Oscillation of nonlinear neutral delay differential Equations

In this paper, we study the oscillatory behavior of first order nonlinear neutral delay differential equations. Several new sufficient conditions which ensure that all solutions are oscillatory are given. The obtained results extend and improve several known results in the literature. Some examples are considered to illustrate the main results.     

Synthesis of bridged aza-rebeccamycin analogues

The syntheses of rebeccamycin analogues possessing a 7-azaindole moiety instead of an indole unit, and with both indole and azaindole moieties linked to the carbohydrate are described. In these bridged aza compounds, the oxygen of the pyranose heterocycle is oriented towards either the indole, or the azaindole unit. In these series, compounds bearing a free imide nitrogen were synthesized by coupling the corresponding aglycones with a sugar pre-tosylated in 2-position via a Mitsunobu reaction. To obtain a precursor for bridged aza-rebeccamycin analogues substituted in 6-position on the sugar moiety, a 2,6-ditosylated sugar was used.     

Investigation of indirubin derivatives: a combination of 3D-QSAR,molecular docking,and ADMET towards the design of new DRAK2 inhibitors

Kinase-related apoptosis-inducing kinase 2 (DRAK2) is a serine/threonine kinase and belongs to the death-associated protein kinase DPAK family, which is responsible for induction of apoptosis in many cell types. Thus, DRAK2 is regarded as a promising target for treatment of autoimmune diseases. To investigate the binding between DRAK2 and indirubin inhibitors and design potent inhibitors, a three-dimensional quantitative structure-activity relationship (3D-QSAR) and molecular docking were performed. Comparative Molecular Similarity Indices Analysis (CoMSIA) was developed using 33 molecules having pIC₅₀ ranging from 8.523 to 5.000 (IC₅₀ in nM). The best CoMSIA model gave a significant coefficient of determination (R²?=?0.93), as well as a (leave-one-out cross-validation coefficient Q² of 0.81. The predictive ability of this model was evaluated by external validation using a test set of eight compounds and yielded a predicted coefficient of determination R²_test of 0.94. The contour maps could provide structural features to improve inhibitory activity. Good consistency between contour maps and molecular docking strongly suggests that the molecular modeling is reliable. Based on these satisfactory results, we designed several new DRAK2 inhibitors and their inhibitory activities were predicted using different models, which are developed on different training and test sets. Additionally, these newly designed inhibitors showed promising results in the preliminary in silico ADMET evaluations compared to the best inhibitor from the studied dataset. This study could be useful in lead identification and optimization for early drug discovery of DRAK2 inhibitors.     

Furanone derivatives as new inhibitors of CDC7 kinase: development of structure activity relationship model using 3D QSAR,molecular docking,and in silico ADMET

Cell division cycle 7 (CDC7) is a serine/threonine kinase, which plays a vital role in the replication initiation of DNA synthesis. Overexpression of the CDC7 in various tumor growths and in cell proliferation makes it a promising target for treatment of cancers. To investigate the binding between the CDC7 and furanone inhibitors, and in order to design highly potent inhibitors, a three-dimensional quantitative structure activity relationship (3D-QSAR) with molecular docking was performed. The optimum CoMSIA model showed significant statistical quality on all validation methods with a determination coefficient (R²?=?0.945), bootstrapping R² mean (BS-R²?=?0.960), and leave-one-out cross-validation (Q²) coefficient of 0.545. The predictability of this model was evaluated by external validation using a test set of nine compounds with a predicted determination coefficient R²_test of 0.96, besides the mean absolute error (MAE) of the test set was 0.258 log units. The extracted contour maps were used to identify the important regions, where the modification was necessary to design a new molecule with improved activity. Furthermore, a good consistency between the molecular docking and contour maps strongly demonstrates that the molecular modeling is reliable. Based on those obtained results, we designed several new potent CDC7 inhibitors, and their inhibitory activities were validated by the molecular models. Additionally, those newly designed inhibitors showed promising results in the preliminary in silico ADMET evaluations.     

Quaternary Germanides RE3TRh4Ge4 (RE = Ce,Pr, Nd; T = Nb,Ta) – A New Coloring Variant of the Aristotype AlB2

The quaternary germanides RE₃TRh₄Ge₄ (RE = Ce, Pr, Nd; T = Nb, Ta) were synthesized from the elements by arc‐melting and subsequent annealing in a muffle furnace. The structure of Ce₃TaRh₄Ge₄ was refined from single‐crystal X‐ray diffractometer data: new type, Pbam, a = 719.9(2), b = 1495.0(3), c = 431.61(8), wR₂ = 0.0678, 1004 F² values, and 40 variables. Isotypy of the remaining phases was evident from X‐ray powder patterns. Ce₃TaRh₄Ge₄ is a new superstructure variant of the aristotype AlB₂ with an ordering of cerium and tantalum on the aluminum site, whereas the honey‐comb network is built up by a 1:1 ordering of rhodium and germanium. This crystal‐chemical relationship is discussed based on a group‐subgroup scheme. The distinctly different size of tantalum and cerium leads to a pronounced puckering of the [Rh₄Ge₄] network, which shows the shortest interatomic distances (253–271 pm Rh–Ge) within the Ce₃TaRh₄Ge₄ structure. Another remarkable structural feature concerns the tantalum coordination with six shorter Ta–Rh bonds (265–266 pm) and six longer Ta–Ge bonds (294–295 pm). The [Rh₄Ge₄] network fully separates the tantalum and cerium atoms (Ce–Ce > 387 pm, Ta–Ta > 431 pm, and Ce–Ta > 359 pm). The electronic density of states DOS from DFT calculations show metallic behavior with large contributions of localized Ce 4f as well as itinerant ones from all constituents at the Fermi level but no significant magnetic polarization on Ce could be identified. The bonding characteristics described based on overlap populations illustrate further the crystal chemistry observations of the different coordination of Ce1 and Ce2 in Ce₃TaRh₄Ge₄. The Rh–Ge interactions within the network are highlighted as dominant. The bonding magnitudes follow the interatomic distances and identify differences of Ta bonding vs. Ce1/Ce2 bonding with the Rh and Ge substructures.     

