Measurements and calculations of H2-broadening and shift parameters of water vapour transitions of the ν1 + ν2 + ν3 band

The water vapour line broadening and shifting for 97 lines in the ν₁ + ν₂ + ν₃ band induced by hydrogen pressure are measured with Bruker IFS 125 HR FTIR spectrometer. The measurements were performed at room temperature, at the spectral resolution of 0.01 cm^?1 and in a wide pressure range of H₂. The calculations of the broadening γ and shift δ coefficients were performed in the semi-classical method framework with use of an effective vibrationally depended interaction potential. Two potential parameters were optimised to improve the quality of calculations. Good agreements with measured broadening coefficients were achieved. The comparison of calculated broadening coefficients γ with the previous measurements is discussed. The analytical expressions that reproduce these coefficients for rotational, ν₂, ν₁, and ν₃ vibrational bands are presented.     

Semismooth Newton method for the lifted reformulation of mathematical programs with?complementarity constraints

We consider a reformulation of mathematical programs with complementarity constraints, where by introducing an artificial variable the constraints are converted into equalities which are once but not twice differentiable. We show that the Lagrange optimality system of such a reformulation is semismooth and BD-regular at the solution under reasonable assumptions. Thus, fast local convergence can be obtained by applying the semismooth Newton method. Moreover, it turns out that the squared residual of the Lagrange system is continuously differentiable (even though the system itself is not), which opens the way for a natural globalization of the local algorithm. Preliminary numerical results are also reported.     

Some Methods Based on the D-Gap Function for Solving Monotone Variational Inequalities

The D-gap function has been useful in developing unconstrained descent methods for solving strongly monotone variational inequality problems. We show that the D-gap function has certain properties that are useful also for monotone variational inequality problems with bounded feasible set. Accordingly, we develop two unconstrained methods based on them that are similar in spirit to a feasible method of Zhu and Marcotte based on the regularized-gap function. We further discuss a third method based on applying the D-gap function to a regularized problem. Preliminary numerical experience is also reported.     

Exact Constants in Telyakovskii’s Two-Sided Estimate of the Sum of a Sine Series with Convex Sequence of Coefficients

Mathematical Notes - It is known that the sum of the sine series $$g\left( {{\rm{b,}}\,x} \right) = \sum\nolimits_{k = 1}^\infty {{b_k}} $$bk sin kx whose coefficients constitute a convex sequence...     

Optimal Two-Sided Estimates on the Interval $$[\pi/2,\pi]$$ of the Sum of the Sine Series with Convex Coefficient Sequence

Mathematical Notes -     

Exact lower estimate of the upper limit of the ratio of the sum of sine series with monotone coefficients to its majorant

An unimprovable lower estimate of the upper limit of the ratio of the sum of sine series with monotone coefficients to its majorant is obtained.     

Measurements of N2-broadening and -shifting parameters of the water vapor spectral lines in the second hexad region

The water vapor line broadening and shifting in the ν₁+ν₂+ν₃ band induced by nitrogen pressure are measured with Bruker IFS 125 HR FTIR spectrometer at the spectral resolution of 0.01 cm⁻¹ for the line with upper states angular momentum up to 11. Line contour parameters are calculated using a semi-empirical approach extended by the use of empirical data to determine some fitting model parameters. We use the complete set of high accuracy vibration-rotation dipole transition moments calculated for all possible transitions using wavefunctions determined from variational nuclear motion calculations and an ab initio dipole moment surface. Calculated values of line contour parameters are in a good agreement with observed parameters.     

High-resolution spectroscopy and preliminary global analysis of C-H stretching vibrations of C2H4 in the 3000 and 6000 cm regions

Ethylene (ethene, H₂C=CH₂) is a naturally occurring compound in ambient air that affects atmospheric chemistry and global climate. The C₂H₄ spectrum is available in databases only for the 1000 and 3000 cm⁻¹ ranges.In this work, the ethylene absorption spectrum was measured in the 6030-6250 cm⁻¹ range with the use of a high resolution Bruker IFS 125HR Fourier-spectrometer and a two-channel opto-acoustic spectrometer with a diode laser. As a secondary standard of wavelengths, the methane absorption spectrum was used in both cases.A preliminary analysis was realized thanks to the tensorial formalism developed by the Dijon group that is implemented in the XTDS software package [39]. We considered the two combination bands ν₅+ν₉ and ν₅+ν₁₁ as an interacting dyad. Parameters for the ν₉/ν₁₁ dyad were fitted simultaneously from a re-analysis of previously recorded supersonic expansion jet FTIR data, while parameters for the v₅=1 Raman level were taken from literature. More than 600 lines could be assigned in the 6030-6250 cm⁻¹ region (and also 682 in the 2950-3150 cm⁻¹ region) and effective Hamiltonian parameters were fitted, including Coriolis interaction parameters. The dyad features are globally quite well reproduced, even if there are still problems at high J values.     

Inexact Josephy–Newton framework for generalized equations and its applications to local analysis of Newtonian methods for constrained optimization

We propose and analyze a perturbed version of the classical Josephy–Newton method for solving generalized equations. This perturbed framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilized version, sequential quadratically constrained quadratic programming, and linearly constrained Lagrangian methods. For the linearly constrained Lagrangian methods, in particular, we obtain superlinear convergence under the second-order sufficient optimality condition and the strict Mangasarian–Fromovitz constraint qualification, while previous results in the literature assume (in addition to second-order sufficiency) the stronger linear independence constraint qualification as well as the strict complementarity condition. For the sequential quadratically constrained quadratic programming methods, we prove primal-dual superlinear/quadratic convergence under the same assumptions as above, which also gives a new result.     

Error Stability Properties of Generalized Gradient-Type Algorithms

We present a unified framework for convergence analysis of generalized subgradient-type algorithms in the presence of perturbations. A principal novel feature of our analysis is that perturbations need not tend to zero in the limit. It is established that the iterates of the algorithms are attracted, in a certain sense, to an -stationary set of the problem, where depends on the magnitude of perturbations. Characterization of the attraction sets is given in the general (nonsmooth and nonconvex) case. The results are further strengthened for convex, weakly sharp, and strongly convex problems. Our analysis extends and unifies previously known results on convergence and stability properties of gradient and subgradient methods, including their incremental, parallel, and heavy ball modifications.