A local saddle point theorem and an application to a nonlocal PDE

We prove a local saddle point theorem that can be viewed as a generalization of the saddle point theorem of Rabinowitz. A difficulty to overcome is that there isn’t any linking. We then apply the theorem to show the existence of solutions of a nonlocal partial differential equations.     

A splitting algorithm for the wavelet transform of cubic splines on a nonuniform grid

For cubic splines with nonuniform nodes, splitting with respect to the even and odd nodes is used to obtain a wavelet expansion algorithm in the form of the solution to a three-diagonal system of linear algebraic equations for the coefficients. Computations by hand are used to investigate the application of this algorithm for numerical differentiation. The results are illustrated by solving a prediction problem.     

Changes in luminescence of semiconductor colloidal quantum dots CdSe@CdS by replacement of hydrophobic ligands with 1-thioglycerol

Luminescent properties of CdSe@CdS colloidal quantum dots upon replacement of hydrophobic stabilizing ligands with water-soluble 1-thioglycerol have been studied. The data obtained have made it possible to optimize the ligand replacement procedure and significantly decrease the loss of the fluorescence quantum yield of the resulting hydrophilic quantum dots.     

Experimental study of gasification of vacuum residue in metal melt by alternating reactor feeding with carbonaceous feedstock and oxidant

Processes occurring in a metal melt during plasma-assisted melt gasification of carbonaceous feedstock have been studied in the mode of alternating feeding the reactor with the carbonaceous feedstock and oxidant. Vacuum residue was used as an oxygen-free carbonaceous material, and air and steam were used as an oxidant. The results of the study show that by alternating the carbonaceous-feedstock pyrolysis step and the step of carbon oxidation in the metal melt, it is possible to produce synthesis gas with any desired H₂/CO ratio.     

Phase equilibria in the Cu–Cu<Subscript>2</Subscript>Se–As system

Phase equilibria in the Cu–Cu₂Se–As were investigated by differential thermal analysis and X-ray powder diffraction analysis. Informative plots describing this system were constructed, viz., the polythermal sections Cu_0.667Se_0.333–As, Cu_0.667Se_0.333–Cu_0.735As_0.265, and Cu_0.8Se_0.2–As, the isothermal section of the phase diagram at 300 K, and the projection of the liquidus surface. The obtained results differ from the published data in length of fields of primary crystallization of phases and in coordinates of a number of invariant equilibrium points.     

Theoretical and experimental study of the transformation of 2-pyridone-5-amide into nitrile

Molecular and crystal structures of 2,4-dimethyl-6-oxo-1,6-dihydropyridine-3-carboxamide (1), 2,4-dimethyl-6-oxo-1,6-dihydropyridine-3-carbonitrile (2), and 2-chloro-4,6-dimethylniсotinonitrile (3), which are the products of sequential transformations, are studied by means of single crystal diffraction. The procedure for synthesizing each compound is described. All of the compounds are characterized using IR and ¹H NMR spectra. Possible reaction pathways are simulated using the density functional theory (DFT).     

Sequential reactions from catalytic hydroformylation toward the synthesis of amino compounds

Different families of new amino compounds were efficiently synthesized, through optimized sequential processes, involving rhodium catalyzed hydroformylation as the key step. The selection of appropriate hydroformylation catalytic systems and reaction conditions allowed obtaining aldehydes derived from several n-alkyl olefins, cholest-4-ene and 3-vinyl-1H-indole, which were subsequently transformed, in one-pot, in to α-amino acids via hydroformylation/Strecker reaction, and in to tertiary amines via hydroaminomethylation, with excellent yields.     

Two crystalline polymorphic forms of α-(<Emphasis Type="Italic">N</Emphasis>-benzoxazolin-2-one)acetic acid

Two crystalline polymorphic forms of α-(N-benzoxazolin-2-one)acetic acid (BAA) are prepared by changing the temperature of its crystallization from solution in ethanol. Crystallographic data of the α-form are determined: a = 12.7769(17) Å, b = 8.2574(9) Å, c = 16.7390(19) Å, β = 105.087(13)°, space group C2/c, V = 1705.2(4) ų, and Z = 8, while those of β form are a = 5.2854(4) Å, b = 5.9880(4) Å, c = 13.4509(5) Å, β = 94.666(4)°, space group P2₁, V = 424.30(4) ų, and Z = 2. It is found that BAA molecules of the α form combine into infinite one-dimensional chains arranged along axis b by means of O?H···O and C?H···O hydrogen bonds, and these chains are crosslinked via C?H···O hydrogen bonds to form a threedimensional structure. The β form has another system of hydrogen bonds, one of which is bifurcated (O4···O2, O4···O3), and the π–π-interactions between the benzoxazolinone fragments of BAA molecules combined into a chain also arranged along axis b are observed. Calorimetric analysis shows that the polymorphic transition from the α form to the β form occurs at 129°C.     

Verbenanone,an octahydro-5H-chromen-5-one from a Hawaiian-plant associated fungus FT431

Verbenanone (1), a new secondary metabolite with a unique (4aS,8aS)-octahydro-5H-chromen-5-one moiety has been obtained from the endophytic fungus FT431, which was isolated from the native Hawaiian plant Verbena sp. The structure of compound 1 was characterized based on NMR and MS spectroscopic analysis. The absolute configuration (AC) of compound 1 was determined by Mosher acids. Compound 1 was tested against A2780 and A2780cisR, but it was inactive.