A Bifunctional Electrocatalyst for Oxygen Evolution and Oxygen Reduction Reactions in Water

Oxygen reduction and water oxidation are two key processes in fuel cell applications. The oxidation of water to dioxygen is a 4 H⁺/4 e^? process, while oxygen can be fully reduced to water by a 4 e^?/4 H⁺ process or partially reduced by fewer electrons to reactive oxygen species such as H₂O₂ and O₂^?. We demonstrate that a novel manganese corrole complex behaves as a bifunctional catalyst for both the electrocatalytic generation of dioxygen as well as the reduction of dioxygen in aqueous media. Furthermore, our combined kinetic, spectroscopic, and electrochemical study of manganese corroles adsorbed on different electrode materials (down to a submolecular level) reveals mechanistic details of the oxygen evolution and reduction processes.     

A Novel Fluorimetric Bulk Optode Membrane Based on NOS Tridentate Schiff Base for Selective Optical Sensing of Al<Superscript>3+</Superscript> Ions

A novel fluorimetric optode has been developed for the highly selective and sensitive for the determination of ultra trace amounts of Al³⁺ ions. The proposed fluorescent optode is based on the incorporation of a simple and effective fluorescent sensor tridentate NOS Schiff base N-(2-hydroxynaphthylidene)-2-aminothiophenol (H₂L) in a plasticized PVC containing KTpClPB as a lipophilic anionic additive. H₂L was synthesized by a facile one-step Schiff base reaction. The plasticized PVC-membrane displays a calibration response for Al³⁺ ions over a wide concentration range from 1.0 × 10^?9 to 4.4 × 10^?3 mol/L. The fluorescence signal of the optode membrane can be easily recovered by immersion in 0.01 M EDTA. In addition to high stability and reproducibility, the sensor shows a unique selectivity towards Al³⁺ ion with respect to common co-existing cations, particularly Ga³⁺and In³⁺. The proposed optode was applied successfully for determination of Al³⁺ in some real samples, including bottled drinking waters, bottled mineral waters and soft drinks.     

Nonsmooth Lur’e Dynamical Systems in Hilbert Spaces

In this paper, we study the well-posedness and stability analysis of set-valued Lur’e dynamical systems in infinite-dimensional Hilbert spaces. The existence and uniqueness results are established under the so-called passivity condition. Our approach uses a regularization procedure for the term involving the maximal monotone operator. The Lyapunov stability as well as the invariance properties are considered in detail. In addition, we give some sufficient conditions ensuring the robust stability of the system in finite-dimensional spaces. The theoretical developments are illustrated by means of two examples dealing with nonregular electrical circuits and an other one in partial differential equations. Our methodology is based on tools from set-valued and variational analysis.     

Synthesis,Docking, and Evaluation of Antimicrobial Activity of a New Series of Acyclo C‐Nucleosides of 1, 2, 4‐Triazolo[4, 3‐a]quinoxaline Derivatives

In this study, 18 new 3‐benzylquinoxalinyl hydrazones bearing carbohydrate moiety and their corresponding triazoloquinoxalines were synthesized in order to investigate their possible antibacterial and antifungal activities. Some of these compounds such as 4b , 4c , 7b , 7c , and 7d showed promising antibacterial and antifungal activities and were found to have more potent activity compared with that of standard drugs. From structure–activity relationship point of view, increasing the size of the substitutions at position 6 or 7 on the quinoxaline nucleus decreased the antimicrobial activity, while the presence of the hydroxyl groups at C2 (R) and C3 (S) of sugar moieties enhanced the activity. Further, molecular docking studies of the active compounds were performed on different targets belonging to different microorganisms and showed good scoring with further understanding of the various interactions with the active sites of interesting enzymes compared with the co‐crystallized ligands.     

Synthesis,Anti‐Microbial,and Cytotoxic Activities Evaluation of Some New Pyrido[2,3‐d]Pyrimidines

Novel pyridine derivatives 1d and 7 , pyrido[2,3‐d]pyrimidine derivatives 2a , 2b , 2c , 2d , 3a , 3b , 3c , 3d , 4a , 4b , 4c , 4d , 5a , 5b , 5c , 5d , 6a , 6b , 6c , 6d , 8a , 8b , and 9a , 9b were synthesized and screened for their anti‐microbial and cytotoxic activities. Compounds 2b , 2c , 3b , 3c , 5b , 5c , 6b , 6c , and 7 showed excellent anti‐microbial activities against all the tested bacteria and fungi compared to the reference drugs. Furthermore, they exhibited high safety profile in cytotoxicity test except 2c and 3c . The structures of the newly synthesized compounds were confirmed by spectral data and elemental analysis.