On subnormal solutions of second order linear periodic differential equations

In this paper, we investigate the existence and the form of subnormal solution for a class of second order periodic linear differential equations, estimate the growth properties of all solutions, and answer the question raised by Gundersen and Steinbart.     

Automorphisms of a rooted tree of countably infinite valency

Automorphisms of a rooted tree of infinite countable valency are studied. Two families of subgroups associated with growths of functions are introduced. This gives a classification of large sublattices of subgroups. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 343, 2007, pp. 199–205.     

A New Approach to Analysis of Polling Systems

In this paper, we consider polling systems with J stations with Poisson arrivals and general service distributions attended by a cyclic server. The service discipline at each station is either exhaustive or gated. We propose a new approach to analysis of the mean waiting times in the polling systems. The outline of our method is as follows. We first define the stochastic process Q that represents an evolution of the system state, and define three types of the performance measures W _i ,H _i and F _i , which are the expected waiting times conditioned on the system state. Then from the analysis of customers at polling instants, we find their linear functional expressions. The steady state average waiting times can be derived from the performance measures by simple limiting procedures. Their actual values can be obtained by solving J(J+1) linear equations.     

Atom-transfer radical polymerization of styrene with bifunctional and monofunctional initiators: Experimental and mathematical modeling results

Bulk atom transfer radical polymerization (ATRP) of styrene was carried out at 110 °C using benzal bromide as bifunctional initiator and 1-bromoethyl benzene as monofunctional initiator. CuBr/2,2′-bipyridyl was used as the ATRP catalyst. The polymerization kinetic data for styrene with both initiators was measured and compared with a mathematical model based on the method of moments and another one using Monte Carlo simulation. An empirical correlation was incorporated into the model to account for diffusion-controlled termination reactions. Both models can predict monomer conversion, polymer molecular weight averages, and polydispersity index. In addition, the Monte Carlo model can also predict the full molecular weight distribution of the polymer. Our experimental results agree with our model predictions that bifunctional initiators can produce polymers with higher molecular weights and narrower molecular weight distributions than monofunctional initiators. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2212–2224, 2007     

High energy spectroscopy in Ce and La compounds

X-ray photoemission, X-ray photoabsorption and bremmstrahlung isochromat spectroscopy in Ce and La compounds are theoretically analyzed by using the single-site Anderson model incorporated with various final state interactions. Discussions are given on the physical information derived from the analysis and also on similarities and differences in spectral features between metallic and insulating systems.     

The Studies of Free Radical Cyclization Reactions Mediated by Sulfonyl Chloride (I)

A study of the free racinoal reaction of vinylcycloprelpane mediated by p-toluenesulfonyl chloride is described.     

The role of pyrrhotite (Fe7S8) and the sample texture in the hydrothermal transformation of pentlandite ((Fe,Ni)9S8) to violarite ((Ni,Fe)3S4)

The catalytic role of pyrrhotite (Fe₇S₈) in the reaction kinetics of the hydrothermal transformation of pentlandite ((Fe,Ni)₉S₈) to violarite ((FeNi₂S₄) was found to depend on the physical form of pyrrhotite. Pyrrhotite in fine scale intergrown with pentlandite boosts the reaction, whereas in a mechanical mixture of pyrrhotite and pentlandite, it plays the opposite role. This phenomenon was interpreted as result of dissolution of pyrrhotite under reaction conditions.     

Chemical derivatization technique in ToF-SIMS for quantification analysis of surface amine groups

A chemical derivatization technique in ToF-SIMS along with principal component analysis (PCA) were used to perform a quantitative study of the surface amine density of the plasma-polymerized ethylenediamine (PPEDA) thin film. We used the scores on principal component (PC) 1 from a PCA of ToF-SIMS data for the PPEDA films and their chemical-derivatized surfaces for comparison with the surface amine densities. These surface amine densities were independently determined by UV-visible spectroscopy. Our work found a good linear relationship between the surface amine densities and the scores on PC 1 from a PCA of the ToF-SIMS data for the chemical-derivatized PPEDA surfaces, but not for the PPEDA thin films themselves. In addition to quantification, our PCA results provided insights into the surface chemical composition of each surface.     

Calibrated lifts of minimal submanifolds

A canonical real line bundle associated to a minimal Lagrangian submanifold in a Kähler-Einstein manifold X is known to be special Lagrangian when considered as a subset of the canonical line bundle of X with a natural Calabi-Yau structure. We first verify this result by standard moving frame computation, and obtain a uniform lower bound for the mass of compact minimal Lagrangian submanifolds in CPn. Similar correspondence is then proved for integrable G₂ and Spin(7) structures on the bundle of anti self dual 2-forms and a Spin bundle respectively of a self dual Einstein 4-manifold N constructed by Bryant and Salamon. In this case, analogues of tangent and normal bundles of certain minimal surfaces in N are calibrated, i.e., associative, coassociative, or Cayley.     

Vector Ordinal Optimization

Ordinal optimization is a tool to reduce the computational burden in simulation-based optimization problems. So far, the major effort in this field focuses on single-objective optimization. In this paper, we extend this to multiobjective optimization and develop vector ordinal optimization, which is different from the one introduced in Ref. 1. Alignment probability and ordered performance curve (OPC) are redefined for multiobjective optimization. Our results lead to quantifiable subset selection sizes in the multiobjective case, which supplies guidance in solving practical problems, as demonstrated by the examples in this paper.This paper was supported in part by Army Contract DAAD19-01-1-0610, AFOSR Contract F49620-01-1-0288, and a contract with United Technology Research Center (UTRC). The first author received additional funding from NSF of China Grants 60074012 and 60274011, Ministry of Education (China), and a Tsinghua University (Beijing, China) Fundamental Research Funding Grant, and the NCET program of China.The authors are grateful to and benefited from two rounds of reviews from three anonymous referees.