The Steiner tree problem I: Formulations,compositions and extension of facets

In this paper we give some integer programming formulations for the Steiner tree problem on undirected and directed graphs and study the associated polyhedra. We give some families of facets for the undirected case along with some compositions and extensions. We also give a projection that relates the Steiner tree polyhedron on an undirected graph to the polyhedron for the corresponding directed graph. This is used to show that the LP-relaxation of the directed formulation is superior to the LP-relaxation of the undirected one.Corresponding author.     

Photon states in anisotropic media

Quantum aspects of optical polarization are discussed for waves traveling in anisotropic dielectric media with a view to relate the dynamics of polarization with that of photon spin and its manipulation by classical polarizers.     

Correlation of selected core-level spectroscopies

Spectral characteristics representing the distribution of unoccupied conduction-band states in the 3d transition-series metals Fe, Co, Ni and Cu, obtained using soft X-ray absorption (SXA), bremsstrahlung isochromat (BI) and characteristic isochromat (CI) methods, are related mathematically to those found in soft X-ray appearance-potential Spectroscopy (SXAPS) on the basis of the one-electron band approximation. These mathematical relationships are used to compute SXAPS spectra from reported experimental data obtained by the SXA, BI and CI methods. For the metals considered, the correlations between the computed and experimental SXAPS spectra are found to be good. The observed discrepancies are attributed to differences in the selection rules of the excitation processes, to the effect of the core vacancy on the final state, and to many-body phenomena which are not included in the simplified one-electron band model.     

N-（2-甲基）苯基甘氨酸的三价和四价金属/非金属衍生物(英)

用N-（2-甲基）苯基甘氨酸合成了几种（硼、铝、铁、砷和锑）及四价（硅、钛和硒）金属/非金属衍生物。合成是在苯溶液中采用了金属/非金属的异丙氧基化合物和N-（2-甲基）苯基甘氨酸按1∶1和1∶2的配比完成的。一般情况下，合成的产物均为有色固体，以及在产物中有异丙氧基基团残留而显吸湿性。对所制成的衍生物均采用了共沸混合物分析、元素分析和光谱测定等进行了表征。     

Synthesis,antimicrobial and anti-inflammatory activities of some novel 5-substituted imidazolone analogs

In view of potent antimicrobial and anti-inflammatory activities exhibited by 5-substituted imidazolones, a variety of novel imidazolone analogs 3a-l were synthesized by the condensation of different substituted oxazolones 1 with various aromatic amines 2. All the synthesized compounds were screened for in vitro activities against a panel of Gram-positive and Gram-negative bacteria and the yeast-like pathogenic fungus Candida albicans. Several analogs produced good or moderate activities particularly against the tested Gram-positive bacteria Micrococcus luteus and Gram-negative bacteria Pseudomonas aeruginosa and. Meanwhile, compounds 3b and 3c displayed marked antifungal activity against C. albicans. In addition, the in vivo anti-inflammatory activity of the synthesized compounds was determined using the carrageenin-induced paw oedema method in rats. Two of 5-substituted imidazolone derivatives, 3k and 3d show good anti-inflammatory activity. The structures of all the newly synthesized compounds were elucidated using IR, ¹H NMR and ¹³C NMR.     

Isolation and conversion of penicillic acid to 6-iodo-α-pyran-2,5-dione: A key intermediate for the synthesis of pectinolide F

Penicillic acid was isolated from Aspergillus sclerotiorum and converted into 6-iodo-α-pyran-2,5-diones using iodolactonization, a key intermediate for the synthesis of pectinolide F. Structures of penicillic acid and its iodolactonized product were confirmed by using NMR experiments.     

Gold‐catalyzed Intermolecular Oxidations of 2‐Ketonyl‐1‐ethynyl Benzenes with N‐Hydoxyanilines to Yield 2‐Aminoindenones via Gold Carbene Intermediates

Gold‐catalyzed oxidations of 2‐ketonyl‐1‐ethynyl benzenes with N‐hydroxyanilines yield 2‐aminoindenone derivatives efficiently. Experimental data suggests that this process involves an α‐oxo gold carbene intermediate, generated from the attack of N‐hydroxyaniline on furylgold carbene intermediate, rather than the typical attack of oxidants on π‐alkynes.     

Rainbow matchings and Hamilton cycles in random graphs

Let be drawn uniformly from all m‐edge, k‐uniform, k‐partite hypergraphs where each part of the partition is a disjoint copy of . We let be an edge colored version, where we color each edge randomly from one of colors. We show that if and where K is sufficiently large then w.h.p. there is a rainbow colored perfect matching. I.e. a perfect matching in which every edge has a different color. We also show that if n is even and where K is sufficiently large then w.h.p. there is a rainbow colored Hamilton cycle in . Here denotes a random edge coloring of with n colors. When n is odd, our proof requires for there to be a rainbow Hamilton cycle. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 503–523, 2016