Is it possible to determine the type of fastening of a vibrating plate from its sounding?

The problem of determining the type of fastening of a circular plate inaccessible to direct observation from the natural frequencies of its symmetric flexural vibrations is considered. The uniqueness theorem for the solution to this inverse problem is proved, and a method for the reconstruction of unknown boundary conditions is indicated. An approximate formula for the determination of unknown boundary conditions from three natural frequencies is obtained. It is assumed that the natural frequencies can be given approximately, within a certain accuracy. The method of an approximate calculation of unknown boundary conditions is illustrated by four examples of different cases of the plate fastening (a free support, an elastic fixing, a floating fixing, and a free edge).     

Stereoselective synthesis of unnatural α-amino acid derivatives through photoredox catalysis

A protocol for stereoselective C-radical addition to a chiral glyoxylate-derived N-sulfinyl imine was developed through visible light-promoted photoredox catalysis, providing a convenient method for the synthesis of unnatural α-amino acids. The developed protocol allows the use of ubiquitous carboxylic acids as radical precursors without prior derivatization. The protocol utilizes near-stoichiometric amounts of the imine and the acid radical precursor in combination with a catalytic amount of an organic acridinium-based photocatalyst. Alternative mechanisms for the developed transformation are discussed and corroborated by experimental and computational studies.

A protocol for stereoselective C-radical addition to a chiral glyoxylate-derived N-sulfinyl imine was developed through visible light-promoted photoredox catalysis, providing a convenient method for the synthesis of unnatural α-amino acids.     

Uniqueness of reconstruction of the Sturm–Liouville problem with spectral polynomials in nonseparated boundary conditions

Uniqueness theorems for solutions of inverse Sturm–Liouville problems with spectral polynomials in nonseparated boundary conditions are proved. As spectral data two spectra and finitely many eigenvalues of the direct problem or, in the case of a symmetric potential, one spectrum and finitely many eigenvalues are used. The obtained results generalize the Levinson uniqueness theorem to the case of nonseparated boundary conditions containing polynomials in the spectral parameter.     

Calculation of the coefficients of expansions in derivative chains of a spectral problem

Translated from Matematicheskie Zametki, Vol. 51, No. 6, pp. 137–139, June, 1992.     

A novel approach to the quantification of urinary aryl-propionamide-derived SARMs by UHPLC–MS/MS

A simple and sensitive procedure for the quantification of two commonly abused aryl-propionamide-derived selective androgen receptor modulators (SARMs), namely S-4 (GTx-007, andarine) and S-22 (GTx-024, MK-2866, ostarine, enobosarm), has been described. Urine samples were prepared for analysis by means of a dispersive liquid–liquid microextraction using methanol and chloroform as dispersive and extracting solvents, respectively. Factors that might influence the extraction process as well as their optimum conditions were evaluated by Box–Benken and central composite designs. After extraction, the analytes were quantified by UHPLC–MS/MS. The proposed procedure was validated on human urine samples. As a result, for both SARMs the detection limits were observed at 0.05 ng/mL and calibration curves were linear in the concentration range of 0.25–50 ng/mL with the coefficient of determination of 0.998.     

Uniqueness of Reconstruction of an nth-Order Differential Operator with Nonseparated Boundary Conditions by Several Spectra

Doklady Mathematics - A uniqueness theorem for reconstruction of an nth-order differential operator with nonseparated boundary conditions from several spectra is proved. This theorem is based on...     

气相色谱法探究聚醚醚酮的热降解及热氧化降解（英文）

Poly(ether ether ketone)(PEEK)was synthesized via polycondensation of hydroquinone with 4,4′-difluorobenzophenone at 320℃for 5 h.Thermal and thermo-oxidative degradation of PEEK was studied over a wide range of temperatures.In an inert medium,decomposition of the polymer occurred in one stage,with the formation of a coke residue accounting for approximately 50%of the original polymer mass.In air,the mass loss curve exhibited two distinct stages.The first stage involved breakdown of the main polymer chain,the speed of which indicated a radical chain failure mechanism.In the second stage,the rate of mass loss clearly decreased,indicating a transition from the radical chain failure mechanism to simple combustion reactions(wherein the polymer combusted completely).To further investigate the nature of the processes occurring during the pyrolysis of PEEK,the investigations were carried out using gas chromatograph under isothermal conditions.It was concluded that during thermal degradation,the decomposition of the polymer starts with the rupture of ketone and ether bonds and proceeds to destruction of the benzene ring at higher temperatures,which is accompanied by the formation of H2O and CH4.Above 500℃,the polymer degradation further involved thermohydrolysis.The thermo-oxidation of PEEK,which was accompanied mainly by the formation ofH2,was noticeable beginning at 325℃.The total yield of the latter indicated oxidation of fragments of the benzene ring.     

Fluorine-functionalized nanoporous graphene as an effective membrane for water desalination

Most water in the world is as saline water in seas and oceans. Desalination technology is a promising method to solve the global water crisis. Recently, many attentions have been paid to the graphene-based membranes in water desalination due to their low production cost and high efficiency. In this paper, molecular dynamics simulations are employed to investigate the effect of functionalized graphene nanosheet (GNS) membranes on the performance of salt separation from seawater in terms of water permeability and salt rejection. For this purpose, the hydrogenated (–H) and fluorinated (–F) pores were created on the GNS membrane. Then, the functionalized graphene membrane was placed in the middle of the simulation box in an aqueous ionic solution containing Na⁺ and Cl^? ions. The applied pressure (in the range of 10–100 MPa) was used as the driving force for transport of water molecules across the reverse osmosis (RO) graphene-based membrane in order to obtain the water permeability and salt rejection. Also, radial distribution functions (RDFs) of ion–water and water–water as well as the water density map around the membrane were obtained. The results indicated that the hydrophilic chemical functions such as fluorine (–F) can improve the water permeability at low pressures.

     

On degenerate boundary conditions in the Sturm–Liouville problem

We describe all degenerate boundary conditions in the homogeneous Sturm–Liouville problem.