Existence theorems for boundary value problems in difference equations

In this research, we study linear difference equations with constant coefficients subject to boundary conditions. Necessary and/or sufficient conditions for the existence of a unique solution will be established. The proofs of the existence and uniqueness theorems are established by means of special types of determinants called Mosaic Vandermonde determinants.     

Synthesis of Thio Analogues of Quinolone Antibacterials

A facile and rapid synthesis of thio compounds, analogues to ciprofloxacin, and norfloxacin is described.     

Invariant Pseudolinearity with Applications

In this paper, we introduce the notion of invariant pseudolinearity for nondifferentiable and nonconvex functions by means of Dini directional derivatives. We present some characterizations of invariant pseudolinear functions. Some characterizations of the solution set of a nonconvex and nondifferentiable, but invariant, pseudolinear program are obtained. The results of this paper extend various results for pseudolinear functions, pseudoinvex functions, and η-pseudolinear functions, and also for pseudoinvex programs, pseudolinear programs, and η-pseudolinear programs.     

Acidified,Wet, Silica-Supported Tetrabutylammonium Periodate: A Convenient and Mild Reagent for Conversion of Thioamides to Their Corresponding Amides Under Solvent-Free Conditions

A series of thioamides are transformed to their corresponding oxo analogues in good to excellent yields with acidified, wet, silica-supported tetrabutylammonium periodate under solvent-free conditions.     

Chemoselective Suzuki–Miyaura reactions of 4-trifluoromethylsulfonyloxy-6-bromocoumarin

Suzuki–Miyaura reactions of 4-trifluoromethylsulfonyloxy-6-bromocoumarin provide a convenient access to arylated coumarins. The reactions proceed with excellent chemoselectivity in favour of position 4.     

An Efficient,One-Pot Synthesis of Dialkyl 5-Hydroxy-4-aryl-2,5-dihydrofuran-2,3-dicarboxylate Derivatives

The reaction between arylglyoxalmonohydrates, dialkyl acetylenedicarboxylates, and triphenylphosphine is described as a simple and efficient method for the synthesis of 5-hydroxy-4-aryl-2,5-dihydrofuran-2,3-dicarboxylate derivatives.     

Identification of Compounds that Selectively Stabilize Specific G‐Quadruplex Structures by Using a Thioflavin T‐Displacement Assay as a Tool

Small molecules are used in the G‐quadruplex (G4) research field in vivo and in vitro, and there are increasing demands for ligands that selectively stabilize different G4 structures. Thioflavin T (ThT) emits an enhanced fluorescence signal when binding to G4 structures. Herein, we show that ThT can be competitively displaced by the binding of small molecules to G4 structures and develop a ThT‐displacement high‐throughput screening assay to find novel and selective G4‐binding compounds. We screened approximately 28 000 compounds by using three different G4 structures and identified eight novel G4 binders. Analysis of the structural conformation and stability of the G4 structures in presence of these compounds demonstrated that the four compounds enhance the thermal stabilization of the structures without affecting their structural conformation. In addition, all four compounds also increased the G4‐structure block of DNA synthesis by Taq DNA polymerase. Also, two of these compounds showed selectivity between certain Schizosaccharomyces pombe G4 structures, thus suggesting that these compounds or their analogues can be used as selective tools for G4 DNA studies.