A branch-and-bound algorithm for hard multiple knapsack problems

The multiple knapsack problem (MKP) is a classical combinatorial optimization problem. A recent algorithm for some classes of the MKP is bin-completion, a bin-oriented, branch-and-bound algorithm. In this paper, we propose path-symmetry and path-dominance criteria for pruning nodes in the MKP branch-and-bound search space. In addition, we integrate the ??bound-and-bound?? upper bound validation technique used in previous MKP solvers. We show experimentally that our new MKP solver, which successfully integrates dominance based pruning, symmetry breaking, and bound-and-bound, significantly outperforms previous solvers on some classes of hard problem instances.     

Stable equivalences of graded algebras

We extend the notion of stable equivalence to the class of locally finite graded algebras. For such an algebra Λ, we focus on the Krull–Schmidt category gr_Λ of finitely generated -graded Λ-modules with degree 0 maps, and the stable category obtained by factoring out those maps that factor through a graded projective module. We say that Λ and Γ are graded stably equivalent if there is an equivalence that commutes with the grading shift. Adapting arguments of Auslander and Reiten involving functor categories, we show that a graded stable equivalence α commutes with the syzygy operator (where defined) and preserves finitely presented modules. As a result, we see that if Λ is right noetherian (resp. right graded coherent), then so is any graded stably equivalent algebra. Furthermore, if Λ is right noetherian or k is artinian, we use almost split sequences to show that a graded stable equivalence preserves finite length modules. Of particular interest in the nonartinian case, we prove that any graded stable equivalence involving an algebra Λ with socΛ=0 must be a graded Morita equivalence.     

Antimicrobial Polyketide Metabolites from Penicillium bissettii and P. glabrum

Screening of several fungi from the New Zealand International Collection of Microorganisms from Plants identified two strains of Penicillium, P. bissettii and P. glabrum, which exhibited antimicrobial activity against Escherichia coli, Klebsiella pneumoniae, and Staphylococcus aureus. Further investigation into the natural products of the fungi, through extraction and fractionation, led to the isolation of five known polyketide metabolites, penicillic acid (1), citromycetin (2), penialdin A (3), penialdin F (4), and myxotrichin B (5). Semi-synthetic derivatization of 1 led to the discovery of a novel dihydro (1a) derivative that provided evidence for the existence of the much-speculated open-chained form of 1. Upon investigation of the antimicrobial activities of the natural products and derivatives, both penicillic acid (1) and penialdin F (4) were found to inhibit the growth of Methicillin-resistant S. aureus. Penialdin F (4) was also found to have some inhibitory activity against Mycobacterium abscessus and M. marinum along with citromycetin (2).     

Synthese von radioaktiv markierten Bromacetyl- und Diazoacetyl-α-melanotropin-Derivaten zum Studium von kovalenten Hormon-Makromolekül-Komplexen

Synthesis of radioactive α-melanotropin derivatives containing a bromoacetyl or diazoacetyl group for studies of covalent hormone-macromolecule complexes α-Melanotropin derivatives and fragments covalently bound to human serum albumin through their N-terminal end exhibit almost the same biological activity as the corresponding free N^α-acetylated peptides [6]. The preparation of such complexes requires derivatives with a ‘reactive’ N-terminal acetyl group. We describe here the synthesis of three α-melanotropin fragments and of two specifically tritiated α-melanotropin derivatives containing N^α-bromoacetyl or N^α-diazoacetyl groups: BrCH₂CO · Glu-His-Phe-Arg-Trp-Gly-Lys-Pro-Val · NH₂, BrCH₂CO · Glu-His-Phe-Arg-Trp-Gly · OH, BrCH₂CO · Trp-Gly-Lys-Pro-Val middot; NH₂, BrCH₂CO · D -Ala-Tyr(³H₂)-Gly-Nva-Glu-His-Phe-Arg-Trp-Gly-Lys-Pro-Val · NH₂, and N₂ = CHCO · Gly-Tyr(³H₂)-Ser-Nva-Glu-His-Phe-Arg-Trp-Gly- Lys-Pro-Val · NH₂. The latter two analogues displayed a specific radioactivity of about 20 and 36 Ci/mmol, and a biological activity of 2 · 10⁹ and 6 · 10⁹ U/mmol respectively. They are also being used for affinity and photoaffinity labelling of receptor molecules and antibody combining sites.     

