Laplace Transformation and Ergodic Potential Kernel for q-Process in Random Environment

This paper introduces some concepts such as q-process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q-processes in random environments.     

Embedding a novel objective function in a two-phased local search for robust vertex coloring

In this paper, we propose a two-phased local search for vertex coloring. The algorithm alternately executes two closely interacting functionalities, i.e., a stochastic and a deterministic local search. The stochastic phase is basically based on biased random sampling that, according to a probability matrix storing the probability a vertex can be assigned to a color, iteratively constructs feasible colorings. The deterministic phase, instead, consists in assigning sequentially, according to a given ordering, each vertex to the color which causes the lowest increase of the solution penalty, and then, when the schedule is constructed, swap operations are executed to improve the performance. The interaction between the two phases is implemented by tunnelling information of what happened during a phase to the successive ones. Beyond the algorithm scheme, the novelty of the approach stems from the fact that the objective function is not minimizing the number of colors but a new penalty function. The proposed approach is tested on known benchmarks for the studied problem available on the public domain. From a comparison to the state of the art it appears that the proposed approach is robust and is able to achieve best known results.     

Randomization of Sharkovskii-type theorems

We formulate an abstract scheme for the randomization of Shar- kovskii-type theorems via transformation to the deterministic case. In particular, Sharkovskii-type theorems for scalar differential equations can be randomized in this way. A random version of the standard Sharkovskii theorem is presented explicitly. Many remarks, comments and illustrating examples are supplied.

     

The Construction of Denumerable q-Processes in Random Environments-The Existence and Uniqueness

The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary and sufficient conditions for the uniqueness of q-process in random environment are given.     

Estimation of population spectrum for linear processes with random coefficients

A set of time series generated by stationary linear processes with an absolutely continuous spectral distribution is analysed. The time series can then be considered realizations of a linear process of random coefficients. Likewise, each spectral density function is a realization of a stochastic process whose function of means is called a population spectrum. We propose a kernel estimator for the population spectrum and give conditions for its consistency. We then illustrate the properties of this estimator in a simulation study and compare its performance with an alternative parametric estimator that can be found in the literature.      

Asymptotic properties of multistate random walks. I. Theory

A calculation is presented of the long-time behavior of various random walk properties (moments, probability of return to the origin, expected number of distinct sites visited) formultistate random walks on periodic lattices. In particular, we consider inhomogeneous periodic lattices, consisting of a periodically repeated unit cell which contains a finite number of internal states (sites). The results are identical to those for perfect lattices except for a renormalization of coefficients. For walks without drift, it is found that all the asymptotic random walk properties are determined by the diffusion coefficients for the multistate random walk. The diffusion coefficients can be obtained by a simple matrix algorithm presented here. Both discrete and continuous time random walks are considered. The results are not restricted to nearest-neighbor random walks but apply as long as the single-step probability distributions associated with each of the internal states have finite means and variances.     

Position dependent and stochastic thinning of point processes

A short probabilistic proof of Kallenberg's theorem [2] on thinning of point processes is given. It is extended to the case where the probability of deletion of a point depends on the position of the point and is itself random. The proof also leads easily to a statement about the rate of convergence in Renyi's theorem on thinning a renewal process.     

Convex fuzzy random variables

A theory of fuzzy random variables is developed that applies to situations involving both randomness and fuzziness. The use of membership functions that are quasi-concave play an important role in the theory. The expectation of a fuzzy random variable is a fuzzy variable (fuzzy set). The usual linearity properties of probabilistic expectation carry over to fuzzy random variables. A special case of a fuzzy Law of Large Number is proven.     

Diffusion and reaction in random media and models of evolution processes

A diffusion equation including source terms, representing randomly distributed sources and sinks is considered. For quasilinear growth rates the eigenvalue problem is equivalent to that of the quantum mechanical motion of electrons in random fields. Correspondingly there exist localized and extended density distributions dependent on the statistics of the random field and on the dimension of the space. Besides applications in physics (nonequilibrium processes in pumped disordered solid materials) a new evolution model is discussed which considers evolution as hill climbing in a random landscape.We dedicate this work to the memory of Ilya M. Lifshitz.     

Poly(propylene isophthalate), poly(propylene succinate), and their random copolymers: Synthesis and thermal properties

Poly(propylene isophthalate) (PPI), poly(propylene succinate) (PPS), and poly(propylene isophthalate/succinate) (PPI‐PPS) random copolymers were synthesized and characterized in terms of chemical structure and molecular weight. The thermal behavior was examined by TGA and DSC. All the polymers showed a good thermal stability. At room temperature, they appeared as semicrystalline materials, except 20PPI‐PPS and 30PPI‐PPS: the main effect of copolymerization was a lowering in the amount of crystallinity and a decrease of T_m with respect to homopolymers. A crystalline phase of PPI and PPS was evidenced at high content of PI or PS units, respectively. Amorphous samples were obtained after melt quenching and an increment of T_g, with the increment of PI units, was observed. This behavior was explained as due to the presence of stiff phenylene groups. The Wood equation described well T_g‐composition data. Lastly, the presence of a rigid‐amorphous phase was evidenced in copolymers, differently from the two homopolymers. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 310–321, 2007.