A note on the index of closed minimal hypersurfaces of flat tori

Generalizing earlier work by Ros in ambient dimension three, we prove an affine lower bound for the Morse index of closed minimal hypersurfaces inside a flat torus in terms of their first Betti number (with purely dimensional coefficients)

Effect of coordinating solvents on the structure of Cu(II)-4,4'-bipyridine coordination polymers

Solvent can play a crucial role in the synthesis of coordination polymers (CPs). Here, this study reports how the coordinating solvent approach (CSA) can be used as an effective tool to control the nature of the final CP. This study exploited the system Cu(II)-4,4 '-bipyridine coupled to different coordinating solvents, such as DMA, DMF and DMSO. This allowed the isolation and structurally characterization of four new CPs: three 2D layered networks and one 1D chain. Moreover, it was evidenced that even adventitious water can play the role of the coordinating solvent in the final CP

The temporal evolution of the Mitu group, south-east Peru – first U-Pb age data

The Eastern Cordillera of southern Peru formed along a crustal zone that has been active as part of the western Gondwana margin since the middle Paleozoic. The present study investigates the Mitu Group of south-east Peru in the area of Abancay-Cusco-Sicuani-Titicaca. This unit comprises continental clastic sediments deposited in syn-sedimentary basins during an extensional period in Permo-Triassic times and has not benefitted from a thorough geochemical-geochronological investigation so far. One of the main reasons for this lack of data is a complex structure of the graben system, tectonically complicated by compressional inversion of the extensional basins during Andean orogeny. Due to dominating coarse-grained clastics, the Mitu Group is devoid of fossils and its age is only poorly bracketed to be Permo -Triassic based on its stratigraphic relation to the underlying Copacabana and overlying Pucara groups. The upper levels of the Copacabana have been constrained by palynology to the Artinskian (Doubinger and Marocco, 1981). However, a hiatus may be observed between the Copacabana and the Mitu groups in most places, rendering the age estimate of the basal Mitu imprecise. The Pucara Group, regarded by Rosas et al. (2007) as thermal sag after Mitu extension, is attributed to the late Triassic - early Jurassic on the basis of ammonite fossils and U-Pb zircon ages from ash beds (Schaltegger et al., 2008). The aim of this study is to provide more accurate and precise age constraints for the age and duration of the Mitu Group by using U-Pb geochronology of volcanic zircon in rhyolitic lavas, and of detrital zircon in clastic sediments. For andesitic volcanic lithologies, age approximations will be obtained by Ar-Ar techniques applied to amphibole and groundmass samples. Field data were obtained from a long and apparently complete section through the Mitu, situated 120km SE of Cusco near the city of Sicuani. This section consists of typical Mitu deposits; continental red beds, breccias and andesitic lavas. However, a zircon-bearing rhyolitic lava at the bottom gives us the opportunity to date the start of Mitu sedimentation by U-Pb ID-TIMS; this analysis will provide a precise age for the base of the Mitu group for the first time. In the Sicuani area the Mitu unconformably overlies the Ambo group, suggesting that the entire Copacabana is missing. Laser-ablation ICP-MS U-Pb data of detrial zircons from a sandstone just below the unconformity indicate a maximum age of latest Carboniferous (303Ma) for the underlying Ambo group. This maximum age overlaps with the palynological age of the lower Copacabana (Azcuy et al., 2002), raising the question whether the Ambo and Copacabana are truly diachronous or just coeval units of different sedimentary facies associations. In another section, 100km W of Cusco, near the city of Abancay, we found Mitu sediments overlying the Copacabana Group. Here the Copacabana contains well preserved plant fossils of the lycopsids family also found elsewhere in Peru and Bolivia. Lack of acidic volcanism during Mitu extension in this region prevents from dating of lavas using the U-Pb method. The detrital zircon population in a sandstone in the lowermost part of the Mitu was analysed for U-Pb ages, using LA-ICP-MS techniques. The youngest zircons in the population are around 235 Ma hence providing a maximum age for the onset of Mitu group sedimentation. The Artinskian age for the upper Copacabana from Doubinger and Marocco (1981) has also been obtained from the Abancay region, establishing a hiatus of some 50 Myrs between the two units. The Mitu Group is intruded by a 220 Ma granite body (Lipa and Saraiva, 2008) indicating significant burial of the sediments at this time. 500km SE of Cusco, on the Bolivian shores of lake Titicaca, the Ambo Group features plant fossils of the Lycopsids family like those found in the Copacabana near Abancay. Our detrital zircon LA-ICPMS study on a quartz arenite just below the fossils indicates a maximum U-Pb age of 343Ma. However a zircon-bearing ash bed will allow for more precise calibration of the fossil age by ID-TIMS techniques. The zircon U-Pb data will provide a test whether the Copacabana and the Ambo group are indeed diachronous or just lateral variations of a sedimentary system

Constraining the age of the Mitu Group, South-East Peru: U-Pb ages of detrital and igneous zircons

