The multiplier approach to the projective Finsler metrizability problem

This paper is concerned with the problem of determining whether a projective-equivalence class of sprays is the geodesic class of a Finsler function. We address both the local and the global aspects of this problem. We present our results entirely in terms of a multiplier, that is, a type (0,2) tensor field along the tangent bundle projection. In the course of the analysis we consider several related issues of interest including the positivity and strong convexity of positively-homogeneous functions, the relation to the so-called Rapcs\'ak conditions, some peculiarities of the two-dimensional case, and geodesic convexity for sprays.Comment: 25 page

Hilbert forms for a Finsler metrizable projective class of sprays

The projective Finsler metrizability problem deals with the question whether a projective-equivalence class of sprays is the geodesic class of a (locally or globally defined) Finsler function. In this paper we use Hilbert-type forms to state a number of different ways of specifying necessary and sufficient conditions for this to be the case, and we show that they are equivalent. We also address several related issues of interest including path spaces, Jacobi fields, totally-geodesic submanifolds of a spray space, and the equivalence of path geometries and projective-equivalence classes of sprays.Comment: 23 page

Rectifiability of Varifolds with Locally Bounded First Variation with Respect to Anisotropic Surface Energies

We extend Allard's celebrated rectifiability theorem to the setting of varifolds with locally bounded first variation with respect to an anisotropic integrand. In particular, we identify a sufficient and necessary condition on the integrand to obtain the rectifiability of every $d$-dimensional varifold with locally bounded first variation and positive $d$-dimensional density. In codimension one, this condition is shown to be equivalent to the strict convexity of the integrand with respect to the tangent plane

Filling minimality of Finslerian 2-discs

We prove that every Riemannian metric on the 2-disc such that all its geodesics are minimal, is a minimal filling of its boundary (within the class of fillings homeomorphic to the disc). This improves an earlier result of the author by removing the assumption that the boundary is convex. More generally, we prove this result for Finsler metrics with area defined as the two-dimensional Holmes-Thompson volume. This implies a generalization of Pu's isosystolic inequality to Finsler metrics, both for Holmes-Thompson and Busemann definitions of Finsler area.Comment: 16 pages, v2: improved introduction and formattin

Deficient Spindle Assembly Checkpoint in Multiple Myeloma

Multiple myeloma (MM) is a hematological disease characterized by an abnormal accumulation of plasma cells in the bone marrow. These cells have frequent cytogenetic abnormalities including translocations of the immunoglobulin heavy chain gene and chromosomal gains and losses. In fact, a singular characteristic differentiating MM from other hematological malignancies is the presence of a high degree of aneuploidies. As chromosomal abnormalities can be generated by alterations in the spindle assembly checkpoint (SAC), the functionality of such checkpoint was tested in MM. When SAC components were analyzed in MM cell lines, the RNA levels of most of them were conserved. Nevertheless, the protein content of some key constituents was very low in several cell lines, as was the case of MAD2 or CDC20 in RPMI-8226 or RPMI-LR5 cells. The recovery of their cellular content did not substantially affect cell growth, but improved their ability to segregate chromosomes. Finally, SAC functionality was tested by challenging cells with agents disrupting microtubule dynamics. Most of the cell lines analyzed exhibited functional defects in this checkpoint. Based on the data obtained, alterations both in SAC components and their functionality have been detected in MM, pointing to this pathway as a potential target in MM treatment

Reparação do retalho axial dorsal em ratos tratados com óleo ozonizado

Axial pattern flaps represents an important option in reconstructive surgery, consisting of an artery and a direct cutaneous vein at their base and allowing a large area of skin to form the flap to cover the wound. However, the technique can present complications, mostly necrosis due to vascular involvement. In this context, ozone therapy can be used to accelerate the healing process of poorly vascularized and contaminated wounds. The objective of this article was to evaluate the effects and repair of the dorsal axial flap in Wistar rats at the receiving bed, using treatment with high-peroxidation ozonized oil. The study was carried out with 18 rats, divided into two groups with 9 animals: GG group (comum sunflower oil) and GO group (ozonized sunflower oil). During the experimental period, macroscopic and microscopic evaluations were carried out, in order to observe the healing and repair of the surgical wound. Data were submitted to statistical analysis. The cosmetic appearance on GO was significantly better than GG. Blood vessel count, hemorrhage and reepithelialization were significantly higher in GO when compared to GG, while the presence of necrosis did not differ between groups. The mean total area of the flaps between the groups was statistically different, higher in the flaps in GO. The results showed that the use of ozonized oil in an axial pattern flap results in a favorable cosmetic appearance and better re-itemization in the treated group.O retalho de padrão axial representa uma importante opção na cirurgia reconstrutiva, sendo composto por uma artéria e uma veia cutânea direta em sua base, permitindo que uma grande área de pele possa constituir o retalho para recobrir a ferida. Entretanto, a técnica pode apresentar complicações, principalmente com a necrose devido ao comprometimento vascular. Nesse contexto, a ozonioterapia pode ser utilizada para acelerar o processo de cicatrização de feridas pouco vascularizadas e contaminadas. Com o presente estudo, objetivou-se avaliar os efeitos e o reparo do retalho axial dorsal em ratos Wistar, empregando tratamento com óleo ozonizado de alta peroxidação. Utilizaram-se 18 ratos, distribuídos em dois grupos com 9 animais, grupo GG (óleo de girassol comum) e grupo GO (óleo de girassol ozonizado). Durante o período experimental foram realizadas avaliações macroscópicas e microscópicas a fim de observar a cicatrização e a reparação da ferida cirúrgica. Os dados foram submetidos a análise estatística.  O aspecto cosmético em GO foi significativamente melhor que GG, e a contagem de vasos sanguíneos, hemorragia e reepitelização foram significativamente maiores em GO quando comparado ao GG. A presença de necrose não diferiu entre os grupos. A média da área total dos retalhos entre os grupos diferiu estatisticamente, sendo maior nos retalhos em GO. Os resultados evidenciaram que a utilização do óleo ozonizado em retalhos de padrão axial resulta em aspecto favorável e melhor reepitelização

Reparação do retalho axial dorsal em ratos tratados com óleo ozonizado

O retalho de padrão axial representa uma importante opção na cirurgia reconstrutiva, sendo composto por uma artéria e uma veia cutânea direta em sua base, permitindo que uma grande área de pele possa constituir o retalho para recobrir a ferida. Entretanto, a técnica pode apresentar complicações, principalmente com a necrose devido ao comprometimento vascular. Nesse contexto, a ozonioterapia pode ser utilizada para acelerar o processo de cicatrização de feridas pouco vascularizadas e contaminadas. Com o presente estudo, objetivou-se avaliar os efeitos e o reparo do retalho axial dorsal em ratos Wistar, empregando tratamento com óleo ozonizado de alta peroxidação. Utilizaram-se 18 ratos, distribuídos em dois grupos com 9 animais, grupo GG (óleo de girassol comum) e grupo GO (óleo de girassol ozonizado). Durante o período experimental foram realizadas avaliações macroscópicas e microscópicas a fim de observar a cicatrização e a reparação da ferida cirúrgica. Os dados foram submetidos a análise estatística.  O aspecto cosmético em GO foi significativamente melhor que GG, e a contagem de vasos sanguíneos, hemorragia e reepitelização foram significativamente maiores em GO quando comparado ao GG. A presença de necrose não diferiu entre os grupos. A média da área total dos retalhos entre os grupos diferiu estatisticamente, sendo maior nos retalhos em GO. Os resultados evidenciaram que a utilização do óleo ozonizado em retalhos de padrão axial resulta em aspecto favorável e melhor reepitelização