Some classes of operators with symbol on the Lipschitz space of a tree

In this paper, we expand the study of the multiplication operators on the Lipschitz space of a tree begun in Colonna and Easley (Integral Equ Oper Theory 68:391–411, 2010) by focusing on their adjoint acting on a certain separable subspace of the Lipschitz space whose dual is isometrically isomorphic to \(\mathbf L^1\). We then study the properties of two useful operators \(\nabla \) and \(\Delta \) and use them (along with the multiplicative symbol \(\psi \)) to define the Toeplitz operator \(T_\psi \) on the space \(\mathbf L^p\) for \(1\le p \le \infty \). We give conditions for its boundedness and study its point spectrum.     

Ambazone salt with p-aminobenzoic acid

In this study, we obtained a novel salt of ambazone (AMB) with p-aminobenzoic acid (PABA) that exhibits improved solubility and antibacterial activity. The salt was produced by solvent-drop grinding and characterized by powder X-ray diffraction, thermal analysis and Fourier transform infrared spectroscopy. The salt nature of the new form was confirmed by infrared spectroscopy based on the characteristic vibrational band of the protonated amino group. Based on the X-ray powder diffraction data, the compound crystallizes in the triclinic P_-1 space group with the following unit cell parameters: a = 14.294 Å, b = 9.162 Å, c = 8.777 Å, α = 95.90°, β = 100.63°, γ = 91.73°. Thermal analysis reveals the thermal events and different decomposition steps of this solid form as compared to the starting compounds. Powder dissolution measurements showed solubility improvement compared with pure ambazone of 2 and 3.3 times in water and phosphate buffer, respectively. Antibacterial tests showed higher activity of the salt to Gram-negative Escherichia coli and Salmonella bacteria as compared to AMB and PABA. The study demonstrates that the pharmaceutical salt of ambazone with p-aminobenzoic acid (AMB–PABA) can be a possible alternative to ambazone in the treatment of infections with Gram-negative bacteria.     

Analytical performance of glucometers in a tertiary care hospital

Point-of-care (POC) testing of glucose (glucometers) represents a convenient alternative to monitor glycemia since the measurement procedure is performed without delay after sampling of the capillary blood, thereby avoiding the metabolism by the blood cells of glucose present in plasma. Likely because of sample instability, there is no proficiency test provider in Brazil for this type of POC sample. In this context, this study aimed to evaluate the analytical performance of glucometers used in a tertiary care hospital. The glucometers used were the Accu-Chek Performa^® model from Roche Diagnostics, which use the principle of amperometry. The reference method was the reaction with modified hexokinase/glucose-6-phosphate in a Dimension^® device. The stability evaluation of the control samples showed that it can be performed up to 90 min after the collection of whole blood samples. In the two rounds performed, only one result of the 17 glucometers evaluated was out of the threshold of two standard deviation. Thus, this method for control of glucometers met the expectations and enabled comparing the glucometers in a hospital. Given the current quality guidelines, daily internal quality control of glucometers is recommended, besides at least two annual comparisons between the results of the glucometers and the reference method and one EQA every 3 months.     

Radon Measure-Valued Solutions for a Class of Quasilinear Parabolic Equations

Initial value problems for quasilinear parabolic equations having Radon measures as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. In contrast, it is the purpose of this paper to define and investigate solutions that for positive times take values in the space of the Radon measures of the initial data. We call such solutions measure-valued, in contrast to function-valued solutionspreviously considered in the literature. We first show that there is a natural notion of measure-valued solution of problem (P) below, in spite of its nonlinear character. A major consequence of our definition is that, if the space dimension is greater than one, the concentrated part of the solution with respect to the Newtonian capacity is constant in time. Subsequently, we prove that there exists exactly one solution of the problem, such that the diffuse part with respect to the Newtonian capacity of the singular part of the solution (with respect to the Lebesgue measure) is concentrated for almost every positive time on the set where “the regular part (with respect to the Lebesgue measure) is large”. Moreover, using a family of entropy inequalities we demonstrate that the singular part of the solution is nonincreasing in time. Finally, the regularity problem is addressed, as we give conditions (depending on the space dimension, the initial data and the rate of convergence at infinity of the nonlinearity ψ) to ensure that the measure-valued solution of problem (P) is, in fact, function-valued.     

Synthesis of a Benzannulated Pyrrolizidine by a Copper‐Catalyzed Intramolecular α‐Arylation Reaction

A synthetic route to the pyrrolo[1,2‐a]indole ring system (benzannulated pyrrolizidine) involving a base‐induced intramolecular aza‐Michael reaction as the key C? N bond‐forming penultimate step, followed by a Cu‐catalyzed intramolecular α‐arylation reaction, to provide the tricyclic framework over six steps is described.     

Biharmonic Green Functions on Homogeneous Trees

The study of biharmonic functions under the ordinary (Euclidean) Laplace operator on the open unit disk \mathbbD{\mathbb{D}} in \mathbbC{\mathbb{C}} arises in connection with plate theory, and in particular, with the biharmonic Green functions which measure, subject to various boundary conditions, the deflection at one point due to a load placed at another point. A homogeneous tree T is widely considered as a discrete analogue of the unit disk endowed with the Poincaré metric. The usual Laplace operator on T corresponds to the hyperbolic Laplacian. In this work, we consider a bounded metric on T for which T is relatively compact and use it to define a flat Laplacian which plays the same role as the ordinary Laplace operator on \mathbbD{\mathbb{D}}. We then study the simply-supported and the clamped biharmonic Green functions with respect to both Laplacians.