Discontinuous local semiflows for Kurzweil equations leading to LaSalle`s invariance principle for differential systems with impulses at variable times

In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle`s invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle`s invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times. (C) 2011 Elsevier Inc. All rights reserved.

Identification of genes associated with local aggressiveness and metastatic behavior in soft tissue tumors

Soft tissue tumors represent a group of neoplasia with different histologic and biological presentations varying from benign, locally confined to very aggressive and metastatic tumors. The molecular mechanisms responsible for such differences are still unknown. The understanding of these molecular alterations mechanism will be critical to discriminate patients who need systemic treatment from those that can be treated only locally and could also guide the development of new drugs` against this tumors. Using 102 tumor samples representing a large spectrum of these tumors, we performed expression profiling and defined differentially expression genes that are likely to be involved in tumors that are locally aggressive and in tumors with metastatic potential. We described a set of 12 genes (SNRPD3, MEGF9, SPTAN-1, AFAP1L2, ENDOD1, SERPIN5, ZWINTAS, TOP2A, UBE2C, ABCF1, MCM2, and ARL6IP5) showing opposite expression when these two conditions were compared. These genes are mainly related to cell-cell and cell-extracellular matrix interactions and cell proliferation and might represent helpful tools for a more precise classification and diagnosis as well as potential drug targets.

Local solvability for a class of evolution equations

Motivated by the celebrated example of Y. Kannai of a linear partial differential operator which is hypoelliptic but not locally solvable, we consider it class of evolution operators with real-analytic coefficients and study their local solvability both in L(2) and in the weak sense. In order to do so we are led to propose a generalization of the Nirenberg-Treves condition (psi) which is suitable to our study. (C) 2009 Published by Elsevier Inc.

Derived tame local and two-point algebras

We determine derived representation type of complete finitely generated local and two-point algebras over an algebraically closed field. (C) 2009 Elsevier Inc. All rights reserved.