An implementation of the simplex method for linear programming problems with variable upper bounds

Special methods for dealing with constraints of the formx _j x _k , called variable upper bounds, were introduced by Schrage. Here we describe a method that circumvents the massive degeneracy inherent in these constraints and show how it can be implemented using triangular basis factorizations.This research was partially supported by National Science Foundation Grant ECS-7921279 and by a Guggenheim fellowship.     

Positive/negative liquid secondary ion mass spectrometry ofLn-EDTA (1:1) complexes. Formation of molecular ion adducts with neutral species of the matrix orLn-EDTA

Summary The mass spectra of 1:1 complexes ofEDTA with lanthanide cations (Ln=Sm, Eu, Gd, Tb or Dy) upon positive/negative LSIMS are presented. In glycerol used as a matrix, adduct-ions such as [M+H]⁺, [M+H+nGly]⁺, [2M+H]⁺, [2M+H+Gly]⁺ (positive LSIMS) or [M-H]^–, [M-H+nGly]^–, [2M-H]^–, [2M-H+Gly]^– (negative LSIMS), wheren=1–3, are formed. Reactions leading to the formation of adduct-ions are suggested.

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Positive/negative Liquid-Sekundärionen-Massenspektrometrie vonLn-EDTA-(1:1)-Komplexen. Bildung von molekularen Ionenaddukten mit neutralen Spezies aus der Matrix oderLn-EDTA

Zusammenfassung Die Massenspektren von 1:1-Komplexen vonEDTA mit Lanthanidenkationen (Ln=Sm, Eu, Gd, Tb oder Dy) mittels positiver/negativer LSIMS werden präsentiert. In Glycerin als Matrix bilden sich Adduktionen wie [M+H]⁺, [M+H+nGly]⁺, [2M+H]⁺, [2M+H+Gly]⁺ (positive LSIMS) oder [M-H]^–, [M-H+nGly]^–, [2M-H]^–, [2M-H+Gly]^– (negative LSIMS), wobein=1–3. Es werden Reaktionen vorgeschlagen, die zur Bildung von Adduktionen führen.

     

A toxic reagent-free method for normal-phase matrix solid-phase dispersion extraction and reversed-phase liquid chromatographic determination of aldrin,dieldrin, and DDTs in animal fats

A method for the determination of aldrin, dieldrin, DDT, DDE, and DDD contamination in animal fats (beef tallow, lard, and chicken fat) without using toxic reagents is developed, that uses high-performance liquid chromatography after the sample has been prepared by matrix solid-phase dispersion (MSPD) with acidic alumina oxide. A reversed-phase C₁-silica column with a mobile phase of 50% (v/v) ethanol solution (in water) and a photo-diode array detector were used for the determination. Average recoveries of the target compounds (0.2–5.0 g g^–1) ranged from 84–98%, with coefficients of variation of <5%. The limits of quantitation were 0.16 g g^–1 for AD, 0.10 g g^–1 for DD, 0.06 g g^–1 for DDT, 0.07 g g^–1 for DDE, and 0.05 g g^–1 for DDD. No toxic reagents were used at all.     

A parametric linear complementarity technique for the computation of equilibrium prices in a single commodity spatial model

This paper presents a parametric linear complementarity technique for the computation of equilibrium prices in a single commodity spatial model. We first reformulate the model as a linear complementarity problem and then apply the parametric principal pivoting algorithm for its solution. This reformulation leads to the study of an arc—arc weighted adjacency matrix associated with a simple digraph having weights on the nodes. Several basic properties of such a matrix are derived. Using these properties, we show how the parametric principal pivoting algorithm can be greatly simplified in this application. Finally, we report some computational experience with the proposed technique for solving some large problems.     

Accounting for Time Series Errors in Partially Linear Model With Single- or Multiple-Runs

This article concerns statistical estimation of the partially linear model (PLM) for time course measurements, which are temporally correlated and allow multiple-runs for repeated measurements to enhance experimental accuracy without extending the number of time points within each trial. Such features arise naturally from biomedical data, for example, in brain fMRI, and call for special treatment beyond classical methods in either a purely nonparametric regression model or a PLM with independent errors. We develop a stepwise procedure for estimating the parametric and nonparametric components of the multiple-run PLM and making inference for parameters of interest, adaptive to either single- or multiple-run, in the presence of error temporal dependence. Simulation study and real fMRI data applications illustrate the computational simplicity and effectiveness of the proposed methods. Supplementary material for this article is available online.     

