On a New Class of Abstract Neutral Integro-Differential Equations and Applications

In this paper we introduce a new class of abstract integro-differential equations with delay and we study the existence of strict solutions. An application involving the heat equation with memory is presented.     

Adaptive control of local errors for elliptic problems using weighted Sobolev norms

We develop an a posteriori error estimator which focuses on the local H¹ error on a region of interest. The estimator bounds a weighted Sobolev norm of the error and is efficient up to oscillation terms. The new idea is very simple and applies to a large class of problems. An adaptive method guided by this estimator is implemented and compared to other local estimators, showing an excellent performance. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1266–1282, 2017     

Homogeneous Ricci almost solitons

It is shown that a locally homogeneous proper Ricci almost soliton is either of constant sectional curvature or locally isometric to a product R×N(c), where N(c) is a space of constant curvature.     

Analysis of the effectiveness of the theseus multi-criteria sorting method: theoretical remarks and experimental evidence

The effectiveness of the THESEUS multi-criteria sorting method is characterized, here, by (i) its capacity for suggesting precise and appropriate assignments; (ii) the probability of suggesting imprecise assignments; and (iii) the probability of suggesting incorrect assignments. We study how these important features are influenced by the number of criteria and categories, the cardinality of the reference set and the level of decision-maker consistency. We present a theoretical characterization and a wide range of experimental results that confirm and complement the formal analysis. The proposed way of analyzing effectiveness may be applied to other multi-criteria sorting methods.     

A marginal contribution coefficient for sequences of nonstationary continuous Markov chains

In this work, a set of sequences of information (time series), under nonstationary regime, with continuous space state, discrete time, and a Markovian dependence, is considered. A new model that expresses the marginal transition density function of one sequence as a linear combination of the marginal transition density functions of all sequences in the set is proposed. The coefficients of this combination are denominated marginal contribution coefficients and represent how much each transition density function contributes to the calculation of a chosen transition density function. The proposed coefficient is a marginal coefficient because it can be computed instantaneously, and it may change from one time to another time since all calculations are performed before stationarity is reached. This clearly differentiates the new coefficient from well‐known measures such as the cross‐correlation and the coherence. The idea behind the model is that if a specific sequence has a high marginal contribution for the transition density function from another sequence, the first may be replaced by the latter without losing much information that means that the knowledge of few densities should be enough to recover the overall behaviour. Simulations, considering 2 chains, are presented so as to check the sensitivity of the proposed model. The methodology is also applied to a real data originated from a wire‐drawing machine whose main function is to decrease the transverse diameter of metal wires. The behaviour of the level of acceleration of each bearing in relation to the other ones is then verified.     

Theoretical study of the stability and properties of magic numbers (m = 5, n = 2) and (m = 6, n = 3) of bimetallic bismuth‐copper nanoclusters; Bim Cun

Inspired by the experimental discovery of magic numbers we present a first study using density functional theory for the structure and properties of neutral and cationic Bi₆Cu₃ and Bi₅Cu₂ clusters. Our results confirm predictions based on Wade's rules. The closed electron shells, characteristic of cationic clusters help impose enhanced stability, while also complying with Wade's rules. Charge distribution analysis, as well as electrostatic potential maps show that in almost all cases, Bi atoms donate charges to Cu atoms. According to the analysis of condensed Fukui indices, Cu atoms inside both clusters are not reactive. Contrastingly, Bi atoms are reactive and may be targeted by different types of attack. This study of the electronic properties may thus help to determine experimental strategies with the capacity to enhance the synthesis of catalysts.     

A simple method for the synthesis of 4-arylselanyl-7-chloroquinolines used as in vitro acetylcholinesterase inhibitors and in vivo memory improvement

We described here an alternative method for the synthesis of 4-arylselanyl-7-chloroquinolines through reactions of 4,7-dichloroquinoline with organylselenols, generated in situ by the reaction of diorganyl diselenides with H₃PO₂ (50 wt% in H₂O). These reactions proceeded efficiently at 60 °C under N₂ atmosphere and are suitable to a range of diorganyl diselenides containing electron-donating and electron-withdrawing groups, affording the corresponding 4-aryl-7-chloroquinolines in high yields. The synthesized compounds were screened for their in vitro acetylcholinesterase (AChE) activity and our results demonstrated that the 7-chloro-4-[(4-fluorophenyl)selanyl]quinoline inhibited the AChE activity and improved memory in mice, making this compound is a potential therapeutic agent for the treatment of Alzheimer disease and other neurodegenerative disorders.     

Physicochemical characterization of dipeptidyl peptidase-4 inhibitor alogliptin in physical mixtures with excipients

Alogliptin (ALG) is a hypoglycemic drug used in diabetes which inhibits the enzyme dipeptidyl peptidase-4 (DPP-4), preventing the degradation of incretins, stimulating insulin secretion. The physicochemical characteristics of ALG were evaluated by differential scanning calorimetry (DSC), thermogravimetry (TG) and scanning electron microscopy equipped with energy-dispersive X-ray spectrometer (SEM/EDS). The compatibility studies were carried out between ALG and excipients (physical mixtures, 1:1) using DSC, TG, diffuse reflectance Fourier transform infrared spectroscopy (FTIR), X-ray powder diffraction (XRPD) and hot-stage microscopy. ALG presented purity near to 99%, melted in the range of 179.4–187.2 °C, followed by decomposition which started in 198.0 °C. SEM/EMS analysis of ALG presented irregular crystals and traces of impurities as copper and lead. DSC investigations obtained by physical mixtures showed minor alterations in the melting ranges of ALG with mannitol, magnesium stearate and commercial tablets. Solubilization of ALG in the fused excipient was observed by hot-stage microscopy between mannitol and ALG, and in tablets. The interaction observed in the mixture with magnesium stearate is due to the melting of the excipient and drug separately, first the excipient and then the drug. FTIR showed additional bands related to the excipients. XRPD proved that ALG has a crystal form and no alterations in the ALG profile were observed after the mixtures. ALG was compatible with all excipients tested. These results were important to understand the characteristics, stability and compatibility of the drug, and proved to be useful in preformulation studies.

