Unprecedented Kinetic Inertness for a Mn2+‐Bispidine Chelate: A Novel Structural Entry for Mn2+‐Based Imaging Agents

The search for more biocompatible alternatives to Gd³⁺‐based MRI agents, and the interest in ⁵²Mn for PET imaging call for ligands that form inert Mn²⁺ chelates. Given the labile nature of Mn²⁺, high inertness is challenging to achieve. The strongly preorganized structure of the 2,4‐pyridyl‐disubstituted bispidol ligand L₁ endows its Mn²⁺ complex with exceptional kinetic inertness. Indeed, MnL₁ did not show any dissociation for 140 days in the presence of 50 equiv. of Zn²⁺ (37 °C, pH 6), while recently reported potential MRI agents MnPyC3A and MnPC2A‐EA have dissociation half‐lives of 0.285 h and 54.4 h under similar conditions. In addition, the relaxivity of MnL₁ (4.28 mm ^?1 s^?1 at 25 °C, 20 MHz) is remarkable for a monohydrated, small Mn²⁺ chelate. In vivo MRI experiments in mice and determination of the tissue Mn content evidence rapid renal clearance of MnL₁. Additionally, L₁ could be radiolabeled with ⁵²Mn and the complex revealed good stability in biological media.     

Synthesis and conformation of fluorinated β-peptidic compounds

Experimental and theoretical data indicate that, for α-fluoroamides, the F-C-C(O)-N(H) moiety adopts an antiperiplanar conformation. In addition, a gauche conformation is favoured between the vicinal C-F and C-N(CO) bonds in N-β-fluoroethylamides. This study details the synthesis of a series of fluorinated β-peptides (1-8) designed to use these stereoelectronic effects to control the conformation of β-peptide bonds. X-ray crystal structures of these compounds revealed the expected conformations: with fluorine β to a nitrogen adopting a gauche conformation, and fluorine α to a C=O group adopting an antiperiplanar conformation. Thus, the strategic placement of fluorine can control the conformation of a β-peptide bond, with the possibility of directing the secondary structures of β-peptides.     

Macroscopic properties of fractured porous media

The macroscopic properties of fractured porous media locally governed by a Laplace equation are determined by several methods. The first one consists in discretizing the porous medium and the fractures and in solving the Laplace equation in the discretized structure. The other methods consist in successive upscalings. The first upscaling replaces the porous medium by a continuum with a given transport property. The second upscaling replaces the fractures by surfaces with equivalent properties. The results of the various methods give very close results. They suggest a simple approximation which is successful when the properties of the fluid and of the continuous porous medium are not too different.     

New static solutions in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) theory

We consider the equations of motion of an anisotropic space-time in f(T) theory, where T is the torsion. New spherically symmetric solutions of black holes and wormholes are obtained with a constant torsion and for the cases for which the radial pressure is proportional to a real constant, to some algebraic functions f(T) and their derivatives f _T (T), or vanishes identically.     

Static anisotropic solutions in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) theory

In previous work, we undertook to study static and anisotropic content in f(T) theory and obtained new spherically symmetric solutions considering a constant torsion and some particular conditions for the pressure. In this paper, still in the framework of f(T) theory, new spherically symmetric solutions are obtained, first considering the general case of an isotropic fluid and later the anisotropic content case in which the generalized conditions for the matter content are considered such that the energy density, the radial and tangential pressures depend on the algebraic f(T) and its derivative f _T (T). Moreover, we obtain the algebraic function f(T) through the reconstruction method for two cases and also study a polytropic model for the stellar structure.     

Low-Degree Approximation of Random Polynomials

Foundations of Computational Mathematics - We prove that with “high probability” a random Kostlan polynomial in $$n+1$$ many variables and of degree d can be approximated by a...     

Weak solutions of a mixed problem in a half-strip for a generalized Kawahara equation

We consider a mixed problem in a half-strip for a generalized Kawahara equation describing long nonlinear waves in inhomogeneous media with weak dispersion. We study the existence and uniqueness of generalized solutions in Sobolev weight spaces.