Invariants of binary differential equations

In this paper, we study binary differential equations a(x, y)dy (2) + 2b(x, y) dx dy + c(x, y)dx (2) = 0, where a, b, and c are real analytic functions. Following the geometric approach of Bruce and Tari in their work on multiplicity of implicit differential equations, we introduce a definition of the index for this class of equations that coincides with the classical Hopf`s definition for positive binary differential equations. Our results also apply to implicit differential equations F(x, y, p) = 0, where F is an analytic function, p = dy/dx, F (p) = 0, and F (pp) not equal aEuro parts per thousand 0 at the singular point. For these equations, we relate the index of the equation at the singular point with the index of the gradient of F and index of the 1-form omega = dy -aEuro parts per thousand pdx defined on the singular surface F = 0.

Differential response of AMPA and NMDA glutamate receptors of Purkinje cells to aging of the chicken cerebellum

Aging can lead to cognitive, affective, learning, memory and motor deficits. Since the cerebellum and glutamatergic neurotransmission are involved in several of those functions, the present work aimed at studying the expression of AMPA and NMDA glutamate receptor subunits in the chick cerebellum during aging. Young (30 days old) and aged (ca. 4 years old) chickens (Gallus gallus) were used in order to evaluate the expression of GluR1, GluR2/3 and NR1 subunits. The cerebella of young and aged chickens were subjected to immunohistochemical and immunoblotting techniques. Numbers of GluR1, GluR2/3 and NR1-positive cells and optical density of the immunoblotting data were analyzed and submitted to statistical analysis using ANOVA and the Bonferroni post hoc test. Mean density of Purkinje cells stained for Giemsa, GluR1, GluR2/3 and NR1 in the cerebellum all showed a statistically significant decrease in aged animals when compared to the young animals (Giemsa, P < 0.01; GluRs and NR1, P < 0.03). However, the ratio of GluR1 and GluR2/3-positive Purkinje cells in relation the total number of Purkinje cells found in each time point decreased with aging (ca. 10%), whereas the ratio of NR1-positive cells increased (ca. 9%). The immunoblotting data showed a significant decrease of GluR1 (ca. 66%) and GluR2/3 (ca. 55%) protein expression with aging, but did not reveal changes for NR1. Our data suggest that aging can lead to differential changes in the pattern of expression of glutamate receptor subunits, which can underlie at least part of the cognitive and motor disorders found in aged animals. (c) 2010 Elsevier Ireland Ltd. All rights reserved.

Differential Antitumor Effects of IgG and IgM Monoclonal Antibodies and Their Synthetic Complementarity-Determining Regions Directed to New Targets of B16F10-Nex2 Melanoma Cells

Malignant melanoma has increased incidence worldwide and causes most skin cancer-related deaths. A few cell surface antigens that can be targets of antitumor immunotherapy have been characterized in melanoma. This is an expanding field because of the ineffectiveness of conventional cancer therapy for the metastatic form of melanoma. In the present work, antimelanoma monoclonal antibodies (mAbs) were raised against B16F10 cells (subclone Nex4, grown in murine serum), with novel specificities and antitumor effects in vitro and in vivo. MAb A4 (IgG2ak) recognizes a surface antigen on B16F10-Nex2 cells identified as protocadherin beta(13). It is cytotoxic in vitro and in vivo to B16F10-Nex2 cells as well as in vitro to human melanoma cell lines. MAb A4M (IgM) strongly reacted with nuclei of permeabilized murine tumor cells, recognizing histone 1. Although it is not cytotoxic in vitro, similarly with mAb A4, mAb A4M significantly reduced the number of lung nodules in mice challenged intravenously with B16F10-Nex2 cells. The V(H) CDR3 peptide from mAb A4 and V(L) CDR1 and CDR2 from mAb A4M showed significant cytotoxic activities in vitro, leading tumor cells to apoptosis. A cyclic peptide representing A4 CDR H3 competed with mAb A4 for binding to melanoma cells. MAb A4M CDRs L1 and L2 in addition to the antitumor effect also inhibited angiogenesis of human umbilical vein endothelial cells in vitro. As shown in the present work, mAbs A4 and A4M and selected CDR peptides are strong candidates to be developed as drugs for antitumor therapy for invasive melanoma.

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.