On the relation between interior critical points and parameters for a class of nonlinear problems with Neumann–Robin boundary conditions

We consider boundary value problem

where   0, λ > 0 are parameters and f  C²[0, ∞) such that f(0) < 0. In this paper we study for the cases p  (0, β) and p  (β, θ) (p is the value of the solution at x = 0 and β, θ are such that f(β) = 0, , the relation between λ and the number of interior critical points of the positive solutions of the above system.     

An efficient and facile one-step synthesis of highly substituted thiophenes

An efficient one-step method for the synthesis of fully substituted thiophenes, from thiomorpholides and α-halo ketones, was developed. A mechanism has also been proposed for the course of reaction.     

1,6-Eliminationsreaktionen an Spirocoleonon; Charakterisierung der ersten Spiro[(methylcyclopropan)-phenanthren]-1,3-dion-Derivate

Preparation of the First Spiro[(methylcyclopropan)-phenanthrene]-1,3-dione Derivatives by 1,6-Elimination Reactions of Spirocoleons Spirocoleons, e.g. coleon J ( 1 ), on treatment with 1,5-diazabicyclo[4.3.0]non-5-ene (DBN) in aprotic solvents, undergo enolization followed by a rapid 1,6-elimination with formation of the hitherto unknown 2-methyl-spiro[cyclopropane-1,2′(1′H)-phenanthrene]-1′,3′(4′bH)-dione system, e.g. 3 . In protic solvents, base-catalyzed solvolysis of the spirocyclopropane predominates.     

Synthesis of 1-(4-methylsulfone-phenyl)-5-(4-fluoro-phenyl)-5-[14C]-1,2,3-triazole and 1-(4-sulfonamide-phenyl)-5-(4-fluoro-phenyl)-5-[14C]-1,2,3-triazole as novel carbon-14 anticonvulsant

Summary Two 1,2,3-triazole anticonvulsants, 1-(4-methylsulfone-phenyl)-5-(4-fluoro-phenyl)-5-[¹⁴C]-1,2,3-triazole and 1-(4-sulfonamide-phenyl)-5-(4-fluoro-phenyl)-5-[¹⁴C]-1,2,3-triazole, both labeled with carbon-14 in the 5-position were prepared from para-fluoro-benzonitrile-[cyano-¹⁴C].     

Functional monomers and polymers 159 synthesis and photochemical reactions of polymers containing thymine photodimer units in the main chain

Polyamides containing thymine photodimer units in the main chain were synthesized, and their photolysis by ultraviolet irradiation below 260 nm were studied in film state. Photodimers of thymine derivatives were obtained by photochemical reaction of the carboxylic acid derivatives of thymine in aqueous solution irradiated above 270 nm. An attempt was made to resolve the isomers of the photodimers, and the two kinds of cis isomers [cis–syn(head to head), and cis–anti(head to tail)] were isolated successfully. The polyamides were prepared by condensation of the photodimers with diamine using an activated ester method. The photodissociation of the thymine photodimer in the polymer main chain caused the breakage of the polymer chains, leading to the production of oligomers and dimer compounds containing thymine bases at the ends of the molecule. The dissociation rate of the polymer did not depend on the kind of the thymine photodimer which was in the main chain of the polymer.     

Facile synthesis of highly substituted 2-pyrone derivatives via a tandem Knoevenagel condensation/lactonization reaction of β-formyl-esters and 1,3-cyclohexadiones

A mild and efficient tandem process for the synthesis of new highly substituted 2-pyrones starting from commercially available 2-arylacetic acids has been developed. The synthesis is based on the Knoevenagel condensation of 1,3-cyclohexadiones with various β-formyl-esters, followed by lactonization in the presence of nano ZnO (20 mol %). Moderate to high yields and readily available cheap starting materials are the key features of the present method.     

Suzuki–Miyaura coupling reaction in water in the presence of robust palladium immobilized on modified magnetic Fe3O4 nanoparticles as a recoverable catalyst

Aryl halides and especially inactive aryl chlorides were coupled to benzenoid aromatic rings in a Suzuki–Miyaura coupling reaction in the absence of organic solvents and toxic phosphine ligands. The reaction was catalysed by a recoverable magnetic nanocatalyst, Pd@Fe₃O₄, in aqueous media. This method is green, and the catalyst is easily removed from the reaction media using an external magnetic field and can be re‐used at least 10 times without any considerable loss in its activity. The catalyst was characterized using scanning and transmission electron microscopies, thermogravimetric analysis, inductively coupled plasma spectroscopy, Fourier transform infrared spectroscopy, CHN analysis, X‐ray diffraction and vibrating sample magnetometry.     

Efficient Synthesis of Bicyclo[3.3.1]nonane Systems via Tandem 1,3-Dinucleophilic Addition of 4-Hydroxy-2-quinolinones to Quinolinium Salts

The synthesis of bicyclo[3.3.1]nonane systems is reported. The synthesis is based on the tandem 1,3-dinucleophilic addition of 4-hydroxy-2-quinolinone to quinolinium salts.