Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

1.° Joannis de Sacrobosco sphaera, à Nicolao Guglero in compendium redacta. — 2.° Joachimi, Mathematici, annotata in sphaeram Procli. — 3.° Ejusdem annotata in Alfraganum. — 4.° Ejusdem annotata in astrologiam. — 5.° Anonymi tractatus de nativitatibus. — 6.° Stephani Norimbergensis prognosticon, à Luca Gaurico, Neapolitano, Bononiae supputatum et examinatum anno 1534.

Mazarinaeus

1.° Anicii Manlii Boëtii de arithmetica liber primus : finis desideratur. — 2.° Ejusdem in Porphyrii isagogen commentariorum fragmenta. — 3.° Ejusdem de consolatione philosophiae libri quinque : primus liber ferè integer desideratur.

Colbertinus

1.° Anonymi tractatus algorismi de fractionibus, sive methodus calculandi minutias : praemittitur calendarium. — 2.° Anonymus de nominibus instrumentorum in astrolabio. — 3.° Liber de operatione astrolabii. — 4.° Anonymi canones, sive regulae tabularum astronomiae : accedunt tabulae. — 5.° Centiloquium Ptolomaei de judiciis astrorum : accedit Haly commentarius. — 6.° Epistola Messahallae de conjunctionibus planetarum. — 7.° Albumasaris tractatus inscriptus : flores de judiciis astrorum. — 8.° Scholium de potestate planetarum et signorum, et de formis eorum. — 9.° Anonymi opusculum de tuendae valetudinis ratione. — 10.° Formulae collationum ecclesiasticarum.

Colbertinus

1.° Anonymi tractatus de compositione et usu astrolabii. — 2.° Joannis Campani liber de aequationibus planetarum. — 3.° Fratris Joannis, ordinis Minorum, summa de astrologia.

Baluzianus

Community College Leader Bulletin, Summer 2008, Vol. 1, Issue 2

Newsletter produced by the Iowa Department of Education, Community College unit. This report has information about staff, grants, statistical data, requirements and more.

Endeavors Update, Iowa Medicaid Enterprise, Vol. 1, Issue 2 October 28, 2010

The Iowa Medicaid Enterprise (IME) is an endeavor, started in 2005, to unite State staff with “best of breed” contractors into a performance-based model for administration of the Medicaid program.

Progama de salud para tutorias de 1º y 2º de la E.S.O. en el colegio Nuestra Señora del Carmen de zaragoza

Este proyecto es un programa para trabajar diferentes temas de salud para alunmos/as de 1º y 2º de la E.S.O. en las tutorias del centro.

Eighty-Sixth General Assembly Senate Rules (Senate Resolution 1 — Adopted 2/4/15), February 6, 2015

Eighty-Sixth General Assembly House Rules (House Resolution 4-Adopted 2-3-2015)

A Continuous Span Aluminum Girder Concrete Deck Bridge - Part 1 of 2: Field Test Performance and Evaluation, 1996

This report addresses the field testing and analysis of those results to establish the behavior of the original Clive Road Bridge that carried highway traffic over Interstate 80 (I-80) in the northwest region of Des Moines, Iowa. The bridge was load tested in 1959, shortly after its construction and in 1993, just prior to its demolition. This report presents some of the results from both field tests, finite element predictions of the behavior of aluminum bridge girders, and load distribution studies.

Gene transfer of a soluble IL-1 type 2 receptor-Ig fusion protein improves cardiac allograft survival in rats.

OBJECTIVE: Interleukin-1 (IL-1) mediates ischemia-reperfusion injury and graft inflammation after heart transplantation. IL-1 affects target cells through two distinct types of transmembrane receptors, type-1 receptor (IL-1R1), which transduces the signal, and the non-signaling type-2 receptor (IL-1R2), which acts as a ligand sink that subtracts IL-1beta from IL-1R1. We analyzed the efficacy of adenovirus (Ad)-mediated gene transfer of a soluble IL-1R2-Ig fusion protein in delaying cardiac allograft rejection and the mechanisms underlying the protective effect. METHODS: IL-1 inhibition by IL-1R2-Ig was tested using an in vitro functional assay whereby endothelial cells preincubated with AdIL-1R2-Ig or control virus were stimulated with recombinant IL-1beta or tumor necrosis factor-alpha (TNF-alpha), and urokinase-type plasminogen activator (u-PA) induction was measured by zymography. AdIL-1R2-Ig was delivered to F344 rat donor hearts ex vivo, which were placed in the abdominal position in LEW hosts. Intragraft inflammatory cell infiltrates and proinflammatory cytokine expression were analyzed by immunohistochemistry and real-time reverse transcriptase-polymerase chain reaction (RT-PCR), respectively. RESULTS: IL-1R2-Ig specifically inhibited IL-1beta-induced u-PA responses in vitro. IL-1R2-Ig gene transfer reduced intragraft monocytes/macrophages and CD4(+) cell infiltrates (p<0.05), TNF-alpha and transforming growth factor-beta (TGF-beta) expression (p<0.05), and prolonged graft survival (15.6+/-5.7 vs 10.3+/-2.5 days with control vector and 10.1+/-2.1 days with buffer alone; p<0.01). AdIL-1R2-Ig combined with a subtherapeutic regimen of cyclosporin A (CsA) was superior to CsA alone (19.4+/-3.0 vs 15.9+/-1.8 days; p<0.05). CONCLUSIONS: Soluble IL-1 type-2 receptor gene transfer attenuates cardiac allograft rejection in a rat model. IL-1 inhibition may be useful as an adjuvant therapy in heart transplantation.