Half-linear equations and characteristic properties of the principal solution

The characteristic properties of the principal solution for half-linear differential equation

(a(t)Φ(x′))′+b(t)Φ(x)=0,     

Structure of neutron stars in R-squared gravity

The effects implied for the structure of compact objects by the modification of General Relativity (GR) produced by the generalization of the Lagrangian density to the form $f(R)=R+\alpha R^2$ , where $R$ is the Ricci curvature scalar, have been recently explored. It seems likely that this squared-gravity may allow heavier Neutron Stars (NSs) than GR. In addition, these objects can be useful to constrain free parameters of modified-gravity theories. The differences between alternative gravity theories are enhanced in the strong gravitational regime. In this regime, because of the complexity of the field equations, perturbative methods become a good choice to treat the problem. Following previous works in the field, we performed a numerical integration of the structure equations that describe NSs in $f(R)$ -gravity, recovering their mass-radius relations, but focusing on particular features that arise from this approach in the profiles of the NS interior. We show that these profiles run in correlation with the second-order derivative of the analytic approximation to the Equation of State (EoS), which leads to regions where the enclosed mass decreases with the radius in a counter-intuitive way. We reproduce all computations with a simple polytropic EoS to separate zeroth-order modified gravity effects.     

Some properties of third order differential operators

Consider the third order differential operator L given by and the related linear differential equation L(x)(t) + x(t) = 0. We study the relations between L, its adjoint operator, the canonical representation of L, the operator obtained by a cyclic permutation of coefficients a _i , i = 1,2,3, in L and the relations between the corresponding equations.We give the commutative diagrams for such equations and show some applications (oscillation, property A).     

Carbonic anhydrase inhibitors. Sulfonamide diuretics revisited--old leads for new applications?

Sulfonamide diuretics such as hydrochlorothiazide, hydroflumethiazide, quinethazone, metolazone, chlorthalidone, indapamide, furosemide and bumetanide were tested as inhibitors of the zinc enzyme carbonic anhydrases (CAs, EC 4.2.1.1). These drugs were discovered in a period when only isoform CA II was known and considered physiologically/pharmacologically relevant. We prove here that although acting as moderate to weak inhibitors of CA II, all these drugs considerably inhibit other isozymes known nowadays to be involved in critical physiologic processes, among the 16 CAs present in vertebrates. Some low nanomolar/subnanomolar inhibitors against such isoforms were detected, such as among others metolazone against CA VII, XII and XIII, chlorthalidone against CA VB, VII, IX, XII and XIII, indapamide against CA VII, IX, XII and XIII, furosemide against CA I, II and XIV, and bumethanide against CA IX and XII. The X-ray crystal structure of the CA II-indapamide adduct was also resolved at high resolution, and the binding of this sulfonamide to the enzyme was compared to that of dichlorophenamide, sulpiride and a pyridinium containing sulfonamide. Indapamide binds to CA II in a manner not seen earlier for any other CA inhibitor, which might be important for the design of compounds with a different inhibition profile.     

Synthesis of 4,5-dihydroisoxazoles by condensation of primary nitro compounds with alkenes by using a copper/base catalytic system

A new procedure for the synthesis of 4.5-dihydroisoxazoles by condensation of primary nitro compounds with olefins by using a copper/base catalytic system is described. The catalytic effect of copper(II) salts is evidenced by comparison of the reaction rates. Thus, activated nitro compounds react faster than with organic catalysis by tertiary amines, whereas nitroalkanes, unable to condense with dipolarophiles in the presence of the base alone, undergo the reaction on addition of a copper(II) catalyst. The observed occurrence of induction periods in most reactions is ascribed to an equilibrium preceding the rate-determining step, and gives a hint as to the proposed reaction mechanism. The results indicate that this method might be of practical and general utility for synthetic practice.     

Electrospray ionization mass spectrometry of a novel family of complexes in which various nitroso compounds are stabilized via coordination to [IrCl5]2-

Electrospray ionization mass spectrometry (ESI-MS) and tandem mass spectrometry (ESI-MS/MS) data of a unique family of complexes of nitroso compounds coordinated to pentachloroiridate(III), [Cl5IrN(O)XR]2- (X=NH, S, CH and R=alkyl, aryl) are presented. These novel complexes are obtained by nucleophilic attack of primary amines, thiols. and alkenes to the coordinated nitrosyl. Despite their lability and low volatility, MS analysis of complexes of the type MN(O)X was done for the first time, complementing other spectroscopic techniques. The intrinsic dissociation chemistry of the gaseous diagnostic ions was studied via ESI-MS/MS and found to be very useful to confirm the proposed connectivities of the parent complexes. In particular, ESI-MS of their solutions allows the detection of series of diagnostic ions, mainly, [M-Cl]-, [M+K]-, [M-NO]-*, and [M-Cl+AcN]- (AcN=acetonitrile), which confirmed the identity of the analyzed complexes to be M=[Cl5IrN(O)XR]2-. Major fragments were formed by losses of NO or N(O)XR. ESI-MS and ESI-MS/MS measurements are therefore shown to be the proper techniques to complement the spectroscopic characterization of this important class of nitroso complexes. An interesting rearrangement that does not take place in solution was observed in the gaseous phase, and a plausible mechanism is discussed.     

Equivalency for Disconjugate Operators

The solutions of the dfferential equation L_nx + a₀(t)x = 0, where L_n is a disconjugate operator and a₀ is of one sign, are studied according to their behavior as t → ∞. We prove equivalence theorems between solutions of this equation and its adjoint in terms of property A and property B. These theorems generalize the results known for n = 3 and for odd order binomial equations. Some applications are given too.