Linear scaling density fitting

Two modifications of the resolution of the identity (RI)/density fitting (DF) approximations are presented. First, we apply linear scaling and J-engine techniques to speed up traditional DF. Second, we develop an algorithm that produces local, accurate fits with effort that scales linearly with system size. The fits produced are continuous, differentiable, well-defined, and do not require preset fitting domains. This metric-independent technique for producing a priori local fits is shown to be accurate and robust even for large systems. Timings are presented for linear scaling RI/DF calculations on large one-, two-, and three-dimensional carbon systems.     

Kobalt(III)ammin-derivate einiger Reineckesalz-Analoga mit Xylidinen

Zusammenfassung Es wurden 34 neue Komplexsalze durch doppelte Umsetzung aus wäßr.-alkohol. Lösungen der folgenden Reineckeat-Analoga: [Cr(NCS)₄(m-xylidin)₂]^–, [Cr(NCS)₄(p-xyl)₂]^– und Hexammin-, Monoacido-pentammin- und Diacido-tetramminkobalt(III)-komplexsalze erhalten. Es wurden in einigen Fällen Unterschiede in physiko-chemischen Eigenschaften, wie Farbtönung, Kristallform, Löslichkeit und papierchromatographischeR _f-Werte, bei den stellungsisomeren Salzen vom Typus: Kation · [Cr(NCS)₄(xyl)₂] und auch bei den Koordinationsisomerpaaren: [Co(DH)₂(m-xyl)₂] [Cr(NCS)₄(p-xyl)₂] und [Co(DH)₂(p-xyl)₂] [Cr(NCS)₄(m-xyl)₂] usw. beobachtet.

---

Cobalt(III)ammine derivatives of some reineckate analogues with xylidines

34 new complex salts were prepared by double conversion of the reineckate analogues [Cr(NCS)₄(m-xylidine)₂]^–, [Cr(NCS)₄(p-xyl)₂]^–, with the hexammine-, monoacido-pentammine- and diacidotetrammine-complexes of Co(III). In some of the position and coordination isomeres differences of the standard physico-chemical properties, i.e. color, crystal form, solubility and paper chromatographyR _f-values were observed.

     

Wetting–dewetting films: The role of structural forces

The liquid wetting and dewetting of solids are ubiquitous phenomena that occur in everyday life. Understanding the nature of these phenomena is beneficial for research and technological applications. However, despite their importance, the phenomena are still not well understood because of the nature of the substrate's surface energy non-ideality and dynamics. This paper illustrates the mechanisms and applications of liquid wetting and dewetting on hydrophilic and hydrophobic substrates. We discuss the classical understanding and application of wetting and film stability criteria based on the Frumkin–Derjaguin disjoining pressure model. The roles of the film critical thickness and capillary pressure on the film instability based on the disjoining pressure isotherm are elucidated, as are the criteria for stable and unstable wet films. We consider the film area in the model for the film stability and the applicable experiments. This paper also addresses the two classic film instability mechanisms for suspended liquid films based on the conditions of the free energy criteria originally proposed by de Vries (nucleation hole formation) and Vrij–Scheludko (capillary waves vs. van der Waals forces) that were later adapted to explain dewetting. We include a discussion of the mechanisms of nanofilm wetting and dewetting on a solid substrate based on nanoparticles' tendency to form a 2D layer and 2D inlayer in the film under the wetting film's surface confinement. We also present our view on the future of wetting–dewetting modeling and its applications in developing emerging technologies. We believe the review and analysis presented here will benefit the current and future understanding of the wetting–dewetting phenomena, as well as aid in the development of novel products and technologies.     

Photochemische Reaktionen 81. Mitteilung [1] Notiz zur UV.-Bestrahlung von γ, δ-Epoxy-eucarvon und dessen Reaktivität gegenüber Botrifluorid-äthylätherat

UV.-irradiation (λ ≥ 327 nm) of the α,β-unsaturated γ,δ-epoxy ketone 2 in pentane gives the isomers oxidoketone 3 and diketone 4, in high yield. On treatment with BF₃O(C₂H₅)₂, 2 undergoes rearrangement to the diketone 4 and the isomeric lactone 8 and yields also the dimer 9.