Vertex-disjoint rainbow triangles in edge-colored graphs

Let $G$ be an edge-colored graph of order $n$. The minimum color degree of $G$, denoted by ${\delta }^c\left(G\right)$, is the largest integer $k$ such that for every vertex $v$, there are at least $k$ distinct colors on edges incident to $v$. We say that an edge-colored graph is rainbow if all its edges have different colors. In this paper, we consider vertex-disjoint rainbow triangles in edge-colored graphs. Li (2013) showed that if ${\delta }^c\left(G\right)\ge (n+1)∕2$, then $G$ contains a rainbow triangle and the lower bound is tight. Motivated by this result, we prove that if $n\ge 20$ and ${\delta }^c\left(G\right)\ge (n+2)∕2$, then $G$ contains two vertex-disjoint rainbow triangles. In particular, we conjecture that if ${\delta }^c\left(G\right)\ge (n+k)∕2$, then $G$ contains $k$ vertex-disjoint rainbow triangles. For any integer $k\ge 2$, we show that if $n\ge 16k-12$ and ${\delta }^c\left(G\right)\ge n∕2+k-1$, then $G$ contains $k$ vertex-disjoint rainbow triangles. Moreover, we provide sufficient conditions for the existence of $k$ edge-disjoint rainbow triangles.     

Challenging Students to View the Concept of Area in Triangles in a Broad Context: Exploiting the Features of Cabri-II

This study focuses on the constructions in terms of area and perimeter in equivalent triangles developed by students aged 12–15 years-old, using the tools provided by Cabri-Geometry II [Labore (1990). Cabri-Geometry (software), Université de Grenoble]. Twenty-five students participated in a learning experiment where they were asked to construct: (a) pairs of equivalent triangles “in as many ways as possible” and to study their area and their perimeter using any of the tools provided and (b) “any possible sequence of modifications of an original triangle into other equivalent ones”. As regards the concept of area and in contrast to a paper and pencil environment, Cabri provided students with different and potential opportunities in terms of: (a) means of construction, (b) control, (c) variety of representations and (d) linking representations, by exploiting its capability for continuous modifications. By exploiting these opportunities in the context of the given open tasks, students were helped by the tools provided to develop a broader view of the concept of area than the typical view they would construct in a typical paper and pencil environment.     

Poly(n-vinylpyrrolidone) hydrogels: 2.Hydrogel composites as wound dressing for tropical environment

POLY(N-VINYLPYRROLIDONE) HYDROGELS: 2. HYDROGEL COMPOSITES AS WOUND DRESSING FOR TROPICAL ENVIRONMENT. The effects of irradiation on hydration and other properties of poly(vinylpyrrolidone) (PVP) hydrogel composites have been investigated. The aqueous solution of vinylpyrrolidone (VP) 10 wt % was mixed with several additives such as agar and polyethylen glycol (PEG). The solution was then irradiated with gamma rays from Cobalt-60 source at room temperature. Several parameters such as elongation at break (EB), tensile strength (TS), degree of swelling (DS), water vapor transmission rate (WVTR), equilibrium water content (EWC), microbial growth and penetration test, and water activity (Aw) were analysed at room temperature of 29 ±2°C humidity of 80 ± 10%. Results show that elongation at break of hydrogel membranes with initial composition of VP with agar, VP with agar and PEG were 240 % and 250 % kGy, the equilibrium water content of membranes were 96 to 90%, whereas degree of swelling were 55 to 10. The WVTR of hydrogel membranes with initial composition of VP with agar and PEG was 70 g m^-2h^-1, while the water activity was 0.9. Such hydrogel membranes exhibits the following properties: They are elastic, transparent, flexible, impermeable for bacteria. They absopt a high capacity of water, attached to healthy skin but not to the wound and they are easy to remove. These properties of the hydrogel membranes allow for applying as a wound dressings in tropical environment.     

Yet another way of calculating moments of the Kesten's distribution and its consequences for Catalan numbers and Catalan triangles

We calculate moments of the so-called Kesten distribution by means of the expansion of the denominator of the density of this distribution and then integrate all summands with respect to the semicircle distribution. By comparing this expression with the formulae for the moments of Kesten's distribution obtained by other means, we find identities involving polynomials whose power coefficients are closely related to Catalan numbers, Catalan triangles, binomial coefficients. Finally, as applications of these identities we obtain various interesting relations between the aforementioned numbers, also concerning Lucas, Fibonacci and Fine numbers.     

Half-Integer Spin Triangles: Old Dogs,New Tricks

Spin triangles, that is, triangular complexes of half-integer spins, are the oldest molecular nanomagnets (MNMs). Their magnetic properties have been studied long before molecular magnetism was delineated as a research field. This Review presents the history of their study, with references to the parallel development of new experimental investigations and new theoretical ideas used for their interpretation. It then presents an indicative list of spin-triangle families to illustrate their chemical diversity. Finally, it makes reference to recent developments in terms of theoretical ideas and new phenomena, as well as to the relevance of spin triangles to spintronic devices and new physics.     

