On the Nevanlinna problem -- Characterization of all Schur-Agler class solutions affiliated with a given kernel

Given a domain $\Omega$ in $\mathbb{C}^m$, and a finite set of points $z_1,z_2,\ldots, z_n\in \Omega$ and $w_1,w_2,\ldots, w_n\in \mathbb{D}$ (the open unit disc in the complex plane), the \textit{Pick interpolation problem} asks when there is a holomorphic function $f:\Omega \rightarrow \overline{\mathbb{D}}$ such that $f(z_i)=w_i,1\leq i\leq n$. Pick gave a condition on the data $\{z_i, w_i:1\leq i\leq n\}$ for such an $interpolant$ to exist if $\Omega=\mathbb{D}$. Nevanlinna characterized all possible functions $f$ that \textit{interpolate} the data. We generalize Nevanlinna's result to a domain $\Omega$ in $\mathbb{C}^m$ admitting holomorphic test functions when the function $f$ comes from the Schur-Agler class and is affiliated with a certain completely positive kernel. The Schur class is a naturally associated Banach algebra of functions with a domain. The success of the theory lies in characterizing the Schur class interpolating functions for three domains - the bidisc, the symmetrized bidisc and the annulus - which are affiliated to given kernels.Comment: arXiv admin note: text overlap with arXiv:1812.00147, Accepted in Studia Mathematic

BIOLOGICAL EVALUATION, QSAR AND MOLECULAR MODELING STUDIES OF 2,4-DICHLOROBENZOIC ACID DERIVATIVES AS ANTIMICROBIAL AGENTS

Objective: The aim of this study was to evaluate 2,4-dichlorobenzoic acid derivatives as antimicrobial agents through in vitro, QSAR and molecular docking studies. Methods: The compounds were subjected to in vitro antimicrobial screening by test tube dilution method and the structural characteristics governing the antimicrobial potential were studied using QSAR methodology. These compounds were also screened for docking simulation to find out binding confirmation of reported compounds with PDB 1aj0 and 5fsa using AutoDock tools and discovery studio. Results: The antimicrobial evaluation data indicated that compounds 13 and 18 were found to be the most effective against all the bacterial strains and Aspergillus niger while compounds 1 and 14 exhibited more antifungal potential against Candida albicans. QSAR studies confirmed the role of molar refractivity and Balaban index (J) as controlling parameters for antimicrobial potential. Molecular modeling study revealed that compounds interact with the active site of PDB by hydrophobic, hydrogen bonding, and Van der Wall interactions. Conclusion: These test compounds were identified as potent candidates for the control of microbial strains tested, and structural relationship with activity may provide valuable information for further design and synthesis of compounds with antimicrobial potential

Notions of Visibility with respect to the Kobayashi distance: Comparison and Applications

In this article, we study several notions of visibility with respect to the Kobayashi distance for relatively compact complex submanifolds in complex Euclidean space. These notions of visibility are generalizations to the context of such submanifolds of notions introduced and studied in recent work by Bharali--Zimmer, Bharali--Maitra and Bracci--Nikolov--Thomas. We also introduce and study the notion of "visibility subspace" of relatively compact, embedded submanifolds. Using this notion, we generalize to such submanifolds a recent result of Bracci--Nikolov--Thomas and use this generalized result to prove a theorem on the continuous extension of Kobayashi isometries. Next we present a sufficient condition, more permissive than those currently known, for a domain to possess the visibility property with respect to Kobayashi almost-geodesics introduced and studied recently by Bharali--Zimmer (we call this BZ-visibility). We concretely illustrate the fact that our condition is more permissive by providing examples. We also prove a Wolff--Denjoy-type theorem that is a generalization of recent results of this kind by Bharali--Zimmer and Bharali--Maitra and that, owing to the examples mentioned, is a proper generalization. Along the way, we note that what is needed for the proof of this sort of theorem to work is a form of visibility that seems to be intermediate between BZ-visibility and visibility with respect to ordinary Kobayashi geodesics.Comment: Comments welcom

Design, Synthesis and Antidiabetic Activity of Novel Sulfamoyl Benzamide Derivatives as Glucokinase Activators

