On the Vector Process Obtained by Iterated Integration of the Telegraph Signal

We analyse the vector process (X ₀(t), X ₁(t),...,X _n(t), t > 0) where , and X ₀(t) is the o two-valued telegraph process.In particular, the hyperbolic equations governing the joint distributions of the process are derived and analysed.Special care is given to the case of the process (X ₀(t), X ₁(t), X ₂(t), t > 0) representing a randomly accelerated motion where some explicit results on the probability distribution are derived.     

迭代过程及其在高阶微分方程中的应用

通过对布朗运动和电报过程的适当迭代,使之迭代过程的转移函数满足不同形式的高阶抛物型或双曲型微分方程．对迭代过程进行适当的时间变换,还可以使迭代过程的转移函数满足系数依赖于时间的高阶微分方程．本文还讨论了迭代布朗运动最大值的分布及其有关性质．     

Strongly indefinite systems with critical Sobolev exponents

We consider an elliptic system of Hamiltonian type on a bounded domain. In the superlinear case with critical growth rates we obtain existence and positivity results for solutions under suitable conditions on the linear terms. Our proof is based on an adaptation of the dual variational method as applied before to the scalar case.

     

Polymer based interfaces as bioinspired 'smart skins'

This work reports on already achieved results and ongoing research on the development of complex interfaces between humans and external environment, based on organic synthetic materials and used as smart 'artificial skins'. They are conceived as wearable and flexible systems with multifunctional characteristics. Their features are designed to mimic or augment a broad-spectrum of properties shown by biological skins of humans and/or animals. The discussion is here limited to those properties whose mimicry/augmentation is achievable with currently available technologies based on polymers and oligomers. Such properties include tactile sensing, thermal sensing/regulation, environmental energy harvesting, chromatic mimetism, ultra-violet protection, adhesion and surface mediation of mobility. Accordingly, bioinspired devices and structures, proposed as suitable functional analogous of natural architectures, are analysed. They consist of organic piezoelectric sensors, thermoelectric and pyroelectric sensors and generators, photoelectric generators, thermal and ultra-violet protection systems, electro-, photo- and thermo-chromic devices, as well as structures for improved adhesion and reduced fluid-dynamic friction.     

A molecular modelling approach to rationalize the stereochemical outcome of the Burkholderia cepacia lipase-catalyzed transesterification of aromatic primary alcohols with vinyl esters with different chain lengths in chloroform

The Burkholderia cepacia lipase-catalyzed transesterification of 2-methyl-3-phenyl-1-propanol with vinyl esters proceeds with high enantioselectivity independently of the acyl chain length and the low enantioselectivity of the same reaction with 2-phenyl-1-propanol is not affected by chain length of the vinyl esters. A molecular modelling approach has been developed in order to rationalize the enzymatic results.     

On the index of caterpillars

The index of a graph is the largest eigenvalue of its adjacency matrix. Among the trees with a fixed order and diameter, a graph with the maximal index is a caterpillar. In the set of caterpillars with a fixed order and diameter, or with a fixed degree sequence, we identify those whose index is maximal.