A modified subgradient extragradient method for solving the variational inequality problem

The subgradient extragradient method for solving the variational inequality (VI) problem, which is introduced by Censor et al. (J. Optim. Theory Appl. 148, 318–335, 2011), replaces the second projection onto the feasible set of the VI, in the extragradient method, with a subgradient projection onto some constructible half-space. Since the method has been introduced, many authors proposed extensions and modifications with applications to various problems. In this paper, we introduce a modified subgradient extragradient method by improving the stepsize of its second step. Convergence of the proposed method is proved under standard and mild conditions and primary numerical experiments illustrate the performance and advantage of this new subgradient extragradient variant.     

Note on the modified relaxation CQ algorithm for the split feasibility problem

In this paper we are concerned with the Split Feasibility Problem (SFP) in which there are given two Hilbert spaces \(H_1\) and \(H_2\), nonempty, closed and convex sets \(C\subseteq H_1\) and \(Q\subseteq H_2\), and a bounded and linear operator \(A:H_1 \rightarrow H_2\). The SFP is then to find a point \(x^*\in C\) such that its image under A belongs to Q, meaning that \(Ax^*\in Q\). This reformulation was employed successfully for solving many inverse problems: for example, in intensity-modulated radiation therapy treatment planning. One of the typical classes of methods that have been used to solve the SFP is the class of projection method. This note focuses on the modified relaxation CQ algorithm with the Armijo-line search rule for solving the SFP. Under common and standard assumptions, we show that the proposed method weakly converges to a solution of the SFP. Numerical examples illustrating our method’s efficiency are presented for solving the LASSO problem in which the goal is to recover a sparse signal from a limited number of observations.     

The pre‐separation of oxygen containing compounds in oxidised heavy paraffinic fractions and their identification by GC‐MS with supersonic molecular beams.

The heavy petroleum fractions produced during refining processes need to be upgraded to useable products to increase their value. Hydrogenated heavy paraffinic fractions can be oxidised to produce high value products that contain a variety of oxygenates. These heavy oxygenated paraffinic fractions need to be characterised to enable the control of oxidation processes and to understand product properties. The accurate identification of the oxygenates present in these fractions by electron ionisation (EI) mass spectrometry is challenging due to the complexity of these heavy fractions. Adding to this challenge is the limited applicability of EI mass spectral libraries due to the absence of molecular ions from the EI mass spectra of many oxygenates. The separation of oxygenates from the complex hydrocarbon matrix prior to high temperature GC‐MS (HT‐GC‐MS) analysis reduces the complexity of these fractions and assists in the accurate identification of these oxygenates. Solid phase extraction (SPE) and supercritical fluid chromatography (SFC) were employed as prefractionation techniques. GC‐MS with supersonic molecular beams (SMBs) (also named GC‐MS with cold‐EI) utilises a SMB interface with which EI is done with vibrationally cold sample compounds in a fly‐through ion source (cold‐EI) resulting in a substantial increase in the molecular ion signal intensity in the mass spectrum. This greatly enhances the accurate identification of the oxygenates in these fractions. This study investigated the ionisation behaviour of oxygenated compounds using cold‐EI. The prefractionation by SPE and SFC and the subsequent analysis with GC‐MS with cold‐EI were applied to an oxygenated heavy paraffinic fraction.     

Lifetimes of electronically excited NO2 in a collision-free differentially pumped supersonic molecular beam

The lifetimes of rotationally cooled NO₂ were measured in the spectral region 5710–5960 Å in a differentially pumped collision- free supersonic molecular beam. Lifetime values (rotationally independent) between 25 and 260 μs were obtained. Over narrow spectral regions, the product of the fluorescence amplitude and the lifetime squared is vibrationally independent, as predicted by theory.     

