Pre Stieltjes Functions

In this paper we characterize the class C_k{{mathcal{C}_k}} of functions f on (0,∞) for which f(x), . . . ,(x ^k f(x))^(k) are completely monotonic for given k. In the limit we obtain the well-known characterization of the class of Stieltjes functions as those functions f defined on the positive half line for which (x ^k f(x))^(k) is completely monotonic on (0,∞) for all k ≥ 0.     

A Principled, Complete, and Efficient Representation of C++

We present a systematic representation of C++, called IPR, for complete semantic analysis and semantics-based program transformations. We describe the ideas and design principles that shaped the IPR. In particular, we describe how general type-based unification is key to minimal compact representation, fast type-safe traversal, and scalability. For example, the representation of a fairly typical non-trivial C++ program in GCC 3.4.2 was 32 times larger than its IPR representation; this led to significant improvements to GCC. IPR is general enough to handle real-world programs involving many translation units, archaic programming styles, and generic programming using C++0x extensions that affect the type system. The difficult issue of how to represent irregular (ad hoc) features in a systematic (non-ad hoc) manner is among the key contributions of this paper. The IPR data structure can represent all of C++ with just 157 simple node types; to compare the ISO C++ grammar has over 700 productions. The IPR is used for a variety of program analysis and transformation tasks, such as visualization, loop simplification, and concept extraction. Finally, we report impacts of this work on existing C++ compilers.     

Instability induced by cross-diffusion in reaction–diffusion systems

In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient conditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cross-diffusion can induce the instability of an equilibrium which is stable for the kinetic system and for the self-diffusion–reaction system.     

Physical processes in azobenzene polymers on irradiation with polarized light

Azobenzenes can serve as model compounds for the study of transcis isomerization in more complex molecules. We have performed time-resolved spectroscopy in solutions containing free azobenzene chromophores and diols with a view to obtaining the energy levels and lifetimes of the excited states. A transition route based on experimental results for the theoretically calculated energy level scheme is proposed. Physical observations of surface relief in thin films of azobenzene polymers when irradiated with polarized light are reported. These include two beam polarization holographic observations and single beam transmission measurements through a mask, followed by atomic force microscope and profiler investigations. It is concluded that none of the prevalent theories can explain all the observed facts.