Paths to stability and uniqueness in two-sided matching markets

The deferred acceptance algorithm introduced by Gale and Shapley is a centralized algorithm, where a social planner solicits the preferences from two sides of a market and generates a stable matching. On the other hand, the algorithm proposed by Knuth is a decentralized algorithm. In this article, we discuss conditions leading to the convergence of Knuth’s decentralized algorithm. In particular, we show that Knuth’s decentralized algorithm converges to a stable matching if either the Sequential Preference Condition (SPC) holds or if the market admits no cycle. In fact, acyclicity turns out to be a special case of SPC. We then consider markets where agents may prefer to remain single rather than being matched with someone. We introduce a generalized version of SPC for such markets. Under this notion of generalized SPC, we show that the market admits a unique stable matching, and that Knuth’s decentralized algorithm converges. The generalized SPC seems to be the most general condition available in the literature for uniqueness in two-sided matching markets.     

A new synthetic approach to 7-hydroxynitidine

Benzo[c]phenanthridine alkaloid, 7-hydroxynitidine, was synthesized from readily available 2-benzyloxy-6-bromo-3,4-dimethoxybenzaldehyde 5 and napthylamine 6 using reductive amination followed by radical cyclization in eight steps. This method is highly efficient and better way to synthesize fully aromatized benzo[c]phenanthridine compounds.     

Direct asymmetric aldol reactions catalyzed by nanocrystalline copper(II) oxide

The direct asymmetric aldol reactions of aromatic and heteroaromatic aldehydes with acetone to afford chiral β-hydroxy carbonyl compounds in good yields and good to moderate enantioselectivities are realized using nanocrystalline copper(II) oxide in the presence of (1S,2S)-(−)-1,2-diphenylethylenediamine at −30 °C. The catalyst can be reused for four cycles with consistent activity and enantioselectivity.     

A Class of Integrable Non-QRT Mappings and Their Deautonomisation

We study classes of mappings which do not belong to the QRT family. We obtain several integrable non-autonomous forms of these mappings extending previous results where only linearisable cases were found. Using our recently introduced method of singularity confinement with full deautonomisation, we analyse a mapping which, while non-integrable, does possess confined singularities and show that our method makes it possible to obtain the exact value of its algebraic entropy.     

Ferrocene derivatives supported on poly(N-vinylpyrrolidin-2-one) (PVP): Synthesis of new water-soluble electrochemically active probes for biomolecules

Carboxy-terminated polyvinylpyrrolidin-2-one (PVP) has been used as a new water-soluble and biocompatible polymeric support for a series of ferrocene labeled amino acid and peptide nucleic acid (PNA) monomer derivatives 4-7. The organometallic polymer-conjugates thus obtained are new and potentially useful as water-soluble electrochemically active probes for biomolecules. In view of such application, their electrochemical activity has been evaluated and has proved very high notwithstanding the complexity and bulkiness of the molecule, affording detection limits down to 10⁻⁸ M in the aqueous medium.     

Production, Purification, and Characterization of a β-Glucosidase of Penicillium funiculosum NCL1

Penicillium funiculosum NCL1, a filamentous fungus, produced significantly higher levels of ??-glucosidase. The effect of initial pH, incubation temperature, and different carbon sources on extracellular ??-glucosidase production was studied in submerged fermentation. At 30?°C with initial pH 5.0, enzyme production was increased by 48-fold upon induction with paper mill waste, as compared to commercial cellulose powder. In zymogram analysis, four isoforms of ??-glucosidases were observed with wheat bran whereas a minimum of one isoform was observed with other carbon sources. A major ??-glucosidase (Bgl3A) with the apparent molecular weight of ~120?kDa, induced by paper mill waste, was purified 19-fold to homogeneity, with a specific activity of 1,796 U/mg. Bgl3A was a monomeric glycoprotein with 29% of neutral carbohydrate content. It showed optimum activity at pH 4.0 and 5.0, optimum temperature at 60?°C, and exhibited a half-life of 1?h at 60?°C. K _m of Bgl3A was found to be 0.057?mM with p-nitrophenyl ??-d-glucoside and V _max was 1,920 U/mg. The purified enzyme exhibited glucose tolerance with a K _i of 1.5?mM. Bgl3A readily hydrolyzed glucosides with ??-linkage. Bgl3A activity was enhanced (156%) by Zn²⁺ and was not affected by other metal cations and reagents. The supplementation of Bgl3A (5 U/mg) with Trichoderma reesei cellulase complex (5 FPU/mg) resulted in about 70% of enhanced glucose production, which emphasizes the industrial importance of Bgl3A.     

Experimental demonstration of terahertz metamaterial absorbers with a broad and flat high absorption band

We present the design, numerical simulations and experimental measurements of terahertz metamaterial absorbers with a broad and flat absorption top over a wide incidence angle range for either transverse electric or transverse magnetic polarization depending on the incident direction. The metamaterial absorber unit cell consists of two sets of structures resonating at different but close frequencies. The overall absorption spectrum is the superposition of individual components and becomes flat at the top over a significant bandwidth. The experimental results are in excellent agreement with numerical simulations.