Dissociaton and energy transfer in molecular impact on surfaces: Experimental and theoretical studies of I2/Mg(100) and I2/sapphire

Solute segregation to antiphase boundaries (APBs) in long-range ordered alloys and its effects on antiphase domain coarsening kinetics have been investigated theoretically, and calculations have been carried out to model the structure and properties of APBs in B2-ordered FeAl alloys. Equilibrium segregation was studied by using the continuum diffuse-interface model of Cahn and Hilliard to calculate profiles of order parameter and composition, as well as interfacial free energy. The migration kinetics of APBs with segregation have been investigated theoretically for the low-velocity regime. A differential equation describing concentration deviations from the equiibrium profile is derived, and approximate solutions to the equation are determined to predict segregation profiles for migrating APBs in FeAl alloys. Measurements of domain coarsening kinetics in FeAl alloys are presented for a temperature range in which segregation was predicted theoretically. A marked slowing of domain coarsening kinetics in this range was observed.     

Spectroscopic identification of the onset of the vibrational quasicontinuum in large molecules

We advance a new spectroscopic criterion for the identification of the threshold of the vibrational quasicontinuum (VQ) in large molecules, which rests on the observation of an onset for a congested vibrational level structure in the electronically excited states of isolated ultracold molecules seeded in supersonic beams. The onset of the VQ in tetracene (C₁₈H₁₂), pentacene (C₂₂H₁₄) and ovalene (C₃₂H₁₄) is exhibited at the excess vibrational energies of 2000 cm^-1 -1000 cm^-1.     

Whole blood analysis for medical diagnostics by GC-MS with Cold EI

This study covers a new method and related instrumentation for whole blood analysis for medical diagnostics. Two-μL whole blood samples were collected using “minimal invasive” diabetes lancet and placed on a thin glass rod mounted on a newly designed BloodProbe. The BloodProbe with the whole blood sample was inserted directly into a ChromatoProbe mounted on the GC inlet, and thus, no sample preparation was involved. The analysis was performed within 10 min using a GC-MS with Cold EI that is based on interfacing GC and MS with supersonic molecular beams (SMB) along with electron ionization of vibrationally cold sample compounds in the SMB (hence the name Cold EI). Our blood analysis revealed several observations: (1) Detailed mass chromatograms were generated with full range of all the nonpolar lipids in blood including fatty acids, cholesterol, cholesteryl esters, vitamin E, monoglycerides, diglycerides, and triglycerides. (2) The analysis of whole blood was found to be as informative as the conventional clinical analysis of blood serum. (3) Cholesteryl esters were more sensitive than free cholesterol alone to the effect of diet of obese people. (4) Major enhancement of several fatty acid methyl esters was found in the blood of a cancer patient with liver dysfunction. (5) Vitamin E as both α- and β-tocopherol was found with person-dependent ratio of these two compounds. (6) Elemental sulfur S₈ was identified in blood. (7) Several drugs and other compounds were found and need further study of their correlation to medical issues.     

Cluster chemical ionization and deuterium exchange mass spectrometry in supersonic molecular Beams

A cluster-based chemical ionization method has been developed that produces protonated molecular ions from molecules introduced through a supersonic molecular beam interface. Mixed clusters of the analyte and a clustering agent (water or methanol) are produced in the expansion region of the beam, and are subsequently ionized by “fly through” electron impact (EI) ionization, which results in a mass spectrum that is a combination of protonated molecular ion peaks together with the conventional EI fragmentation pattern. The technique is presented and discussed as a tool complementary to electron impact ionization in supersonic molecular beams. Surface-induced dissociation on a rhenium oxide surface is also applied to simplify the mass spectra of clusters and reveal the analyte spectrum. The high gas flow rates involved with the supersonic molecular beam interface that enable the easy introduction of the clustering agents also have been used to introduce deuterating agents. An easy-to-use, fast, and routine on-line deuterium exchange method was developed to exchange active hydrogens (NH, OH). This method, combined with electron impact ionization, is demonstrated and discussed in terms of the unique information available through the EI fragmentation patterns, its ability to help in isomer identification, and possible applications with fast gas chromatography-mass spectrometry in supersonic molecular beams.