The present work has been planned to design, synthesize and evaluate the antidiabetic potential of a series of sulfamoyl benzamide derivatives as potential glucokinase (GK) activators. A new series of sulfamoyl benzamide derivatives was synthesized starting from 3-nitrobenzoic acid and characterized. In silico docking studies were performed to determine the binding interactions for the best fit conformations in the allosteric site of GK enzyme. Based on the results of in silico studies, the selected molecules were tested for their antidiabetic activity in animal studies (alloxan induced diabetic animal model). Compound 7 exhibited highest antidiabetic activity in animal studies. The results of in vivo antidiabetic activity studies were found to be in parallel to that of docking studies. These newly synthesized sulfamoyl benzamide derivatives thus can be treated as the initial hits for the development of novel, safe, effective and orally bioavailable GK activators as therapeutic agents for the treatment of type 2 diabetes

Self-Healing, Robust, Liquid-Repellent Coatings Exploiting the Donor-Acceptor Self-Assembly

Liquid-repellent coatings with rapid self-healing and strong substrate adhesion have tremendous potential for industrial applications, but their formulation is challenging. We exploit synergistic chemistry between donor-acceptor self-assembly units of polyurethane and hydrophobic metal-organic framework (MOF) nanoparticles to overcome this challenge. The nanocomposite features a nanohierarchical morphology with excellent liquid repellence. Using polyurethane as a base polymer, the incorporated donor-acceptor self-assembly enables high strength, excellent self-healing property, and strong adhesion strength on multiple substrates. The interaction mechanism of donor-acceptor self-assembly was revealed via density functional theory and infrared spectroscopy. The superhydrophobicity of polyurethane was achieved by introducing alkyl-functionalized MOF nanoparticles and post-application silanization. The combination of the self-healing polymer and nanohierarchical MOF nanoparticles results in self-cleaning capability, resistance to tape peel and high-speed liquid jet impacts, recoverable liquid repellence over a self-healed notch, and low ice adhesion up to 50 icing/deicing cycles. By exploiting the porosity of MOF nanoparticles in our nanocomposites, fluorine-free, slippery liquid-infused porous surfaces with stable, low ice adhesion strengths were also achieved by infusing silicone oil into the coatings

Precision covalent organic frameworks for surface nucleation control

Unwanted accumulation of ice and lime scale crystals on surfaces is a long-standing challenge with major economic and sustainability implications. Passive inhibition of icing and scaling by liquid-repellent surfaces are often inadequate, susceptible to surface failure under harsh conditions, and unsuitable for long-term/real-life usages. Such surfaces often require a multiplicity of additional features such as optical transparency, robust impact resistance, and ability to prevent contamination from low surface energy liquids. Unfortunately, most promising advances have relied on using perfluoro compounds, which are bio-persistent and/or highly toxic. Here it is shown that organic, reticular mesoporous structures, covalent organic frameworks (COFs), may offer a solution. By exploiting simple and scalable synthesis of defect-free COFs and rational post-synthetic functionalization, nanocoatings with precision nanoporosity (morphology) are prepared that can inhibit nucleation at the molecular level without compromising the related contamination prevention and robustness. The results offer a simple strategy to exploit the nanoconfinement effect, which remarkably delays the nucleation of ice and scale formation on surfaces. Ice nucleation is suppressed down to −28 °C, scale formation is avoided for >2 weeks in supersaturated conditions, and jets of organic solvents impacting at Weber numbers >105 are resisted with surfaces that also offer optical transparency (>92%)

Ischemic stroke and concomitant gastrointestinal complications- a fatal combination for patient recovery

Stroke is primarily a neurodegenerative disease but can also severely impact the functions of other vital organs and deteriorate disease outcomes. A malfunction of the gastrointestinal tract (GIT), commonly observed in stroke patients, is often characterized by severe bowel obstruction, intestinal microbiota changes and inflammation. Over-activated immune cells after stroke are the major contributors to endorse intestinal inflammation and may induce damage to single-layer epithelial cell barriers. The post-stroke leakage of intestinal barriers may allow the translocation and dissemination of resident microflora to systemic organs and cause sepsis. This overshooting systemic immune reaction fuels ongoing inflammation in the degenerating brain and slows recovery. Currently, the therapeutic options to treat these GIT-associated anomalies are very limited and further research is required to develop novel treatments. In this mini-review, we first discuss the current knowledge from clinical studies and experimental stroke models that provide strong evidence of the existence of post-stroke GIT complications. Then, we review the literature regarding novel therapeutic approaches that might help to maintain GIT homeostasis and improve neurological outcomes in stroke patients