     

Cationic rhodium mono-phosphine fragments partnered with carborane monoanions [closo-CB11H6X6]- (X = H, Br). Synthesis, structures and reactivity with alkenes

Addition of the new phosphonium carborane salts [HPR(3)][closo-CB(11)H(6)X(6)] (R = (i)Pr, Cy, Cyp; X = H 1a-c, X = Br 2a-c; Cy = C(6)H(11), Cyp = C(5)H(9)) to [Rh(nbd)(mu-OMe)](2) under a H(2) atmosphere gives the complexes Rh(PR(3))H(2)(closo-CB(11)H(12)) 3 (R = (i)Pr 3a, Cy 3b, Cyp 3c) and Rh(PR(3))H(2)(closo-CB(11)H(6)Br(6)) 4 (R = (i)Pr 4a, Cy 4b, Cyp 4c). These complexes have been characterised spectroscopically, and for 4b by single crystal X-ray crystallography. These data show that the {Rh(PR(3))H(2)}(+) fragment is interacting with the lower hemisphere of the [closo-CB(11)H(6)X(6)](-) anion on the NMR timescale, through three Rh-H-B or Rh-Br interactions for complexes 3 and 4 respectively. The metal fragment is fluxional over the lower surface of the cage anion, and mechanisms for this process are discussed. Complexes 3a-c are only stable under an atmosphere of H(2). Removing this, or placing under a vacuum, results in H(2) loss and the formation of the dimer species Rh(2)(PR(3))(2)(closo-CB(11)H(12))(2) 5a (R = (i)Pr), 5b (R = Cy), 5c (R = Cyp). These dimers have been characterised spectroscopically and for 5b by X-ray diffraction. The solid state structure shows a dimer with two closely associated carborane monoanions surrounding a [Rh(2)(PCy(3))(2)](2+) core. One carborane interacts with the metal core through three Rh-H-B bonds, while the other interacts through two Rh-H-B bonds and a direct Rh-B link. The electronic structure of this molecule is best described as having a dative Rh(I) --> Rh(III), d(8)--> d(6), interaction and a formal electron count of 16 and 18 electrons for the two rhodium centres respectively. Addition of H(2) to complexes 5a-c regenerate 3a-c. Addition of alkene (ethene or 1-hexene) to 5a-c or 3a-c results in dehydrogenative borylation, with 1, 2, and 3-B-vinyl substituted cages observed by ESI-MS: [closo-(RHC[double bond, length as m-dash]CH)(x)CB(11)H(12-x)](-)x = 1-3, R = H, C(4)H(9). Addition of H(2) to this mixture converts the B-vinyl groups to B-ethyl; while sequential addition of 4 cycles of ethene (excess) and H(2) to CH(2)Cl(2) solutions of 5a-c results in multiple substitution of the cage (as measured by ESI-MS), with an approximately Gaussian distribution between 3 and 9 substitutions. Compositionally pure material was not obtained. Complexes 4a-c do not lose H(2). Addition of tert-butylethene (tbe) to 4a gives the new complex Rh(P(i)Pr(3))(eta(2)-H(2)C=CH(t)Bu)(closo-CB(11)H(6)Br(6)) 6, characterised spectroscopically and by X-ray diffraction, which show coordination of the alkene ligand and bidentate coordination of the [closo-CB(11)H(6)Br(6)](-) anion. By contrast, addition of tbe to 4b or 4c results in transfer dehydrogenation to give the rhodium complexes Rh{PCy(2)(eta(2)-C(6)H(9))}(closo-CB(11)H(6)Br(6)) 7 and Rh{PCyp(2)(eta(2)-C(5)H(7))}(closo-CB(11)H(6)Br(6)) 9, which contain phosphine-alkene ligands. Complex has been characterised crystallographically.     

Mechanisms behind the faceting of catanionic vesicles by polycations: chain crystallization and segregation

Vesicles composed of an anionic and a cationic surfactant, with a net negative charge, associate strongly with a hydrophobically modified polycation (LM200) and with an unmodified polycation with higher charge density (JR400), forming viscoelastic gel-like structures. Calorimetric results show that in these gels, LM200 induces a rise of the chain melting temperature (Tm) of the vesicles, whereas JR400 has the opposite effect. For both polymer-vesicle systems, the shear viscosity exhibits an inflection point at Tm, and for the LM200 system the measured relaxation times are significantly higher below Tm. The neat vesicles and the polycation-bound vesicles have a polygonal-like faceted shape when the surfactant chains in the bilayer are crystallized, as probed by cryo-transmission electron microscopy. Above Tm, the neat and the LM200-bound vesicles regain a spheroidal shape, whereas those in the JR400 system remain with a deformed faceted shape even above Tm. These shape changes are interpreted in terms of different mechanisms for the polymer-vesicle interaction, which seem to be highly dependent on polymer architecture, namely charge density and hydrophobic modification. A crystallization-segregation mechanism is proposed for the LM200-vesicle system, while, for the JR400-vesicle one, charge polarization-lateral segregation effects induced by the polycation in the catanionic bilayer are envisaged.