Beam profile measurement with CR-39 track detector for low-energy ions

A CR-39 track detector was successfully used to measure the outline of thin low-energy ion beams. After the etching, the surface of the detector was examined with an observation system composed of a Normarski microscope, a CCD camera and a digital image processing computer. Beam images obtained with the system were in good agreement on the outline of the beam formed with a beam aperture. Also, the resolving power in the beam outline measurement was roughly explained from the consideration of the ion range and the etch-pit growth in the chemical etching for the CR-39 detector.     

Optimal convergence in naming game with geography-based negotiation on small-world networks

We propose a negotiation strategy to address the effect of geography on the dynamics of naming games over small-world networks. Communication and negotiation frequencies between two agents are determined by their geographical distance in terms of a parameter characterizing the correlation between interaction strength and the distance. A finding is that there exists an optimal parameter value leading to fastest convergence to global consensus on naming. Numerical computations and a theoretical analysis are provided to substantiate our findings.     

Thermal Behavior of Hexogen Phlegmatized with Montan Waxes

Hexogen can be used pressed only if its crystals are covered by some polymeric material [1], either natural or artificial. Montan waxes, as natural polymeric materials, were used for the phlegmatization. The melting process of seven types of waxes was analyzed by differential scanning calorimetry. The thermal decomposition processes of hexogens and phlegmatized hexogens were investigated by dynamic differential scanning calorimetry and dynamic thermogravimetric analyses. Kinetic parameters of the decomposition processes of hexogens were evaluated by using data obtained from differential scanning calorimetric curves. This revised version was published online in August 2006 with corrections to the Cover Date.     

Comparison theorems for diffusion processes

We prove comparison theorems for diffusion processes onR ^d. From these theorems we derive lower and upper bounds for the transition probabilities of a diffusion process. In contrast to the known estimates for fundamental solutions of parabolic equations our bounds do not depend on the moduli of continuity of the coefficients of the differential operator.     

Continuous dependence estimates for viscosity solutions of integro-PDEs

We present a general framework for deriving continuous dependence estimates for, possibly polynomially growing, viscosity solutions of fully nonlinear degenerate parabolic integro-PDEs. We use this framework to provide explicit estimates for the continuous dependence on the coefficients and the “Lévy measure” in the Bellman/Isaacs integro-PDEs arising in stochastic control/differential games. Moreover, these explicit estimates are used to prove regularity results and rates of convergence for some singular perturbation problems. Finally, we illustrate our results on some integro-PDEs arising when attempting to price European/American options in an incomplete stock market driven by a geometric Lévy process. Many of the results obtained herein are new even in the convex case where stochastic control theory provides an alternative to our pure PDE methods.     

On the growth of meromorphic solutions of the Schwarzian differential equations

We study the properties of meromorphic solutions of the Schwarzian differential equations in the complex plane by using some techniques from the study of the class Wp. We find some upper bounds of the order of meromorphic solutions for some types of the Schwarzian differential equations. We also show that there are no wandering domains nor Baker domains for meromorphic solutions of certain Schwarzian differential equations.     

Similarity of $$sgn x( - \tfrac{{d^2 }}{{dx^2 }} + c\delta )$$ Type Operators to Normal and Self-adjoint Operators

Mathematical Notes -     

一类复微分方程的代数体函数可允许解

应用Nevanlinna值分布理论，对一般复微分方程的代数体函数可允许解的存在性作了探讨，改进了文[7～8]中的主要结果．