Constructing Separable Arnold Snakes of Morse Polynomials

We give a new and constructive proof of the existence of a special class of univariate polynomials whose graphs have preassigned shapes. By definition, all the critical points of a Morse polynomial function are real and distinct and all its critical values are distinct. Thus we can associate to it an alternating permutation: the so-called Arnold snake, given by the relative positions of its critical values. We realise any separable alternating permutation as the Arnold snake of a Morse polynomial.Comment: 35 pages, 32 figure

Maximus the confessor and René Girard: a hermeneutic approach

For Maximus the Confessor, the Holy Scriptures is a guide for the ascetic ascension and the commandment to imitate the Lord means love. For R. Girard, Christ’s passions take down the resorts of the victim’s mechanism, signaling the mimetic functioning of culture and the false sacredness instituted by violence. In hermeneutic approach, the two discourses unveil their similitude, proving alternative paths from the text of the Scriptures to their significance

Measuring the local non-convexity of real algebraic curves

The goal of this paper is to measure the non-convexity of compact and smooth connected components of real algebraic plane curves. We study these curves first in a general setting and then in an asymptotic one. In particular, we consider sufficiently small levels of a real bivariate polynomial in a small enough neighbourhood of a strict local minimum at the origin of the real affine plane. We introduce and describe a new combinatorial object, called the Poincare-Reeb graph, whose role is to encode the shape of such curves and to allow us to quantify their non-convexity. Moreover, we prove that in this setting the Poincare-Reeb graph is a plane tree and can be used as a tool to study the asymptotic behaviour of level curves near a strict local minimum. Finally, using the real polar curve, we show that locally the shape of the levels stabilises and that no spiralling phenomena occur near the origin.Comment: 32 pages, 34 figure

The structure of the moduli spaces of toric dynamical systems

We consider complex balanced mass-action systems, also called toric dynamical systems. They are polynomial dynamical systems arising from reaction networks and have remarkable dynamical properties. We study the topological structure of their moduli spaces (i.e., the toric locus). First we show that the complex balanced equilibria depend continuously on the parameter values. Using this result, we prove that the moduli space of any toric dynamical system is connected. In particular, we emphasize the product structure of the moduli space: it is homeomorphic to the product of the set of complex balanced flux vectors and the affine invariant polyhedron.Comment: 16 pages, 4 figure

The structure of the moduli spaces of toric dynamical systems

We consider complex-balanced mass-action systems, or toric dynamical systems. They are remarkably stable polynomial dynamical systems arising from reaction networks seen as Euclidean embedded graphs. We study the moduli spaces of toric dynamical systems, called the toric locus: given a reaction network, we are interested in the topological structure of the set of parameters giving rise to toric dynamical systems. First we show that the complex-balanced equilibria depend continuously on the parameter values. Using this result, we prove that the toric locus of any toric dynamical system is connected. In particular, we emphasize its product structure: it is homeomorphic to the product of the set of complex-balanced flux vectors and the affine invariant polyhedron. Finally, we show that the toric locus is invariant with respect to bijective affine transformations of the generating reaction network.Comment: 31 pages, 5 figure

Efektifitas Promosi Kesehatan melalui Audio Visual Tentang Pemeriksaan Payudara Sendiri (Sadari) terhadap Peningkatan Pengetahuan Remaja Putri

The purpose of this research is to determinedthe effectiveness ofhealthpromotion by audio visual about breast self examination (BSE) for increasing girl\u27s knowledge about BSE. The design of thisresearch is Quasy experimentdesigned by Pre-post test with control group weredivided intoexperiment groupandcontrol group. The research was conductedongirl\u27s inthe “SMAN 2 Pekanbaru”. The total sample are 78peoplewhowere takenby using systematic random sampling techniquesby noticing tothe inclusion criteria. Measuring instruments that usedin both groupsarequestionnairesthat have beentested for validityandrealibility. Analysisis usedunivariateandbivariateanalyzesusing independentanddependentsample ttest. The results showed there was asignificantincreasing intherate ofchange in girl\u27s knowledge about BSE in experimental grouphas givenhealthpromotionaboutBSE with p(0.000) < α (0,05). It means thathealthpromotionaboutBSE is effectiveforimproving girl\u27s knowledge about BSE. The results of this research isrecommend to every health care have to giving health promotion about BSE by audio visual to increasing knowledge about BSE

A generalization of the space of complete quadrics

To any homogeneous polynomial h we naturally associate a variety Ωh&nbsp;which maps birationally onto the graph Γh of the gradient map ∇h and which agrees with the space of complete quadrics when h is the determinant of the generic symmetric matrix. We give a sufficient criterion for Ωh being smooth which applies for example when h is an elementary symmetric polynomial. In this case Ωh is a smooth toric variety associated to a certain generalized permutohedron. We also give examples when Ωh is not smooth

The post-socialist city of Brașov: Challenges and perils

The change of political regimes in the former socialist countries of Central and Eastern Europe at the end of the last century has revalued the building plots in cities and reconfigured the stakes of urban space ownership. Brașov is one of the most attractive cities of Romania, residentially speaking. Nonetheless, the convergence of real estate developers’ and their direct beneficiaries’ interests raises the risk of choking the city and modifying the characteristic features of its central area. The solutions of inadvertently building new real estate in the old and highly valued neighborhoods of the city diminish the quality of urban residence

Permutations encoding the local shape of level curves of real polynomials via generic projections

The non-convexity of a smooth and compact connected component of a real algebraic plane curve can be measured by a combinatorial object called the Poincare-Reeb tree associated to the curve and to a direction of projection. In this paper we show that if the chosen projection avoids the bitangents and the inflectional tangencies to the small enough level curves of a real bivariate polynomial function near a strict local minimum at the origin, then the asymptotic Poincare-Reeb tree becomes a complete binary tree and its vertices become endowed with a total order relation. Such a projection direction is called generic. We prove that for any such asymptotic family of level curves, there are finitely many intervals on the real projective line outside of which all the directions are generic with respect to all the curves in the family. If the choice of the direction of projection is generic, then the local shape of the curves can be encoded in terms of alternating permutations, that we call snakes. The snakes offer an effective description of the local geometry and topology, well-suited for further computations.Comment: 33 pages; 34 figure