Popular edges and dominant matchings

Given a bipartite graph \(G = (A \cup B,E)\) with strict preference lists and given an edge \(e^* \in E\), we ask if there exists a popular matching in G that contains \(e^*\). We call this the popular edge problem. A matching M is popular if there is no matching \(M'\) such that the vertices that prefer \(M'\) to M outnumber those that prefer M to \(M'\). It is known that every stable matching is popular; however G may have no stable matching with the edge \(e^*\). In this paper we identify another natural subclass of popular matchings called “dominant matchings” and show that if there is a popular matching that contains the edge \(e^*\), then there is either a stable matching that contains \(e^*\) or a dominant matching that contains \(e^*\). This allows us to design a linear time algorithm for identifying the set of popular edges. When preference lists are complete, we show an \(O(n^3)\) algorithm to find a popular matching containing a given set of edges or report that none exists, where \(n = |A| + |B|\).     

Highly enantioselective CH oxidation of vic-Diols with Shi's oxazolidinone dioxiranes

[reaction: see text] Through an analogical study of the transition states of CH oxidation and asymmetric epoxidation of terminal alkenes, the first dioxirane-mediated catalytic highly enantioselective CH oxidation method was realized with Shi's oxazolidinone ketone derivatives. Very good enantioselectivity (up to 92% ee) may be obtained for both asymmetrization of meso vic-diols and kinetic resolution of racemic vic-diols.     

Propagation of an electromagnetic soliton in an anisotropic biquadratic ferromagnetic medium

Information storage technology based on anisotropic ferromagnets with sufficiently high magneto-optical effects has received much attention in recent years.Magneto-optical recording combines the merits of magnetic and optical techniques.We investigate the magneto-optical effects on a biquadratic ferromagnet and show that the dynamics of the system are governed by a perturbed nonlinear Schro¨dinger equation.The evolutions of amplitude and velocity of the soliton are found to be time independent,thereby admitting the lossless propagation of the electromagnetic soliton in the medium,which may have potential applications in soliton based optical communication systems.We also exploit the role of perturbation,which has a significant impact on the propagation of an electromagnetic soliton.     

Study of optical shuttering action in supramolecular hydrogen bonded nematogens

Supramolecular hydrogen bonded mesogens are formed between p-n-undecyloxy benzoic acid (11BAO) and p-n-alkyl benzoic acids (nBA, where n?=?2–8). The isolated mesogens are characterized by distinct techniques in order to appreciate the optical, thermal, electrical, and dielectric properties. The optical tilt angle measurement is studied for all the members of this homologous series and is found to concur with the mean field theory predicted value. An interesting factor to notice is the observation of optical shuttering action in nematic phase of the entire series which privilege these materials to be used as light modulators. Dielectric measurements were carried out and the dispersion curves were discussed in terms of relaxation frequency and activation energies.     

An Efficient One‐pot Three‐component Method for the Synthesis of 5‐Amino‐3‐(2‐oxo‐2H‐chromen‐3‐yl)‐7‐aryl‐7H‐thiazolo[3,2‐a]pyridine‐6,8‐dicarbonitriles

A facile, convenient, and adequate method has been developed for the synthesis of novel 5‐amino‐3‐(2‐oxo‐2H‐chromen‐3‐yl)‐7‐aryl‐7H‐thiazolo[3,2‐a]pyridine‐6,8‐dicarbonitriles ( 6 ) by employing 2‐(4‐(2‐oxo‐2H‐chromen‐3‐yl)thiazol‐2‐yl)acetonitrile ( 3 ) as an important precursor. Initially, we have synthesized the target compounds in a stepwise manner and then approached a tandem method to examine the feasibility of one‐pot method. Subsequently, one‐pot three‐component protocol has been established for the synthesis of title compounds by the reaction of 3 with benzaldehyde and malononitrile in refluxing ethanol engender a new six‐membered thiazolo[3,2‐a] pyridine as a hybrid scaffold. Reaction conditions were optimized for this reaction and a broad substrate scope with various aryl and heteroaryl aldehydes make this protocol very practical, attractive, and worthy. Mechanistic aspects for the formation of these compounds were outlined comprehensively. Characterization of these newly synthesized compounds was achieved by means of IR, ¹H NMR, ¹³C NMR, and HRMS.     

