On Mills's conjecture on matroids with many common bases

In this paper, we shall prove a conjecture of Mills: for two (k+1)-connected matroids whose symmetric difference between their collections of bases has size at most k, there is a matroid that is obtained from one of these matroids by relaxing n₁ circuit-hyperplanes and from the other by relaxing n₂ circuit-hyperplanes, where n₁ and n₂ are non-negative integers such that n₁+n₂k     

Preparation and Characterization of Poly(D,L-Lactide) (PLA) and Poly(D,L-Lactide)-Poly(Ethylene Glycol) (PLA-PEG) Nanocapsules Containing Antitumoral Agent Methotrexate

Summary: The aims of the present work were to prepare and characterize nanocapsules containing antitumoral agent methotrexate (MTX) from poly(D ,L -lactide) (PLA) and poly(D ,L -lactide)-poly(ethylene glycol) diblock copolymer (PLA-PEG) with the purpose of administrating this drug by topical ocular route for primary ocular lymphoma treatment. Nanocapsules were prepared by the interfacial deposition of preformed polymer. The influences of the initial amount of MTX on the encapsulation efficiency, drug recovery and drug content, as well as the physicochemical properties of the particles were evaluated. The particle mean diameters were 246 and 146 nm, and zeta potential values were −38.8 and −33.6 mV, for the MTX-loaded nanocapsules prepared from PLA and PLA-PEG, respectively. The methotrexate content in the particles increased with the increasing in the drug amount added to the formulations, but the drug recovery decreased significantly. After 4 h of in vitro release, 28 and 86% of MTX was released from PLA and PLA-PEG nanocapsules, respectively.     

Carbon-based materials applied to the development of chemically modified sensors: Trends to environmental applications**

Nowadays, carbon-based materials applied to the development of chemically modified sensors have been highlighted once they can generate methods with high sensitivity, stability, conductivity, accuracy and low cost. Hence, these sensors have been used in environmental monitoring in aneco-friendlyy, sensitive, fast, efficient, inexpensive and robust way. In this review, firstly we described about carbon-based materials and their derivatives, followed by the chemically modified carbon-based sensors manufacturing overview and their applications in environmental analytical chemistry related to inorganic and organic compounds determinations. Future perspectives on trends of the carbon-based materials applications in the sensor modifications are also described.     

A stability and numerical study of the solutions of a Timoshenko system with distributed delay

In this work, we analyze the stability of the semigroup associated with a Timoshenko beam model with distributed delay in the rotation angle equation. We show that the type of stability resulting from the semigroup is directly related to some model coefficients, which constitute the velocities of the system's component equations. In the case of stability of the polynomial type, we prove that rate obtained is optimal. We conclude the work performing a numerical study of the solutions and their energies, associated to discrete system.     

Synthesis of [60]Fullerene Hybrids Endowed with Steroids and Monosaccharides: Theoretical Underpinning as Promising anti-SARS-CoV-2 Agents

Cyclopropanation reactions between C₆₀ and different malonates decorated with monosaccharides and steroids using the Bingel-Hirsch methodology have allowed the obtention of a new family of hybrid compounds in good yields. A complete set of instrumental techniques has allowed us to fully characterize the hybrid derivatives and to determine the chemical structure of monocycloadducts. Besides, the proposed structures were investigated by cyclic voltammetry, which evidenced the exclusive reductive pattern of fullerene Bingel-type monoadducts. Theoretical calculations at the DFT-D3(BJ)/PBE 6-311G(d,p) level of the synthesized conjugates predict the most stable conformation and determine the factors that control the hybrid molecules′ geometry. Some parameters such as polarity, lipophilicity, polar surface area, hydrophilicity index, and solvent-accessible surface area were also estimated, predicting its potential permeability and capability as cell membrane penetrators. Additionally, a molecular docking simulation has been carried out using the main protease of SARS-CoV-2 (Mpro) as the receptor, thus paving the way to study the potential application of these hybrids in biomedicine.