A smoothing algorithm for finite min–max–min problems

We generalize a smoothing algorithm for finite min–max to finite min–max–min problems. We apply a smoothing technique twice, once to eliminate the inner min operator and once to eliminate the max operator. In mini–max problems, where only the max operator is eliminated, the approximation function is decreasing with respect to the smoothing parameter. Such a property is convenient to establish algorithm convergence, but it does not hold when both operators are eliminated. To maintain the desired property, an additional term is added to the approximation. We establish convergence of a steepest descent algorithm and provide a numerical example.     

K-shell ionization by protons for Cr, Cu, In and by alpha-particles for Cr, Cu

K-shell ionization cross sections have been determined for Cr, Cu and In at proton bombardment in the energy region from 0.9 to 2.5 MeV. The same cross sections were determined for Cr and Cu at alpha bombardment in the 0.9–4.0 MeV region. The experimental results are compared with five different theoretical calculations.     

A simple method for thermoanalysis of evolved gases

Thermoanalytical processes involving the splitting-off of ammonia, water, halogens, inorganic acids or acid anhydrides can be simply observed by using a specimen-holder in which specific reactions with the decomposition products can be induced. A special glass or quartz double crucible can be used for this purpose; the products arising in the lower part of the crucible can be oxidized selectively with reagents placed in the upper part, or can be bound or transformed into other compounds. This double crucible is also suitable for studying reactions taking place between solid and gaseous substances.     

First Synthesis and Utilization of Oripavidine – A Concise and Efficient Route to Important Morphinans and Apomorphines

The synthesis and transformation of oripavidine ( 8 ) offer an efficient and simple route to highly active dopamine agonist apomorphines and a variety of important 14β‐hydroxy‐morphinan derivatives. Natural origin thebaine ( 6 ), the starting compound of the procedure, was converted into its N‐{[1,2‐bis(ethoxycarbonyl)hydrazinyl]methyl} counterpart. L ‐Selectride was found to be an efficient agent to perform a one‐pot O‐ and N‐deprotection at positions 3 and 17, respectively.     

Surface monitoring of HEMT structures

The data of Atomic Force Microscopy (AFM) surface monitoring and of mobility investigations in the HEMT structures based on the AlGaAs/InGaAs/GaAs heterostructures with pseudomorphic InGaAs channel are presented. The level of HEMT nanomaterial self-organization (LNSO) were obtained using the treatment the AFM data by the method of multifractal analysis. Direct correlation between the mobility values and LNSO was found for the most of studied HEMT structures that reflect the close relation between the LNSO values and the HEMT bulk properties. In the structures with LNSO changing from 1.13 to 1.45 the 1.5 time mobility decrease at 300 K and 4 times at 77 K was observed. The results obtained allow to suppose that the LNSO calculation based on surface monitoring of HEMT structures can be used for the optimization of their parameters and of their formation process.     

Spectroscopy of the <Superscript>5</Superscript>H superheavy hydrogen isotope

The formation of the ⁵H superheavy hydrogen isotope was experimentally sought in the reactions induced by stopped π^? mesons absorbed by ⁹Be nuclei. Peaks in missing-mass spectra were observed in two reaction channels, ⁹Be(π^?, pt)X and ⁹Be(π^?, dd)X, and were attributed to the ⁵H resonance states. The lowest state has parameters Er=5.5±0.2 MeV and Г=5.4±0.5 MeV [E_r is the resonance energy measured from the (triton + two neutrons) threshold]. Therefore, ⁵H is bound more weakly than ⁴H. Excited states of ⁵H were also observed. All three resonance levels (E_1r=10.6±0.3 MeV, Г_1r=6.8±0.5 MeV; E_2r=18.5±0.4 MeV, Г_2r=4.8±1.3 MeV; E_3r=26.7±0.4 MeV, Г_3r=3.6±1.3 MeV) can decay into five free nucleons.     

Parametric global optimisation for bilevel programming

We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based on recently developed parametric programming algorithms. We first describe how we can recast and solve the inner (follower’s) problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables of the outer (leader’s) problem. By inserting the obtained rational reaction sets in the upper level problem the overall problem is transformed into a set of independent quadratic, linear or mixed integer linear programming problems, which can be solved to global optimality. In particular, we solve bilevel quadratic and bilevel mixed integer linear problems, with or without right-hand-side uncertainty. A number of examples are presented to illustrate the steps and details of the proposed global optimisation strategy.