2-dimensional localization of acoustic waves in random perturbation of periodic media

In this work we study internal band edges localization of acoustic waves in 2-dimensional space obtained by random perturbation of some periodic media. Our results rely on the study of Lifshitz tails for the integrated density of states for random acoustic operators of the form . Localization is then deduced by the standard multiscale argument.     

On a resolvent approach for perturbed semigroups and application to $$L^1$$-neutron transport theory

We give new sufficient and practical conditions in terms of the generators ensuring the stability of the critical or the essential type of a perturbed \(C_0\)-semigroup in general Banach spaces. We apply our theoretical results in order to investigate the control and in particular the time asymptotic behavior of solutions to a broad class of transport equations in \(L^1\)-spaces and higher dimension. Our results improve, complete and enrich several earlier works.     

Nonlinear impulsive partial functional differential inclusions with state-dependent delay and multivalued jumps

In this paper, we shall establish sufficient conditions for the existence of integral solutions for some nondensely defined impulsive semilinear functional differential inclusions with state-dependent delay in separable Banach spaces. We shall rely on a fixed point theorem for the sum of completely continuous and contraction operators.     

Dunkl-Schrödinger semigroups and applications

We obtain dispersive estimates for the linear Dunkl–Schrödinger equations with and without quadratic potential. As a consequence, we prove the local well-posedness for semilinear Dunkl–Schrödinger equations with polynomial nonlinearity in certain magnetic field. Furthermore, we study many applications: as the uncertainty principles for the Dunkl transform via the Dunkl–Schrödinger semigroups, the embedding theorems for the Sobolev spaces associated with the generalized Hermite semigroup. Finally, almost every where convergence of the solutions of the Dunkl–Schrödinger equation is also considered.     

Mechanism of nanocapsules formation by the emulsion-diffusion process

A detailed investigation into the mechanisms of nanocapsule formation by means of the two stages "emulsion-diffusion" process is reported. Such widely used process is still poorly understood. An emulsion of oil, polymer and ethyl acetate is fabricated as a first step; dilution with pure water allows ethyl acetate to diffuse out from the droplets, leaving a suspension of nanocapsules at the end. It has been shown that the size of nanocapsules was related to the chemical composition of the organic phase and the size of primary emulsion through a simple geometrical relationship. As a consequence, most of the properties of the nanocapsules were decided at the emulsification step. The influence of several formulation and processing parameters of the primary emulsion was studied accordingly. The thin polymer membrane of nanocapsules was observed by means of cryo-fracture electron microscopy. Finally two experiments were designed for a mechanistic investigation of the diffusion step. A step-by-step diffusion of the organic solvent takes place by successive partition equilibria of ethyl acetate between the droplets and aqueous phase. A time-resolved experiment shows the fast diffusion (less than 20 ms) related to the small droplet size of the emulsion.     

Paley–Wiener Theorems of Generalized Fourier Transform Associated with a Cherednik Type Operator on the Real Line

We consider a singular differential-difference operator \(\Lambda \) on the real line which generalizes the Cherednik operator associated with the reflection group \(\mathbb {Z}_2\) on \(\mathbb {R}\). We establish the Paley–Wiener theorems for the generalized Fourier transform on \(\mathbb {R}\) tied to \(\Lambda \).     

Catechins: Therapeutic Perspectives in COVID-19-Associated Acute Kidney Injury

Data obtained from several intensive care units around the world have provided substantial evidence of the strong association between impairment of the renal function and in-hospital deaths of critically ill COVID-19 patients, especially those with comorbidities and requiring renal replacement therapy (RRT). Acute kidney injury (AKI) is a common renal disorder of various etiologies characterized by a sudden and sustained decrease of renal function. Studies have shown that 5–46% of COVID-19 patients develop AKI during hospital stay, and the mortality of those patients may reach up to 100% depending on various factors, such as organ failures and RRT requirement. Catechins are natural products that have multiple pharmacological activities, including anti-coronavirus and reno-protective activities against kidney injury induced by nephrotoxic agents, obstructive nephropathies and AKI accompanying metabolic and cardiovascular disorders. Therefore, in this review, we discuss the anti-SARS-CoV-2 and reno-protective effects of catechins from a mechanistic perspective. We believe that catechins may serve as promising therapeutics in COVID-19-associated AKI due to their well-recognized anti-SARS-CoV-2, and antioxidant and anti-inflammatory properties that mediate their reno-protective activities.     

Thiophenylhydrazonoacetates in heterocyclic synthesis

Benzo[b]thiophen-2-yl-hydrazonoesters 4 were synthesized by coupling of 2-diazo-4,5,6,7-tetrahydrobenzo[b]thiophene-3-carboxamide ( 1 ) with either ethyl cyanoacetate or ethyl acetoacetate. The reactivity of 4 toward a variety of nitrogen nucleophiles was investigated to yield pyrazole, isoxazole, pyrimidine, triazine, pyrazolopyridine, and pyrazolopyrimidine derivatives. © 2003 Wiley Periodicals, Inc. 15:15–20, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/.hc10205