The effect of data scaling on dual prices and sensitivity analysis in linear programs

In many practical situations scaling the data is necessary to solve linear programs. This note explores the relationships in translating the sensitivity analysis between the original and the scaled problems.     

Diffractive lenses for high-power terahertz radiation beams

Techniques for manufacturing silicon binary (two-level) diffractive lenses and polypropylene kinoform diffractive lenses for the terahertz spectrum range are described. The elements are 1 and 0.8 mm thick, respectively. The silicon lens is manufactured in two versions: with no coating and with a parylene C (polyparaxylylene) antireflection coating. Characteristics of the diffractive optical elements are studied in the beam of a pulse-periodic free electron laser at a radiation wavelength of 141 μm and a repetition rate of 5.6MHz. The radiation resistance of the parylene coating, tested on the Novosibirsk free electron laser, was not impaired when the coating was exposed to an average power density of 4 kW cm^?2, the peak power in a 100-picosecond pulse being almost 8 MW cm^?2.     

Performance of Waterborne Polyurethanes in Inhibition of Gas Hydrate Formation and Corrosion: Influence of Hydrophobic Fragments

The design of new dual-function inhibitors simultaneously preventing hydrate formation and corrosion is a relevant issue for the oil and gas industry. The structure-property relationship for a promising class of hybrid inhibitors based on waterborne polyurethanes (WPU) was studied in this work. Variation of diethanolamines differing in the size and branching of N-substituents (methyl, n-butyl, and tert-butyl), as well as the amount of these groups, allowed the structure of polymer molecules to be preset during their synthesis. To assess the hydrate and corrosion inhibition efficiency of developed reagents pressurized rocking cells, electrochemistry and weight-loss techniques were used. A distinct effect of these variables altering the hydrophobicity of obtained compounds on their target properties was revealed. Polymers with increased content of diethanolamine fragments with n- or tert-butyl as N-substituent (WPU-6 and WPU-7, respectively) worked as dual-function inhibitors, showing nearly the same efficiency as commercial ones at low concentration (0.25 wt%), with the branched one (tert-butyl; WPU-7) turning out to be more effective as a corrosion inhibitor. Commercial kinetic hydrate inhibitor Luvicap 55 W and corrosion inhibitor Armohib CI-28 were taken as reference samples. Preliminary study reveals that WPU-6 and WPU-7 polyurethanes as well as Luvicap 55 W are all poorly biodegradable compounds; BOD_t/COD_cr (ratio of Biochemical oxygen demand and Chemical oxygen demand) value is 0.234 and 0.294 for WPU-6 and WPU-7, respectively, compared to 0.251 for commercial kinetic hydrate inhibitor Luvicap 55 W. Since the obtained polyurethanes have a bifunctional effect and operate at low enough concentrations, their employment is expected to reduce both operating costs and environmental impact.     

The duality principle and inversion of Laplace–Stielties transforms

The fundamental relation between the Laplace transform, the Stielties transform, and the generalized integral equation of refraction is revealed, and a duality principle is formulated for the solution of inverse problems of radio physics. New formulas of the Laplace-transform inversion satisfying the duality principle are obtained. There is no necessity of contour integration in a complex plane for the relations found, which considerably simplifies the reconstruction of originals and makes it possible to control systematic errors in the experimental data.     

Iterative calculation, manufacture and investigation of DOE forming unimodal complex distribution

We present results of iterative calculation, manufacture and experimental as well as theoretical investigations of a novel diffractive optical element (DOE) which transforms a Gaussian TEM₀₀ input beam into a unimodal Gauss–Hermite (1, 0) complex distribution. The iterative calculation procedure is based on the application of the method of generalized projections. The projection operator onto a set of modal functions is implemented through partition of the focal plane into a ‘useful’ and an ‘auxiliary’ domain. This element is manufactured as a 16 level surface profile by (variable dose) electron-beam direct-writing into a PMMA resist film, and a subsequent development procedure of the resist. The final element consists of a fused-silica substrate coated with the structured PMMA film. Both computational and experimental results are presented and demonstrate a good conformity with each other. The achieved results show good prospects of such an approach for the formation of unimodal distributions.     

