Interior-point methods for linear optimization based on a kernel function with a trigonometric barrier term

In this paper, we present a new barrier function for primal–dual interior-point methods in linear optimization. The proposed kernel function has a trigonometric barrier term. It is shown that in the interior-point methods based on this function for large-update methods, the iteration bound is improved significantly. For small-update interior-point methods, the iteration bound is the best currently known bound for primal–dual interior-point methods.     

Evaporation of Electrolyte during SVET Measurements: The Scale of the Problem and the Solutions

The objective of this work is to investigate the scale of the effect of spontaneous solution evaporation during SVET (Scanning Vibrating Electrode Technique) measurements and demonstrate how it biases the final results. When SVET maps are continuously acquired for more than several hours, the measured currents are smaller than expected. This is attributed to solvent (typically water) evaporation which leads to an increase in solution conductivity over time. If this is not considered when converting the measured potential differences into the local current densities, the SVET results display currents smaller than the true ones. Here, this effect is studied with a platinum disk electrode as source of a constant current and a model corroding system consisting of the AA2024/CFRP galvanic couple. Corrective actions are proposed to mitigate the problem, either in the experimental set‐up or as numerical correction.     

Une remarque sur l'orthogonalité de l'image au noyau d'une dérivation généralisée

In this paper we introduce the notion of the pair of operators having the Fuglede-Putnam property in a two-sided ideal of . The characterization of this class allows us to generalize the recent result of F. Kittaneh. We also give some applications of this result.

     

Generalized Humbert polynomials and second-order partial differential operators

We define a new class of Humbert's polynomials which generalizes the well-known class of Gegenbauer, Legendre, Pincherle, Horadam-Mahon, Kinney, Hordam-Pethe, Gould and Pathan-Khan polynomials. We prove that these generalized polynomials are eigenfunctions of the Hamiltonian of the Calogero-Sutherland model. We show several differential equations having these polynomials for solutions.     

Emulating complex business cycles by using an electronic analogue

Long run growth of the US national economic system, for example, reveals a strong oscillatory behavior due to complex interactions of aggregates. However, modelizations of such dynamics often assume that instability is the outcome of linear and additive cycles determined by exogenous shocks. In this work, a modelization of endogenous nonlinear and inseparable cycles is retained to explain the highly complex business cycle phenomenon. Bouali’s system is built to this scope. Its numerical simulations exhibit a rich repertoire of nonlinear dynamical phenomena, but this paper introduces its electronic implementation. The robust plug and play chaotic circuit is designed to be easily realized using standard components in a rigorous, fast and inexpensive way. We find that experimental results display periodicity, bifurcations and chaos that match with high accuracy the corresponding theoretical values.     

Lévy–Khinchin formula for the infinite symmetric group

Let ${\mathfrak{S}(\infty)}$ be the infinite symmetric group, inductive limit of the increasing sequence of the symmetric groups ${\mathfrak{S}(n)}$ . We establish an integral representation for the central functions of negative type on ${\mathfrak{S}(\infty)}$ , i.e. a Lévy–Khinchin formula, by following a method introduced by Berg, Christensen and Ressel (Harmonic Analysis on Semigroups. Theory of Positive Definite and Related Functions. Springer, Berlin, 1984).     

Existence of Positive Solutions for a Class of Quasilinear Singular Elliptic Systems Involving Caffarelli-Kohn-Nirenberg Exponent with Sign-Changing Weight Functions

The paper deals with the existence of weak positive solutions for a new class of quasilinear singular elliptic systems involving critical Caffarelli–Kohn–Nirenberg exponent with sign-changing weight functions using the method of sub-super solutions. Our results are natural extensions from the previous ones in [3].     

Differential calculus on the Faber polynomials

The Faber polynomials are presented as a coordinate system to study the geometry of the manifold of coefficients of univalent functions.     

α-Zirconium orthophosphate as a new Zn-free anticorrosive pigment in organic coatings

Journal of Solid State Electrochemistry - In the framework of the anticorrosive pigment research without heavy metals like zinc or chromium, a new lamellar phosphate pigment, namely zirconium...     

Multifunctional Derivatives of Spiropyrrolidine Tethered Indeno-Quinoxaline Heterocyclic Hybrids as Potent Antimicrobial,Antioxidant and Antidiabetic Agents: Design,Synthesis, In Vitro and In Silico Approaches

To combat emerging antimicrobial-resistant microbes, there is an urgent need to develop new antimicrobials with better therapeutic profiles. For this, a series of 13 new spiropyrrolidine derivatives were designed, synthesized, characterized and evaluated for their in vitro antimicrobial, antioxidant and antidiabetic potential. Antimicrobial results revealed that the designed compounds displayed good activity against clinical isolated strains, with 5d being the most potent (MIC 3.95 mM against Staphylococcus aureus ATCC 25923) compared to tetracycline (MIC 576.01 mM). The antioxidant activity was assessed by trapping DPPH, ABTS and FRAP assays. The results suggest remarkable antioxidant potential of all synthesized compounds, particularly 5c, exhibiting the strongest activity with IC₅₀ of 3.26 ± 0.32 mM (DPPH), 7.03 ± 0.07 mM (ABTS) and 3.69 ± 0.72 mM (FRAP). Tested for their α-amylase inhibitory effect, the examined analogues display a variable degree of α-amylase activity with IC₅₀ ranging between 0.55 ± 0.38 mM and 2.19 ± 0.23 mM compared to acarbose (IC₅₀ 1.19 ± 0.02 mM), with the most active compounds being 5d, followed by 5c and 5j, affording IC₅₀ of 0.55 ± 0.38 mM, 0.92 ± 0.10 mM, and 0.95 ± 0.14 mM, respectively. Preliminary structure–activity relationships revealed the importance of such substituents in enhancing the activity. Furthermore, the ADME screening test was applied to optimize the physicochemical properties and determine their drug-like characteristics. Binding interactions and stability between ligands and active residues of the investigated enzymes were confirmed through molecular docking and dynamic simulation study. These findings provided guidance for further developing leading new spiropyrrolidine scaffolds with improved dual antimicrobial and antidiabetic activities.