The inverse problem for pencils of differential operators on the half-line with turning points

The inverse spectral problem of recovering pencils of second-order differential operators on the half-line with turning points is studied. We give a formulation of the inverse problem, establish properties of the spectral characteristics, and prove the uniqueness theorem for the solution of the inverse problem. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 5, pp. 237–246, 2006.     

On recovering differential systems on a finite interval from spectra

Inverse spectral problems are studied for non-self-adjoint systems of ordinary differential equations on a finite interval. We establish properties of spectral characteristics and provide a procedure for constructing the solution of the inverse problem of recovering the coefficients of differential systems from given spectra. Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Vol. 255, pp. 273–287.     

A priori method of evaluating uncertainties in qualitative chromatographic analysis: probabilistic approach

Probabilistic algorithms to evaluate result reliability in qualitative chromatographic analysis are discussed in the paper. The elementary uncertainty (P₀), concerned with a single test (comparison of sample and reference peak positions), is treated as the sum of misidentification and omission probabilities. Both constituents are calculated separately using the simplified model and Laplace functions. In the model, the main reasons for elementary uncertainties are random normally distributed deviations during retention characteristic measurement. Algorithms to calculate both constituents of P₀ have to take into account real measurement precision, supposed composition of the sample, content of the database, chosen coincidence criterion and other factors. At a high selectivity of retention, the 3 value is recommended as the most convenient coincidence criterion. It leads to more reliable and unambiguous attribution of peaks in the chromatogram. For cases that are more complicated, the probabilistic algorithms based upon Bernoulli theorem are proposed to calculate the summary uncertainty of identification, concerned with the multiple test. They take into account P₀ value, the number of repeated single tests (n) in the similar or different conditions, and chosen identification criterion K (minimal number of coincidences). The above-mentioned algorithms lead to a priori optimisation of the mode of operation of any identification software system associated with the chromatograph. They can be useful during a metrological validation of corresponding qualitative analysis methods.Presented at the Second International Conference on Metrology—Trends and Applications in Calibration and Testing Laboratories, November 4–6, 2003, Eilat, Israel.The opinions reflected in this paper are those of the author only. AQUAL does not necessarily endorse them.     

Nonlinear dielectric properties of planar structures based on ferroelectric betaine phosphite films

Ferroelectric films of partly deuterated betaine phosphite are grown on NdGaO₃(001) substrates with an interdigitated system of electrodes on their surfaces by evaporation at room temperature. These films have a high capacitance in the ferroelectric phase transition range. The dielectric nonlinearity of the grown structures is studied in small-signal and strong-signal response modes and in the intermediate region between these two modes by measuring the capacitance in a dc bias field, dielectric hysteresis loops, and the Fourier spectra of an output signal in the Sawyer-Tower circuit. In the phase transition range, the capacitance control ratio at a bias voltage U _bias = 40 V is K ? 7. The dielectric nonlinearity of the structures in the paraelectric phase is described by the Landau theory of second-order phase transitions. The additional contribution to the nonlinearity in the ferroelectric phase is related to the motion of domain walls and manifests itself when the input signal amplitude is higher than U _st ～ 0.7–1.0 V. The relaxation times of domain walls are determined from an analysis of the frequency dependences of the dielectric hysteresis.     

Catalytic Hydrosilylation of Substituted Acetophenones by 1,1,3,3-Tetrametyldisiloxane with Complexes Rhodium (I) and Platinum (II)

The hydrosilylation of a range of para-substituted acetophenones XC₆H₄COCH₃ (X = H, Me, MeO, F, Cl, NO₂) with 1,1,3,3-tetramethyl disiloxane mediated by complexes of rhodium (I) and platinum (II) was investigated. The complexes of platinum (II) are less effective than complexes of rhodium (I), but display greater selectivity. Six 1-(1′-arylethoxy)-1,1,3,3-tetramethyl disiloxanes have been synthesized by hydrosilylation using several coupling catalysts.     

An inverse problem for operators of a triangular structure

An inverse problem for operators of a triangular structure is studied. An algorithm for the solution and necessary and sufficient conditions for the solvability of this problem are obtained, moreover uniqueness is proved. Applications to difference and differential operators are considered.     

Inverse Problem for Quasi-Periodic Differential Pencils with Jump Conditions Inside the Interval

Non-self-adjoint second-order differential pencils on a finite interval with non-separated quasi-periodic boundary conditions and jump conditions are studied. We establish properties of spectral characteristics and investigate the inverse spectral problem of recovering the operator from its spectral data. For this inverse problem we prove the corresponding uniqueness theorem and provide an algorithm for constructing its solution.     

Molecular structure and conformations of para-methylbenzene sulfonamide and ortho-methylbenzene sulfonamide: gas electron diffraction and quantum chemical calculations study

The molecular structure and conformational properties of para-methylbenzene sulfonamide (4-MBSA) and ortho-methylbenzene sulfonamide (2-MBSA) have been studied by gas electron diffraction (GED) and quantum chemical methods (B3LYP/6-311+G** and MP2/6-31G**). Quantum chemical calculations predict the existence of two conformers for 4-MBSA with the S-N bond perpendicular to the benzene plane and the NH2 group either eclipsing or staggering the S-O bonds of the SO2 group. Both conformers possess CS symmetry. The eclipsed form is predicted to be favored by DeltaE = 0.63 kcal/mol (B3LYP) or 1.00 kcal/mol (MP2). According to the calculations, the S-N bond in 2-MBSA can possess planar direction opposite the methyl group (phi(C2C1SN) = 180 degrees ) or nonplanar direction (phi(C2C1SN) approximately 60 degrees ). In both cases, the NH2 group can adopt eclipsed or staggered orientation, resulting in a total of four stable conformers. The nonplanar eclipsed conformer (C1 symmetry) and the planar eclipsed form (CS symmetry) are predicted to be favored. According to the GED analysis, the saturated vapor over solid 4-MBSA at T = 151(3) degrees C consists as mixture of the eclipsed (78(19) %) and staggered (22(19) %) forms. The saturated vapor over solid 2-MBSA at T = 157(3) degrees C consists as a mixture of the nonplanar eclipsed (69(11) %) and planar eclipsed (31(11) %) forms.     

Inverse spectral problems for differential pencils with boundary conditions dependent on the spectral parameter

In this paper, we discuss two inverse problems for differential pencils with boundary conditions dependent on the spectral parameter. We will prove the Hochstadt–Lieberman type theorem of 1 – 3 except for arbitrary one eigenvalue and the Borg type theorem of 1 – 3 except for at most arbitrary two eigenvalues, respectively. The new results are generalizations of the related results. Copyright © 2016 John Wiley & Sons, Ltd.