The novel arsenate Na4Co7−xAl2/3x(AsO4)6 (x = 1.37): crystal structure,charge‐distribution and bond‐valence‐sum investigations

The title compound, tetrasodium cobalt aluminium hexaarsenate, Na₄Co_7−xAl_2/3x(AsO₄)₆ (x = 1.37), is isostructural with K₄Ni₇(AsO₄)₆; however, in its crystal structure, some of the Co²⁺ ions are substituted by Al³⁺ in a fully occupied octahedral site (site symmetry 2/m) and a partially occupied tetrahedral site (site symmetry 2). A third octahedral site is fully occupied by Co²⁺ ions only. One of the two independent tetrahedral As atoms and two of its attached O atoms reside on a mirror plane, as do two of the three independent Na⁺ cations, all of which are present at half‐occupancy. The proposed structural model based on a careful investigation of the crystal data is supported by charge‐distribution (CHARDI) analysis and bond‐valence‐sum (BVS) calculations. The correlation between the X‐ray refinement and the validation results is discussed.     

New method to obtain the acute sill of an ecological model with complex polynomial perturbation

This research aims to highlight and examine an example of ecological complexity. By taking into account the interference between predator and prey, we introduce an ecological system with a general functional response. This model is perturbed by a novel class of fluctuations in the polynomial form. Analytically, we present an alternative method to obtain the acute threshold between stationarity and predator disappearance. Our analysis enriches and improves the work of Zhou et al. (2021) by unifying the criteria of said asymptotic characteristics. Numerically, we audit the accuracy of our threshold in three particular situations: linear, quadratic and cubic perturbations. We establish that the increasing order of disturbance has a passive influence on the extinction time of predators. This finding highlights that complex noise sources have a positive role in the transient dynamics of ecological systems.     

Gorenstein n-X-Injective and n-X-Flat Modules with Respect to a Special Finitely Presented Module

Let R be a ring,X a class of R-modules and n ≥ 1 an integer.We intro-duce the concepts of Gorenstein n-X-injective and n-X-flat modules via special finitely presented modules.Besides,we obtain some equivalent properties of these modules on n-X-coherent rings.Then we investigate the relations among Gorenstein n-X-injective,n-X-flat,injective and fiat modules on X-FC-rings (i.e.,self n-X-injective and n-X-coherent rings).Several known results are generalized to this new context.     

Silver cluster-biomolecule hybrids: from basics towards sensors

We focus on the functional role of small silver clusters in model hybrid systems involving peptides in the context of a new generation of nanostructured materials for biosensing. The optical properties of hybrids in the gas phase and at support will be addressed with the aim to bridge fundamental and application aspects. We show that extension and enhancement of absorption of peptides can be achieved by small silver clusters due to the interaction of intense intracluster excitations with the π-π* excitations of chromophoric aminoacids. Moreover, we demonstrate that the binding of a peptide to a supported silver cluster can be detected by the optical fingerprint. This illustrates that supported silver clusters can serve as building blocks for biosensing materials. Moreover, the clusters can be used simultaneously to immobilize biomolecules and to increase the sensitivity of detection, thus replacing the standard use of organic dyes and providing label-free detection. Complementary to that, we show that protected silver clusters containing a cluster core and a shell liganded by thiolates exhibit absorption properties with intense transitions in the visible regime which are also suitable for biosensing applications.     

Solving Fredholm integral equations by approximating kernels by spline quasi-interpolants

We study two methods for solving a univariate Fredholm integral equation of the second kind, based on (left and right) partial approximations of the kernel K by a discrete quartic spline quasi-interpolant. The principle of each method is to approximate the kernel with respect to one variable, the other remaining free. This leads to an approximation of K by a degenerate kernel. We give error estimates for smooth functions, and we show that the method based on the left (resp. right) approximation of the kernel has an approximation order O(h ⁵) (resp. O(h ⁶)). We also compare the obtained formulae with projection methods.