A note on the radial solutions for the supercritical Henon equation

We prove the existence of a positive radial solution for the H\'enon equation with arbitrary growth. The solution is found by means of a shooting method and turns out to be an increasing function of the radial variable. Some numerical experiments suggest the existence of many positive oscillating solutions.Comment: 13 pages, 4 figure

Singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities

We consider a class of singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities. The dependence on the spatial coordinates comes from the presence of a potential and of a function representing a saturation effect. We investigate the existence of nontrivial nonnegative solutions concentrating around local minima of both the potential and of the saturation function. Necessary conditions to locate the possible concentration points are also given

Study on the Neural Cell Adhesion Molecules in Heart Development of Chicken

Cell adhesion molecules mediate specific cell-cell interactions during embryogenesis and tissue formation. Among cell-cell adhesion molecules (CAMs), we have been particularly interested in the neural cell adhesion molecule (NCAM) which is the prototypical member of the family of Ca++ -independent CAMs. Previous studies of NCAM cDNAs have revealed an alternatively spliced set of small exons (12A, 12B, 12C, 12D) that encode a region in the extracellular portion of the molecule known as the muscle specific domain (MSD). The entire MSD region can be expressed in skeletal muscle, heart, and skin; only exons 12A and 12D have been found in brain. These studies, however, did not reveal which NCAM polypeptides contain the MSD region or the immunohistochemical distribution of these NCAM molecules. To address these questions, we prepared antibodies against the oligopeptides encoded by exons 12A and 12B and by exons 12C and 12D and used these antibodies to study the forms of NCAM containing the MSD region expressed during embryonic chicken heart development. These antibodies recognize certain forms of NCAM found in the heart but do not recognize brain NCAM. In the heart, each of the splice variants of NCAM (ld, sd, and ssd) that differ in their mode of attachment to the plasma membrane or in the size of their cytoplasmic domain is expressed in a form containing and in a form lacking the MSD region. No microheterogeneity is observed in the size of NCAM molecules containing the MSD region, even at the level of CNBr fragments, suggesting that exons 12A-D are expressed as a single unit. We have identified six different isoforms of heart NCAM which exhibit changing temporal and spatial patterns of expression during development: the three forms of NCAM, ld, sd, and ssd, can also be expressed in a form containing the MSD sequence. Depending on the site and the stage of development, the percentage of NCAM molecules containing the MSD region can vary from nearly a to 100 percent. In general, this percentage increases during development. In immunohistochemical studies of hearts from stage 18 embryos, forms of NCAM containing the MSD region colocalized with Z-discs. No other adhesion molecules were found in this distribution at this early stage of development. Studies on isolated cells in vitro demonstrate that the colocalization with Z discs of NCAM molecules containing the MSD region does not depend on cell-cell contact and raise the possibility that this form of NCAM is involved in cell-extracellular matrix interactions. The association of NCAM molecules containing the MSD region with Z discs suggests that this form of NCAM is involved in early myofibrillogenesis

Fast, Preisach-like characterization of hysteretic systems

Proposed is a substantially simplified, Preisach-like model for characterization of hysteretic systems, in particular magnetic systems. The main idea is to replace a two-dimensional Preisach density with just two real functions, describing in a {\em unique way} the reversible and irreversible processes. As a byproduct of our model we prove, that the major hysteresis loop alone is insufficient to produce the unique Preisach map. Keywords: magnetic hysteresis; magnetization processes; materials testing; modeling.Comment: 7 double spaced pages, 4 figures. Presented at 5th International Symposium on Hysteresis and Micromagnetic Modeling, Budapest, Hungary, May 30th - June 1st, 200

Distributionally Robust Decentralized Volt-Var Control with Network Reconfiguration

This paper presents a decentralized volt-var control (VVC) and network reconfiguration strategy to address the challenges arising from the growing integration of distributed energy resources, particularly photovoltaic (PV) generation units, in active distribution networks. To reconcile control measures with different time resolutions and empower local control centers to handle intermittency locally, the proposed approach leverages a two-stage distributionally robust optimization; decisions on slow-responding control measures and set points that link neighboring subnetworks are made in advance while considering all plausible distributions of uncertain PV outputs. We present a decomposition algorithm with an acceleration scheme for solving the proposed model. Numerical experiments on the IEEE 123 bus distribution system are given to demonstrate its outstanding out-of-sample performance and computational efficiency, which suggests that the proposed method can effectively localize uncertainty via risk-informed proactive timely decisions