematics of third- and fifth-grade students enrolled in a large urban school district was conducted in the spring of 1994 as part of a review of the mathematics program. Student responses to survey items were analyzed with respect to gender and grade level. Although girls and boys were equally likely to indicate that they like mathematics, in both Grades 3 and 5, boys were more likely than girls to report being good at mathematics. This result has often been reported for older students but has rarely been explored in younger children. Some gender and grade differences were observed in students' attitudes towards the specific strands of mathematics. Both girls and boys in Grade 5 were more likely than students in Grade 3 to believe that mathematics was relevant to their lives. Virtually all children thought that both girls and boys needed to study mathematics. No gender or grade differences in students' beliefs regarding the process of learning mathematics were observed. The results support the need for further research to identify variables that influence the development of student perceptions and attitudes toward mathematics during elementary school.     

Finite-time dividend-ruin models

We consider the finite-time horizon dividend-ruin model where the firm pays out dividends to its shareholders according to a dividend-barrier strategy and becomes ruined when the firm’s asset value falls below the default threshold. The asset value process is modeled as a restricted Geometric Brownian process with an upper reflecting (dividend) barrier and a lower absorbing (ruin) barrier. Analytical solutions to the value function of the restricted asset value process are provided. We also solve for the survival probability and the expected present value of future dividend payouts over a given time horizon. The sensitivities of the firm asset value and dividend payouts to the dividend barrier, volatility of the firm asset value and firm’s credit quality are also examined.     

Effect of plasticizer dibutyl phthalate on the thermal decomposition of nitrocellulose

This paper aims to investigate the effects of plasticizer dibutyl phthalate (DBP) on the thermal decomposition of nitrocellulose (NC) by using a series of analytical apparatuses. In the present study, the detailed structures of pure NC (NC-P) and NC with DBP (NC-D) were revealed by scanning electron microscope. It was found that the fibers in NC-D are more closely aligned than those in NC-P, which makes the thermal behaviors of NC-D different from NC-P. The thermal stability of both NC-P and NC-D was examined by means of simultaneous TG-DSC apparatus (STA). Three different kinetic methods (Kissinger–Akahira–Sunose method, Ozawa–Flynn–Wall method, and Friedman method) were applied for determining the activation energy E of these two NC samples. Moreover, the experimental data were compared with sigmoidal models and pre-exponential factor was calculated by compensation effect. Besides, in situ Fourier transform infrared (FTIR) and a TGA instrument coupled with Frontier FTIR spectrometer were employed to investigate the characteristic functional groups of decomposition residues and gaseous products at different temperatures, respectively. The results show that NC-P and NC-D have similar decomposition products and decomposition mechanisms.     

Estimates for dimensions of spaces of siegel modular cusp forms

Every Siegel modular form has a Fourier-Jacobi expansion. This paper provides various sets of Fourier coefficients whose vanishing implies that the associated cusp form is identically zero. We call such setsestimates because in the Fourier series case, an upper bound for the dimension of the vector space of cusp forms is provided by the cardinality of the set. Our general estimates have, among others, those estimates of Siegel and Eichler as corollaries. In particular, one new corollary of our general estimates appears to be superior for computational purposes to all other known estimates. To illustrate the use of this corollary, we prove the known result that the theta series of the latticesD ₁₆ ⁺ andE ₈ ⊕E ₈ are the same in degreen = 3 by computing just one Fourier coefficient. 1991 Mathematics Subject Classification. 11F46 (11F30, 11F27).     

Development of capillary zone electrophoresis-electrospray ionization-mass spectrometry for the determination of lamotrigine in human plasma

A method of coupling capillary zone electrophoresis (CZE) with electrospray ionization-mass spectrometry (ESI-MS) detection has been developed for monitoring an antiepileptic drug, lamotrigine (LTG) in human plasma. The CZE-MS was developed in three stages: (i) CZE separation and ESI-MS detection of LTG and tyramine (TRM, internal standard) were simultaneously optimized by studying the influence of CZE background electrolyte (BGE) pH, BGE ionic strength, and nebulizer pressure of the MS sprayer; (ii) sheath liquid parameters, such as pH, ionic strength, organic modifier content, and flow rate of the sheath liquid, were systematically varied under optimum CZE-MS conditions developed in the first stage; (iii) MS sprayer chamber parameters (drying gas temperature and drying gas flow rate) were varied for the best MS detection of LTG. The developed assay was finally applied for the determination of LTG in plasma samples. The linear range of LTG in plasma sample assay was between 0.1-5.0 microg/mL with a limit of detection as low as 0.05 microg/mL and run time less than 6 min. Finally, the concentration-time profile of LTG in human plasma sample was found to correlate well when CZE-ESI-MS was compared to a more established method of high-performance liquid chromatography with ultraviolet detection.