H2 Convergence of Solutions of a Biharmonic Problem on a Truncated Convex Sector Near the Angle π

We consider a biharmonic problem Δ²u_ω = f_ω with Navier type boundary conditions u_ω = Δu_ω = 0, on a family of truncated sectors Ω_ω in ?² of radius r, 0 < r < 1 and opening angle ω, ω ∈ (2π/3, π] when ω is close to π. The family of right-hand sides (f_ω)_{ω∈(2π/3, π]} is assumed to depend smoothly on ω in L²(Ω_ω). The main result is that u_ω converges to u_π when ω → π with respect to the H²-norm. We can also show that the H²-topology is optimal for such a convergence result.

     

One-dimensional stochastic heat equation with discontinuous conductance

We introduce a new stochastic partial differential equation with second-order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by a space–time white noise. Such equation could be used in mathematical modeling of diffusion phenomena in medium consisting of two kinds of materials and undergoing stochastic perturbations. We prove the existence of the solution and we present explicit expressions of its covariance and variance functions. Some regularity properties of the solution sample paths are also analyzed.     

General decay for a porous thermoelastic system with a memory

In this paper, we consider a linear damped porous thermoelastic system of memory type where the heat conduction is given by Cattaneo’s Law . We establish a general decay results using an appropriate Lyapunov functional.     

Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier–Stokes asymptotics

In this paper, we develop a numerical method to solve Boltzmann like equations of kinetic theory which is able to capture the compressible Navier–Stokes dynamics at small Knudsen numbers. Our approach is based on the micro/macro decomposition technique, which applies to general collision operators. This decomposition is performed in all the phase space and leads to an equivalent formulation of the Boltzmann (or BGK) equation that couples a kinetic equation with macroscopic ones. This new formulation is then discretized with a semi-implicit time scheme combined with a staggered grid space discretization. Finally, several numerical tests are presented in order to illustrate the efficiency of our approach. Incidentally, we also introduce in this paper a modification of a standard splitting method that allows to preserve the compressible Navier–Stokes asymptotics in the case of the simplified BGK model. Up to our knowledge, this property is not known for general collision operators.     

3D-pharmacophore study molecular docking and synthesis of pyrido[2,3-d]pyrimidine-4(1H) dione derivatives with in vitro potential anticancer and antioxidant activities

Some poly functionalized heterocyclic-compounds containing pyridine-moieties were readily assembled by combining differently functionalized pyridopyrimidine-6-carbonitrile derivatives 1a,b with different electrophilic and nucleophilic reagents via short synthetic routes. The structures of the prepared derivatives were ascertained from their-spectral-and elemental analyses. Some of the synthesized compounds were tested as plausible antitumor agents. Most of those tested compounds likes 7 , 9 , 10 , 11a showed cytotoxic potencies against different tumor cell lines. In addition, the assessments for their antioxidant activities have also been done and compound 9 exhibited the highest antioxidant activity while compounds 7 and 10 showed moderate activities. Finally, molecular docking studies were carried out which favorably indicated a high support for the experimental-results.     

Structural basis of pyrazolopyrimidine derivatives as CAMKIIδ kinase inhibitors: insights from 3D QSAR,docking studies and in silico ADMET evaluation

Ca²⁺/calmodulin-dependent protein kinase II (CAMKIIδ) belongs to the serine/threonine kinase family, which is involved in a broad range of cellular events in cell survival and proliferation as well as a number of other signal transduction pathways. Thus, it is regarded a promising target for treatment of cancers. In the present paper, a three-dimensional quantitative structure–activity relationship and molecular docking were applied to investigate a series of new CAMKIIδ inhibitors of pyrazolopyrimidine derivatives. The determination coefficient (R²) and leave-one-out cross-validation coefficient (Q²) of CoMSIA model are 0.676 and 0.956, respectively. The predictive ability of this model was evaluated by the external validation using a test set of eight compounds with a predicted determination coefficient \(R^{ 2}_{\text{test}}\) of 0.80, besides the mean absolute error of the test set was 0.328 log units. Docking results are in concordance with CoMSIA contour maps, gave the information for interactive mode exploration. Based on those satisfactory results, newly designed molecules were predicted with highly potent CAMKIIδ inhibitory activity, additionally, they have showed promising results in the preliminary in silico ADMET evaluations. This study could expand our understanding of pyrazolopyrimidine derivatives as inhibitors of CAMKIIδ and would be of great help in lead optimization for early drug discovery of highly potent CAMKIIδ inhibitors.     

First insights into the electronic properties of a Cu(II) center embedded in the PN3 cap of a calix[6]arene-based ligand

The first metal complex based on the calix[6]PN3 cryptand is described. The solid-state and solution studies show a 5-coordinate Cu(II) center due to its coordination to the PN3 cap and to an exchangeable guest molecule. Spectroscopic and electrochemical studies evidence surprising properties of the metal ion, which are tentatively assigned to the unusual P-Cu(II) bond enforced by the cryptand.     

Self-assembly reactions between the cis-protected metal corners (N-N)MII (N-N = ethylenediamine, 4,4'-substituted 2,2'-bipyridine; M = Pd, Pt) and the fluorinated edge 1,4-bis(4-pyridyl)tetrafluorobenzene

The self-assembly reactions between the fluorinated ditopic ligand 1,4-bis(4-pyridyl)tetrafluorobenzene (A) and different nitrogen-protected palladium(II) and platinum(II) complexes have been investigated. While dynamic equilibria between molecular triangles and squares were observed when the diimine compounds 4,4'-R2bipy (bipy = 2,2'-bipyridine; R = H, Me, t-Bu) were employed as ancillary ligands, only square species were obtained from ethylenediamine (en) derivatives. Characterization of the obtained metallomacrocycles was accomplished by 1H and 19F NMR spectroscopy in combination with electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI-FT-ICR). Molecular dynamics simulations (UFF) have been performed to interpret the influence of the fluorinated ring on the square/triangle relative stability. Density functional calculations using the GIAO method have been employed for the interpretation of the chemical shift assignments. The study of the ability of these compounds to act as hosts of electron-rich aromatic guests has shown that the palladium ethylenediamine square is capable of establishing this type of intermolecular interaction exclusively in aqueous media. The host-guest stoichiometry and association constants have been determinated by 1H NMR spectroscopy.     

Improvement of piezoelectric transformer performances using SSHI and SSHI-max methods

The piezoelectric transformers reach densities of power more significant than their magnetic counterparts. However, one of the principal factors limiting the density of power is the acceptable maximum deformation by material constituting the transformer. The heating of the piezoelectric transformers is mainly of mechanical origin. This heating generates a degradation of the characteristics which in its turn generates an additional heating being able to lead to a phenomenon of thermal avalanche. In this work, two nonlinear methods [synchronized switch harvesting on inductor (SSHI) and SSHI-max] have been explored to improve the performance of the Rosen transformer basing on the tension generated by the secondary so as to increase the capacity of mechanic-electric conversion. The simulation results show that SSHI and SSHI-max techniques significantly increase the capacity of mechanic-electric conversion of inserts stuck on a vibrating structure and consequently, the power recovered in electric form. The comparative results of voltage gain, efficiency and the transmitted power of the transformer, before and after SSHI-max and SSHI control are given. These ones indicated that the two nonlinear techniques are promising as applications to improve the performances of the piezo-transformers.