An efficient one-pot three-component synthesis of 2-(4-(2-oxo-2H-chromen-3-yl)thiazol-2-yl)-3-arylacrylonitriles and their cytotoxic activity evaluation with molecular docking

A facile, convenient and one-pot three-component method has been outlined for the synthesis of title compounds by treating equimolar amounts of 3-(2-bromoacetyl)-2H-chromen-2-one (2) with 2-cyanothioacetamide (3) and various aryl/heteryl aldehydes (5 or 7) independently. The effect of solvent and catalyst on this one-pot reaction has been studied and the use of l-proline in ethanol was found to be effective to achieve the target compounds (6 & 8) in fair yields. These synthesized compounds were further assessed for the anti-hepatoma activity, and their action mechanism was also investigated by using molecular docking studies. All the compounds 6(a-h) & 8(a-f) manifested excellent potency for anti-hepatoma activity. It should be noted that, compounds 6e, 6f have exhibited almost equipotent activity with reference to standard drug Nexavar.     

Purification and identification of 4-allylbenzene-1,2-diol: an antilisterial and biofilm preventing compound from the leaves of Piper betle L. var Pachaikodi

Antibiotic-resistant food-borne Listeriosis has been rising with up to 30% mortality threat in humans since several decades. Hence, discovering antilisterial from the extracts of ethnomedicinal plants may be of value as a novel antidote. In our preceding study, we reported that ethanolic extract of Piper betle L. var Pachaikodi leaves exhibited antibacterial activity towards Listeria monocytogenes MTCC 657. Consequently in the present study, the bioactive molecule responsible for anti-Listeria activity was purified and identified as 4-allylbenzene-1,2-diol. This identified bioactive compound may have significance while used as antimicrobials and/or food additives in food processing sector as evidenced by dual action: biofilm inhibition and pore formation on cell membrane.     

Popular branchings and their dual certificates

Mathematical Programming - Let G be a digraph where every node has preferences over its incoming edges. The preferences of a node extend naturally to preferences over branchings, i.e., directed...     

Cetyl‐alcohol‐reinforced hollow fiber solid/liquid‐phase microextraction and HPLC–DAD analysis of ezetimibe and simvastatin in human plasma and urine

A new cetyl‐alcohol‐reinforced hollow fiber solid/liquid‐phase microextraction (CA–HF–SLPME) followed by high‐performance liquid chromatography–diode array detection (HPLC–DAD) method was developed for simultaneous determination of ezetimibe and simvastatin in human plasma and urine samples. To prepare the CA–HF–SLPME device, the cetyl‐alcohol was immobilized into the pores of a 2.5 cm hollow fiber micro‐tube and the lumen of the micro‐tube was filled with 1‐octanol with the two ends sealed. Afterwards, the prepared device was introduced into 10 mL of the sample solution containing the analytes with agitation. Under optimized conditions, calibration curves plotted in spiked plasma and urine samples were linear in the ranges of 0.363–25/0.49–25 μg L^?1 for ezetimibe/simvastatin and 0.193–25/0.312–25 μg L^?1 for ezetimibe/simvastatin in plasma and urine samples, respectively. The limit of detection was 0.109/0.174 μg L^?1 for ezetimibe/simvastatin in plasma and 0.058/0.093 μg L^?1 for ezetimibe/simvastatin in urine. As a potential application, the proposed method was applied to determine the concentration of selected analytes in patient plasma and urine samples after medication and satisfactory results were achieved. In comparison with reference methods, the CA–HF–SLPME–HPLC–DAD method demonstrates considerable potential in the biopharmaceutical analysis of selected drugs.     

Electrochemical and photocatalytic investigation of nickel oxide for energy storage and wastewater treatment

Nickel oxide (NiO) was synthesized via a one-step facile method. X-ray diffraction analysis confirmed the face-centered cubic structure of NiO. The bonding nature and surface purity were confirmed via Fourier-transform infrared spectroscopy. NiO revealed partial spherical morphology with less particle aggregation. The optical bandgap of NiO was found to be 3.75 eV. Cyclic voltammetry revealed well-defined oxidation and reduction peaks for NiO. The charge–discharge curve exhibited specific capacitance of 184.6 F/g at current density of 0.3 A/g. NiO electrode exhibited longer cyclic stability of 93 % up to 1500 cycles. In addition, NiO + H₂O₂ revealed efficient photocatalytic degradation of methylene blue (organic pollutant) under visible-light irradiation with degradation efficiency of ~88 %. These results confirm that nanosized NiO is more suitable for dual application.