Heavy-Atom Tunneling in Bicyclo[4.1.0]hepta-2,4,6-trienes

Heavy-atom tunneling limits the lifetime and observability of bicyclo[4.1.0]hepta-2,4,6-triene, a key intermediate in the rearrangement of phenylcarbene. Bicyclo[4.1.0]hepta-2,4,6-triene had been proposed as the primary intermediate of the rearrangement of phenylcarbene, but despite many efforts evaded its characterization even in cryogenic matrices. By introducing fluorine substituents into the ortho-positions of the phenyl ring of phenylcarbene, the highly strained cyclopropene 1,5-difluorobicyclo[4.1.0]hepta-2,4,6-triene becomes stable enough to be characterized in argon matrices. However, even at 3 K this cyclopropene is only metastable and rearranges via heavy-atom tunneling to the corresponding cycloheptatetraene. Calculations suggest that fluorination is necessary to slow down the tunneling rearrangement of the bicycloheptatriene. The parent bicycloheptatriene rapidly rearranges via heavy-atom tunneling and therefore cannot be detected under matrix isolation conditions.     

Microwave-Responsive Flexible Room-Temperature Phosphorescence Materials Based on Poly(vinylidene fluoride) Polymer

The development of flexible, room-temperature phosphorescence (RTP) materials remains challenging owing to the quenching of their unstable triplet excitons via molecular motion. Therefore, a polymer matrix with T_g higher than room temperature is required to prevent polymer segment movement. In this study, a RTP material was developed by incorporating a 4-biphenylboronic acid (BPBA) phosphor into a poly(vinylidene fluoride) (PVDF) matrix (T_g=−27.1 °C), which exhibits a remarkable UV-light-dependent oxygen consumption phosphorescence with a lifetime of 1275.7 ms. The adjustable RTP performance is influenced by the crystallinity and polymorph (α, β, and γ phases) fraction of PVDF, therefore, the low T_g of the PVDF matrix enables the polymeric segmental motion upon microwave irradiation. Consequently, a reduction in the crystallinity and an increase in the α phase fraction in PVDF film induces RTP after 2.45 GHz microwave irradiation. These findings open up new avenues for constructing crystalline and phase-dependent RTP materials while demonstrating a promising approach toward microwave detection.     

Application of matrix solid-phase dispersion to the determination of amitrole and urazole residues in apples by capillary electrophoresis with electrochemical detection

A new method based on matrix solid-phase dispersion (MSPD) extraction was studied for the extraction of amitrole (3-amino-1,2,4-triazole), and its metabolite urazole (3,5-dihydroxy-1,2,4-triazole), in apple samples. The influence of experimental conditions on the yield of the extraction process and on the efficiency of the cleanup step was evaluated. Determination was carried out by capillary electrophoresis (CE) with electrochemical detection, demonstrating the compatibility between MSPD and CE techniques. The method has been successfully applied to different apple varieties. Recoveries in samples spiked at 1.6 and 1.7 μg g⁻¹ for amitrole and urazole were 88 and 82%, respectively. The limits of detection were 0.4 μg g⁻¹ for both compounds using electrochemical detection.     

Determination of trace elements in bone by two-jet plasma atomic emission spectrometry

This paper describes an analytical method for trace element determination in bone tissues. The study of the influence of the bone matrix showed that the addition of 25% ground bone to graphite powder with introduced impurities did not affect the analytical signal of elements in the spectral excitation in a two-jet plasma. On basis of these investigations a method for direct multielement analysis of bone tissues was suggested. The sample preparation procedure consisted in mixing powdered bone (particle size 30 μm or less) with a spectroscopic buffer (graphite powder plus NaCl) in ratio 1:3 or to a greater extent depending on the analyte concentration. Reference samples based on graphite powder were used for construction of calibration curves. The NaCl concentration in analyzed and calibration samples was 15 wt%. The effect of particle size was revealed from the determination of Ba, Sr, and Mg. To eliminate this effect, treatment of the samples with nitric acid was proposed. The validation of the technique was confirmed by comparison of the analysis results of a bone sample with those obtained by inductively coupled plasma atomic emission spectrometry after wet acid digestion. The limits of detection estimated for 20 elements were the following (μg g^-1): 0.1 (Ag), 1.0 (Al), 1.0 (Ba), 0.1 (Be), 1.2 (Bi), 0.4 (Cd), 1.0 (Co), 0.2 (Cu), 0.6 (Cr), 1.9 (In), 2 (Fe), 0.3 (Ga), 0.4 (Mn), 0.4 (Mo), 0.7 (Ni), 1.0 (Pb), 0.7 (Sn), 0.8 (Tl), 5 (Sr), 1.0 (Zn).     

On the perturbation of the group generalized inverse for a class of bounded operators in Banach spaces

Given a bounded operator A on a Banach space X with Drazin inverse AD and index r, we study the class of group invertible bounded operators B such that I+AD(B−A) is invertible and R(B)∩N(Ar)={0}. We show that they can be written with respect to the decomposition X=R(Ar)⊕N(Ar) as a matrix operator, , where B₁ and are invertible. Several characterizations of the perturbed operators are established, extending matrix results. We analyze the perturbation of the Drazin inverse and we provide explicit upper bounds of ‖B^?−AD‖ and ‖BB^?−ADA‖. We obtain a result on the continuity of the group inverse for operators on Banach spaces.