Acyclic Hypergraph Projections

Hypergraphs can be partitioned into two classes: tree (acyclic) hypergraphs and cyclic hypergraphs. This paper analyzes a new class of cyclic hypergraphs called Xrings. HypergraphHis an Xring if the hyperedges ofHcan be circularly ordered so that for every vertex, all hyperedges containing the vertex are consecutive; in addition, the vertices of no hyperedge may be a subset of the vertices of another hyperedge, and no vertex may appear in exactly one hyperedge. LetH₁andH₂be two hypergraphs. A tree projection ofH₁with respect toH₂is an acyclic hypergraphH₃such that the vertices of each hyperedge inH₁appear among the vertices of some hyperedge ofH₃and the vertices of each hyperedge inH₃appear among the vertices of some hyperedge ofH₂. A polynomial time algorithm is presented for deciding, given XringH₁and arbitrary hypergraphH₂, whether there exists a tree projection ofH₂with respect toH₁. It is shown that hypergraphHis an Xring iff a modified adjacency graph ofHis a circular-arc graph. A linear time Xring recognition algorithm, for GYO reduced hypergraphs as inputs, is presented.     

Laser desorption fast gas chromatography–Mass spectrometry in supersonic molecular beams

A novel method for fast analysis is presented. It is based on laser desorption injection followed by fast gas chromatography-mass spectrometry (GC-MS) in supersonic molecular beams. The sample was placed in an open air or purged laser desorption compartment, held at atmospheric pressure and near room temperature conditions. Desorption was performed with a XeCl Excimer pulsed laser with pulse energy of typically 3 mJ on the surface. About 20 pulses at 50 Hz were applied for sample injection, resulting in about 0.4 s injection time and one or a few micrograms sample vapor or small particles. The laser desorbed sample was further thermally vaporized at a heated frit glass filter located at the fast GC inlet. Ultrafast GC separation and quantification was achieved with a 50-cm-long megabore column operated with a high carrier gas flow rate of up to 240 mL/min. The high carrier gas flow rate provided effective and efficient entrainment of the laser desorbed species in the sweeping gas. Following the fast GC separation, the sample was analyzed by mass spectrometry in supersonic molecular beams. Both electron ionization and hyperthermal surface ionization were employed for enhanced selectivity and sensitivity. Typical laser desorption analysis time was under 10 s. The laser desorption fast GC-MS was studied and demonstrated with the following sample/matrices combinations, all without sample preparation or extraction: (a) traces of dioctylphthalate plasticizer oil on stainless steel surface and the efficiency of its cleaning; (b) the detection of methylparathion and aldicarb pesticides on orange leaves; (c) water surface analysis for the presence of methylparathion pesticide; (d) caffeine analysis in regular and decaffeinated coffee powder; (e) paracetamol and codeine drug analysis in pain relieving drug tablets; (f) caffeine trace analysis in raw urine; (g) blood analysis for the presence of 1 ppm lidocaine drug. The features and advantages of the laser desorption fast GC-MS are demonstrated and discussed.     

A von Neumann alternating method for finding common solutions to variational inequalities

By modifying von Neumann’s alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our attention to the two-set CSVIP, which entails finding common solutions to two unrelated variational inequalities in Hilbert space.     

Common Solutions to Variational Inequalities

We study the new variational inequality problem, called the Common Solutions to Variational Inequalities Problem (CSVIP). This problem consists of finding common solutions to a system of unrelated variational inequalities corresponding to set-valued mappings in Hilbert space. We present an iterative procedure for solving this problem and establish its strong convergence. Relations with other problems of solving systems of variational inequalities, both old and new, are discussed as well.     

A mild,rapid and convenient esterification of half esters of malonic acid

A new method for the esterification of half esters of malonic acid with chloroformates is described. The reaction proceeds $\text{via}$ the mixed anhydride followed by spontaneous decarboxylation.     

A New Double-Projection Method for Solving Variational Inequalities in Banach Spaces

In this paper, we study the variational inequalities involving monotone and Lipschitz continuous mapping in Banach spaces. A new and simple iterative method, which combines Halpern’s technique and the subgradient extragradient idea, is given. Under mild and standard assumptions, we establish the strong convergence of our algorithm in a uniformly smooth and convex Banach spaces. We also present a modification of our method using a line-search approach, this enable to obtain strong convergence in real and reflexive Banach spaces, without the prior knowledge of the Lipschitz constant. Numerical experiments illustrate the performances of our new algorithm and provide a comparison with related algorithms. Our results generalize and extend some of the existing works in Hilbert spaces to Banach spaces as well as provide an extension from weak to strong convergence.     

Iron porphyrins catalyze the synthesis of non-protected amino acid esters from ammonia and diazoacetates

Iron complexes of porphyrins (and corroles to a lesser extent) are the first catalysts to utilize ammonia for the synthesis of N-free amino acid esters.