Logging damage and injured tree mortality in tropical forest management

Using insights from the forest ecology literature, we analyze the effect of injured trees on stand composition and carbon stored in above‐ground biomass and the implications for forest management decisions. Results from a Faustmann model with data for a tropical forest on Kalimantan show that up to 50% of the basal area of the stand before harvest can consist of injured trees. Considering injured trees leads to an increase in the amount of carbon in above‐ground biomass of up to 165%. These effects are larger under reduced impact logging than under conventional logging. The effects on land expectation value and cutting cycle are relatively small. The results suggest that considering injured trees in models for tropical forest management is important for the correct assessment of the potential of financial programs to store carbon and conserve forest ecosystem services in managed tropical forests, such as reducing emissions from deforestation and forest degradation and payment for ecosystem services. Recommendations for Resource Managers

• Considering the role of injured trees is important for managing tropical forests
• These trees can cover up to 50% of basal area and contain more than 50% of the carbon stored in above‐ground biomass
• Reduced impact logging leads to a larger basal area of injured trees and more carbon stored in injured trees than conventional logging
• Injured trees play an important role when assessing the potential for carbon storage in the context of payment for forest ecosystem services.

     

Back to the future: A retrospective assessment of model‐based scenarios for the management of the shrimp fishery in French Guiana facing global change

While the number of models dedicated to predicting the consequences of alternative resource management strategies has increased, instances in which authors look back at past predictions to learn from discrepancies between these and observed developments are scarce. In the past decades, the French Guiana shrimp fishery has experienced shrimp market globalization and decreasing levels of shrimp recruitment due to environmental changes. In 2006, a bio‐economic model of this fishery was developed to simulate its possible responses to economic and environmental scenarios up to 2016. Here, we compare here these predictions to the observed trajectories. While the number of active vessels corresponds to that which was predicted, the estimated shrimp stock does not. Important driving factors had not been anticipated, including a general strike, natural disasters, and the end of the global financial crisis. These results show the importance of participative approaches involving stakeholders in the co‐construction and shared representation of scenarios. Recommendations for resource managers

• Effective fisheries resources management and a fortiori, the capacity of the fisheries to adapt to global change, requires understanding of both ecological and economics dynamics.
• The temporal trajectory of the trawling shrimp fisheries has been well monitored, and the decline of both stock and fleet is understood regarding ecological and economic changes: Changes in the environmental conditions of shrimp recruitment, and oil price increase and selling price decrease.
• However, our bio‐economic modeling work showed that, even with a good understanding of the dynamics explaining past trajectories, unpredictable events (strike, natural disasters…) have acted as other key driving factors altering the capacity of the model to represent possible futures.
• These results led us to recommend a better integration of the expertise of social and political scientists in developing models of bio‐economic systems to increase the quality of scenario predictions, and to argue for more participative approaches involving the stakeholders.

     

Different Species of Mercury in the Livers of Tropical Dolphins

Abstract

Four kinds of mercury species (inorganic mercury (Hg_inorg), methylmercury (MeHg), total organic mercury (ΣHg_org), and insoluble mercury, deemed to be mercuric selenide (HgSe), were determined in the livers of dolphins from the Brazilian coast. The MeHg was identified and quantified in the toluene layer on a Gas Chromatograph with an Electron Capture Detector (GC-ECD). The ΣHg_org was isolated by acid leaching (H₂SO₄-KBr-CuSO₄) and then extracted into CH₂Cl₂. The ΣHg_org and Hg_inorg were determined by Cold-Vapor Atomic Absorption Spectroscopy (CV-AAS). The MeHg was the smallest fraction of Hg_tot, with a median of 9%, whereas the highest fraction of the Hg_tot was as HgSe, corresponding to 53%. The fractions of Hg_inorg and ΣHg_org corresponded to 30% and 39%, respectively. The lowest fraction of MeHg and the highest fraction of HgSe in the liver of all animals are related to different capacities or strategies of detoxification of methylmercury in this organ.     

One‐Step Multicomponent Self‐Assembly of a First‐Generation Sierpiński Triangle: From Fractal Design to Chemical Reality

A novel terpyridine‐based architecture that mimics a first‐generation Sierpiński triangle has been synthesized by multicomponent assembly and features tpy? Cd^II? tpy connectivity (tpy=terpyridine). The key terpyridine ligands were synthesized by the Suzuki cross‐coupling reaction. Mixing two different terpyridine‐based ligands and Cd^II in a precise stoichiometric ratio (1:1:3) produced the desired fractal architecture in near‐quantitative yield. Characterization was accomplished by NMR spectroscopy, mass spectrometry, and transmission electron microscopy.