Concerning an Example of Paskiewich

We generalize the construction proposed by A. Paskiewich of an example of an orthonormal system which establishes the sharpness of the Men’shov-Rademacher theorem. The connection of his example with that of Men’shov is elucidated.__________Translated from Matematicheskie Zametki, vol. 78, no. 2, 2005, pp. 286–291.Original Russian Text Copyright © 2005 by A. P. Solodov.     

Sorbitol-Based Demulsifying Agents and Their Surfactant Properties

Sorbitol-based block copolymers of ethylene and propylene oxides were synthesized and characterized as surfactants and demulsifiers.__________Translated from Zhurnal Prikladnoi Khimii, Vol. 78, No. 6, 2005, pp. 966–971.Original Russian Text Copyright © 2005 by Solodov, Varnavskaya, Khvatova, Fakhrutdinov, Lebedev, Diyarov.     

Global convergence of an SQP method without boundedness assumptions on any of the iterative sequences

Usual global convergence results for sequential quadratic programming (SQP) algorithms with linesearch rely on some a priori assumptions about the generated sequences, such as boundedness of the primal sequence and/or of the dual sequence and/or of the sequence of values of a penalty function used in the linesearch procedure. Different convergence statements use different combinations of assumptions, but they all assume boundedness of at least one of the sequences mentioned above. In the given context boundedness assumptions are particularly undesirable, because even for non-pathological and well-behaved problems the associated penalty functions (whose descent is used to produce primal iterates) may not be bounded below for any value of the penalty parameter. Consequently, boundedness assumptions on the iterates are not easily justifiable. By introducing a very simple and computationally cheap safeguard in the linesearch procedure, we prove boundedness of the primal sequence in the case when the feasible set is nonempty, convex, and bounded. If, in addition, the Slater condition holds, we obtain a complete global convergence result without any a priori assumptions on the iterative sequences. The safeguard consists of not accepting a further increase of constraints violation at iterates which are infeasible beyond a chosen threshold, which can always be ensured by the proposed modified SQP linesearch criterion. The author is supported in part by CNPq Grants 301508/2005-4, 490200/2005-2, 550317/2005-8, by PRONEX–Optimization, and by FAPERJ Grant E-26/151.942/2004.     

Estimates with Sharp Constants of the Sums of Sine Series with Monotone Coefficients of Certain Classes in Terms of the Salem Majorant

New estimates of the sums of sine series with monotone coefficients of special classes in terms of the Salem majorant are obtained. The asymptotic sharpness of the obtained estimates for sequences of coefficients from the classes under consideration is proved.     

Measurements and calculations of Ar-broadening parameters of water vapour transitions in a wide spectral region

The water vapour line-broadening (γ) and shift (δ) coefficients for 310 lines of 10 vibrational bands ν₁, ν₃, 2ν₂, ν₁+ ν₂, ν₂+ ν_3, 2ν₂ +ν₃, 2ν₁, ν₁+ ν₃, 2ν₃ and ν₁ +2ν₂ induced by argon pressure were measured with a Bruker IFS HR 125 spectrometer. The measurements were performed at room temperature, at the spectral resolution of 0.01 cm^–1 and over a wide pressure range of Ar. The calculations of the broadening coefficients γ and δ were performed in the framework of the semi-classical method. The intermolecular potential was taken as the sum of the atom–atom potential and the vibrationally and rotationally dependent isotropic induction+dispersion potential. The measured γ and δ were combined with literature data for the ν₂ and 3ν₁+ν₃, 2ν₁+2ν₂+ν₃ vibrational bands, and the optimal sets of potential parameters that gave the best agreement with the measured broadening coefficients for each vibrational band separately were found. Then, combined experimental data of 13 vibrational bands of H₂O perturbed by Ar were used to determine the analytical dependence of some potential parameters on vibrational quantum numbers.     

Shock ignition of thermonuclear fuel with high areal density

A novel method by C. Zhou and R. Betti [Bull. Am. Phys. Soc. 50, 140 (2005)] to assemble and ignite thermonuclear fuel is presented. Massive cryogenic shells are first imploded by direct laser light with a low implosion velocity and on a low adiabat leading to fuel assemblies with large areal densities. The assembled fuel is ignited from a central hot spot heated by the collision of a spherically convergent ignitor shock and the return shock. The resulting fuel assembly features a hot-spot pressure greater than the surrounding dense fuel pressure. Such a nonisobaric assembly requires a lower energy threshold for ignition than the conventional isobaric one. The ignitor shock can be launched by a spike in the laser power or by particle beams. The thermonuclear gain can be significantly larger than in conventional isobaric ignition for equal driver energy.     

Error bounds for proximal point subproblems and associated inexact proximal point algorithms

We study various error measures for approximate solution of proximal point regularizations of the variational inequality problem, and of the closely related problem of finding a zero of a maximal monotone operator. A new merit function is proposed for proximal point subproblems associated with the latter. This merit function is based on Burachik-Iusem-Svaiter’s concept of ε-enlargement of a maximal monotone operator. For variational inequalities, we establish a precise relationship between the regularized gap function, which is a natural error measure in this context, and our new merit function. Some error bounds are derived using both merit functions for the corresponding formulations of the proximal subproblem. We further use the regularized gap function to devise a new inexact proximal point algorithm for solving monotone variational inequalities. This inexact proximal point method preserves all the desirable global and local convergence properties of the classical exact/inexact method, while providing a constructive error tolerance criterion, suitable for further practical applications. The use of other tolerance rules is also discussed. Received: April 28, 1999 / Accepted: March 24, 2000?Published online July 20, 2000     

Forcing strong convergence of proximal point iterations in a Hilbert space

This paper concerns with convergence properties of the classical proximal point algorithm for finding zeroes of maximal monotone operators in an infinite-dimensional Hilbert space. It is well known that the proximal point algorithm converges weakly to a solution under very mild assumptions. However, it was shown by Güler [11] that the iterates may fail to converge strongly in the infinite-dimensional case. We propose a new proximal-type algorithm which does converge strongly, provided the problem has a solution. Moreover, our algorithm solves proximal point subproblems inexactly, with a constructive stopping criterion introduced in [31]. Strong convergence is forced by combining proximal point iterations with simple projection steps onto intersection of two halfspaces containing the solution set. Additional cost of this extra projection step is essentially negligible since it amounts, at most, to solving a linear system of two equations in two unknowns. Received January 6, 1998 / Revised version received August 9, 1999?Published online November 30, 1999     

Observation of the bottomonium ground state in the decay Upsilon(3S)-->gammaetab

We report the results of a search for the bottomonium ground state etab(1S) in the photon energy spectrum with a sample of (109+/-1) million of Upsilon(3S) recorded at the Upsilon(3S) energy with the BABAR detector at the PEP-II B factory at SLAC. We observe a peak in the photon energy spectrum at Egamma=921.2(-2.8)+2.1(stat)+/-2.4(syst) MeV with a significance of 10 standard deviations. We interpret the observed peak as being due to monochromatic photons from the radiative transition Upsilon(3S)-->gammaetab(1S). This photon energy corresponds to an etab(1S) mass of 9388.9(-2.3)+3.1(stat)+/-2.7(syst) MeV/c2. The hyperfine Upsilon(1S)-etab(1S) mass splitting is 71.4(-3.1)+2.3(stat)+/-2.7(syst) MeV/c2. The branching fraction for this radiative Upsilon(3S) decay is estimated to be [4.8+/-0.5(stat)+/-1.2(syst)]x10(-4).