Formation of diffractive microrelief on diamond film surface

The fabrication of diamond-based optical elements for high-power CO₂ lasers is of particular interest because of low optical absorption, high thermal conductivity and weak temperature dependence of the refractive index of diamond. In earlier publications, we presented the results of the implementation of ion-chemical etching technology for generating a diffraction grating on the surface of a diamond film. The results on generating diamond diffractive optical elements and a sub-wavelength antireflection structure by plasma etching were also presented. In this paper, we study the generation of the grating on the diamond surface by ion-chemical etching. The choice of (Ar+O₂) mixture as a working gas and use of niobium as a masking layer are substantiated. The results of studying a diffraction microrelief generated on the diamond-film surface through ion-chemical etching are discussed.     

Variable-temperature x-ray structural investigation of [Fe[HC(3,5-Me2pz)3]2](BF4)2 (pz= pyrazolyl ring): observation of a thermally induced spin state change from all high spin to an equal high spin-low spin mixture, concomitant with the onset of nonmerohedral twinning

The complex [Fe[HC(3,5-Me(2)pz)(3)](2)](BF(4))(2) (pz = pyrazolyl ring) undergoes a phase transition that occurs concomitantly with a thermally induced spin conversion between the high-spin (HS, S = 2) and low-spin (LS, S = 0) states. Above 204 K the compound is completely HS with the structure in the C2/c space group with Z = 4. A crystal structure determination of this phase was performed at 220 K yielding the cell constants a = 20.338(2) A, b = 10.332(1) A, c = 19.644(2) A, beta = 111.097(2) degrees, and V = 3851.5(6) A(3). There is one unique iron(II) site at this temperature. Below 206 K the compound converts to a 50:50 mixture of HS and LS. The radical change in the coordination sphere for half of the iron(II) sites, most notably a shortening of the Fe-N bond distances by ca. 0.2 A, that accompanies this magnetic transition causes a phase transition. The crystal system changes from C-centered monoclinic to primitive triclinic with Z = 2 with two half-molecules on independent inversion centers. A crystal structure determination was performed at 173 K in space group P1 with a = 10.287(2) A, b = 11.355(3) A, c = 18.949(4) A, alpha = 90.852(4) degrees, beta = 105.245(4) degrees, gamma = 116.304(4) degrees, and V = 1892.3(8) A(3). All specimens investigated below the phase transition temperature were determined to be nonmerohedral twins. Temperature cycling between these two forms does not appear to degrade crystal quality. Previous magnetic susceptibility measurements indicate a second, irreversible increase in the magnetic moment the first time the crystals are cooled below 85 K. A crystal structure determination at 220 K of a specimen precooled to 78 K was not significantly different from those not cooled below 220 K.     

Synthesis and Antimycotic Properties of Hydroxy Sulfides Derived from exo- and endo-4-phenyl-3,5,8-trioxabicyclo[5.1.0]octanes

Both exo- and endo-isomers of 4-phenyl-3,5,8-trioxabicyclo[5.1.0]octane were reacted with thiophenol to afford individual diastereomers of hydroxy sulfides which were further processed in search for new antimycotic substances.     

Effect of Sinkhole Position Symmetry on the Formation of Nonstationary Vortex Funnels

The effect of the sinkhole position on the formation of nonstationary vortex funnels during fluid outflow from a tank whose diameter is much greater than the sinkhole diameter is studied experimentally. The devices for filling the tank were so designed that the opening of a sinkhole on the axis of a cylindrical tank immediately after it had been filled did not lead to the formation of a vortex funnel during fluid outflow. The formation of vortex funnels, when before the sinkhole was opened a disk immersed in the fluid was rotated, is investigated. In this case, a certain time after the outflow started, above the sinkhole a vortex funnel was formed. This time measured by means of digital filming depended on the sinkhole position and increased with the distance between the sinkhole and the axis. The results obtained make it possible to conclude that the symmetry strongly affects the process of vortex funnel formation.