The present study investigates the Mitu Group of south-east Peru (13-16°S), which consists of continental clastic sedimentary rocks and interbedded basaltic to andesitic lavas. There is a paucity of geochemical and geochronological data from the Mitu Group, and the interpretation of its evolution is complicated by i) rapid changes in fault structure along-strike of the graben system, and ii) inversion during Andean orogenesis. Due to dominating coarsegrained clastics, the Mitu Group is devoid of fossils and its age is poorly bracketed to the Permo-Triassic, based on its stratigraphic relationships with the underlying Copacabana and overlying Pucará groups. The upper strata of the Copacabana Group have been constrained by palynology to the Artinskian, while marine fossils at the base of the Pucará Group indicate a Norian age. The Pucará Group is only present in northern Peru, whereas the Mitu Group has an erosional contact with overlying Cretaceous sandstones in the study area. Preliminary data suggest that the lower Mitu Group is middle Triassic, leaving a significant hiatus between the Copacabana and Mitu groups

Compactness analysis for free boundary minimal hypersurfaces

We investigate compactness phenomena involving free boundary minimal hypersurfaces in Riemannian manifolds of dimension less than eight. We provide natural geometric conditions that ensure strong one-sheeted graphical subsequential convergence, discuss the limit behaviour when multi-sheeted convergence happens and derive various consequences in terms of finiteness and topological control

Compactness of the Space of Minimal Hypersurfaces with Bounded Volume and p-th Jacobi Eigenvalue

Given a closed Riemannian manifold of dimension less than eight, we prove a compactness result for the space of closed, embedded minimal hypersurfaces satisfying a volume bound and a uniform lower bound on the first eigenvalue of the stability operator. When the latter assumption is replaced by a uniform lower bound on the p-th Jacobi eigenvalue for p≥2 one gains strong convergence to a smooth limit submanifold away from at most p−1 points

Bubbling analysis and geometric convergence results for free boundary minimal surfaces

We investigate the limit behaviour of sequences of free boundary minimal hypersurfaces with bounded index and volume, by presenting a detailed blow-up analysis near the points where curvature concentration occurs. Thereby, we derive a general quantization identity for the total curvature functional, valid in ambient dimension less than eight and applicable to possibly improper limit hypersurfaces. In dimension three, this identity can be combined with the Gauss-Bonnet theorem to provide a constraint relating the topology of the free boundary minimal surfaces in a converging sequence, of their limit, and of the bubbles or half-bubbles that occur as blow-up models. We present various geometric applications of these tools, including a description of the behaviour of index one free boundary minimal surfaces inside a 3-manifold of non-negative scalar curvature and strictly mean convex boundary. In particular, in the case of compact, simply connected, strictly mean convex domains in $\mathbb{R}^3$ unconditional convergence occurs for all topological types except the disk and the annulus, and in those cases the possible degenerations are classified

TIMING OF GLYCEROL ADDITION ON SPERM QUALITY IN CRYOPRESERVATION OF CANINE SEMEN

El objetivo del presente trabajo fue evaluar el efecto del momento de adición del glicerol durante el proceso de enfriamiento sobre la calidad espermática del semen canino. Se utilizaron 15 eyaculados de 4 perros adultos. Cada muestra de semen fue dividida en alícuotas para someterlas a tres métodos de adición de glicerol (T1: al inicio; T2: al inicio y final; T3: al final de la curva de enfriamiento). El semen se envasó en pajillas de 0.5 ml y se congeló en nitrógeno líquido. Se evaluó la motilidad progresiva y la integridad funcional de membrana posdescongelamiento. No se encontró diferencia estadística entre los tres métodos de adición del glicerol, pudiéndose simplificar el proceso de criopreservación al añadir todo el glicerol al inicio de la curva de enfriamiento.The objective of the study was to evaluate the timing of adding glycerol during thecooling process on sperm quality of canine semen. Fifteen ejaculates from 4 mature dogswere used. Each sample was divided in aliquots and three methods of adding glycerolwere used (T1: at the beginning; T2; at the beginning and at the end; T3: at the end of thecooling process). Semen samples were packed in 0.5 ml straws and frozen in liquid nitrogen.The post-thawing progressive motility and the functional integrity of membrane wereevaluated. None statistical difference was observed due to the three treatments, indicatingthat the process of cryopreservation can be simplified by adding all the glycerol at thebeginning of the cooling curve

Ferrous to Ferric Transition in Fe-Phthalocyanine Driven by NO2 Exposure

Due to its unique magnetic properties offered by the open-shell electronic structure of the central metal ion, and for being an effective catalyst in a wide variety of reactions, iron phthalocyanine has drawn significant interest from the scientific community. Nevertheless, upon surface deposition, the magnetic properties of the molecular layer can be significantly affected by the coupling occurring at the interface, and the more reactive the surface, the stronger is the impact on the spin state. Here, we show that on Cu(100), indeed, the strong hybridization between the Fe d-states of FePc and the sp-band of the copper substrate modifies the charge distribution in the molecule, significantly influencing the magnetic properties of the iron ion. The FeII ion is stabilized in the low singlet spin state (S=0), leading to the complete quenching of the molecule magnetic moment. By exploiting the FePc/Cu(100) interface, we demonstrate that NO2 dissociation can be used to gradually change the magnetic properties of the iron ion, by trimming the gas dosage. For lower doses, the FePc film is decoupled from the copper substrate, restoring the gas phase triplet spin state (S=1). A higher dose induces the transition from ferrous to ferric phthalocyanine, in its intermediate spin state, with enhanced magnetic moment due to the interaction with the atomic ligands. Remarkably, in this way, three different spin configurations have been observed within the same metalorganic/metal interface by exposing it to different doses of NO2 at room temperature