A maximum degree theorem for diameter-2-critical graphs

A graph is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. Let G be a diameter-2-critical graph of order n. Murty and Simon conjectured that the number of edges in G is at most ?n ²/4? and that the extremal graphs are the complete bipartite graphs K _?n/2?,?n/2?. Fan [Discrete Math. 67 (1987), 235–240] proved the conjecture for n ≤ 24 and for n = 26, while Füredi [J. Graph Theory 16 (1992), 81–98] proved the conjecture for n > n ₀ where n ₀ is a tower of 2’s of height about 10¹⁴. The conjecture has yet to be proven for other values of n. Let Δ denote the maximum degree of G. We prove the following maximum degree theorems for diameter-2-critical graphs. If Δ ≥ 0.7 n, then the Murty-Simon Conjecture is true. If n ≥ 2000 and Δ ≥ 0.6789 n, then the Murty-Simon Conjecture is true.     

Rapid extraction and preservation of genomic DNA from human samples

Simple and rapid extraction of human genomic DNA remains a bottleneck for genome analysis and disease diagnosis. Current methods using microfilters require cumbersome, multiple handling steps in part because salt conditions must be controlled for attraction and elution of DNA in porous silica. We report a novel extraction method of human genomic DNA from buccal swab and saliva samples. DNA is attracted onto a gold-coated microchip by an electric field and capillary action while the captured DNA is eluted by thermal heating at 70 °C. A prototype device was designed to handle four microchips, and a compatible protocol was developed. The extracted DNA using microchips was characterized by qPCR for different sample volumes, using different lengths of PCR amplicon, and nuclear and mitochondrial genes. In comparison with a commercial kit, an equivalent yield of DNA extraction was achieved with fewer steps. Room-temperature preservation for 1 month was demonstrated for captured DNA, facilitating straightforward collection, delivery, and handling of genomic DNA in an environment-friendly protocol.

Mastoid Obliteration Using Three‐Dimensional Composite Scaffolds Consisting of Polycaprolactone/β‐Tricalcium Phosphate/Collagen Nanofibers: An In Vitro and In Vivo Study

Two different composite scaffolds, solid‐freeform‐fabricated PCL/β‐TCP supplemented with and without collagen nanofibers are fabricated. These scaffolds are evaluated whether a combination of collagen nanofibers with PCL/β‐TCP can promote osteogenesis in a mastoid obliteration. To assess the effects of the cellular activities of osteoblast‐like‐cells (MG63), SEM images and MTT assays are conducted. Experimental mastoid obliteration is performed using guinea pigs that are divided group A (PCL/β‐TCP/collagen‐nanofiber scaffold) and group B (PCL/β‐TCP scaffold). The results reveal that PCL/β‐TCP/collagen scaffold provide much broader cell attachment sites than PCL/β‐TCP scaffold. The µ‐CT and fluorescent microscopy results reveal that the acceleration of early new bone formation within the pores and scaffold itself at week 4 post‐operation is more effective in group A. In addition, based on the results of the histological and µ‐CT at 12 weeks post‐surgery, the effective regeneration of bone in the PCL/β‐TCP/collagen scaffold is appeared.

     

Ultrathin Hexagonal Hybrid Nanosheets Synthesized by Graphene Oxide‐Assisted Exfoliation of β‐Co(OH)2 Mesocrystals

In the present study, we report the synthesis of a high‐quality, single‐crystal hexagonal β‐Co(OH)₂ nanosheet, exhibiting a thickness down to ten atomic layers and an aspect ratio exceeding 900, by using graphene oxide (GO) as an exfoliant of β‐Co(OH)₂ nanoflowers. Unlike conventional approaches using ionic precursors in which morphological control is realized by structure‐directing molecules, the β‐Co(OH)₂ flower‐like superstructures were first grown by a nanoparticle‐mediated crystallization process, which results in large 3D superstructure consisting of ultrathin nanosheets interspaced by polydimethoxyaniline (PDMA). Thereafter, β‐Co(OH)₂ nanoflowers were chemically exfoliated by surface‐active GO under hydrothermal conditions into unilamellar single‐crystal nanosheets. In this reaction, GO acts as a two‐dimensional (2D) amphiphile to facilitate the exfoliation process through tailored interactions between organic and inorganic molecules. Meanwhile, the on‐site conjugation of GO and Co(OH)₂ promotes the thermodynamic stability of freestanding ultrathin nanosheets and restrains further growth through Oswald ripening. The unique 2D structure combined with functionalities of the hybrid ultrathin Co(OH)₂ nanosheets on rGO resulted in a remarkably enhanced lithium‐ion storage performance as anode materials, maintaining a reversible capacity of 860 mA h g^?1 for as many as 30 cycles. Since mesocrystals are ubiquitous and rich in morphological diversity, the strategy of the GO‐assisted exfoliation of mesocrystals developed here provides an opportunity for the synthesis of new functional nanostructures that could bear importance in clean renewable energy, catalysis, photoelectronics, and photonics.     

Almost Minimum Diameter Orientations of Semicomplete Multipartite and Extended Digraphs

 An orientation of a digraph D is a spanning subdigraph of D obtained from D by deleting exactly one arc between x and y for every pair x≠y of vertices such that both x y and y x are in D. Almost minimum diameter orientations of certain semicomplete multipartite and extended digraphs are considered, several generalizations of results on orientations of undirected graphs are obtained, some conjectures are posed. Received: August 31, 2000 Final version received: October 30, 2001 Acknowledgments. Part of this work was done when the first author was visiting the Department of Mathematics, National University of Singapore. The departmental hospitality and financial support are very much appreciated.     

Experimental Characterization of On-Chip Single and Double-Coupling Spiral Inductors

Experimental investigations on on-chip single and double-coupling square spiral inductors on silicon substrate are performed. For each pair of double-coupling inductors, they have the same edge distance, but with different turn numbers. Based on the measured S-parameters using de-embedding procedure, the inductance and Q-factor of the single square inductor are examined at first, and good agreement is obtained in the extracted inductance, compared to the predicted values using a closed-form series inductance equation. While for double-coupling spiral inductors, the smaller the product of two turn numbers, the weaker coupling will be, and in particular at low frequencies.     

The vibrational spectra of the boron halides and their molecular complexes, part 5 An ab initio study of the infrared spectrum of the boron trifluoride-carbon dioxide complex

The optimized structures, interaction energies, Mulliken charges and vibrational spectra of three conformers of a 1:1 complex between boron trifluoride and carbon dioxide have been determined by means of ab initio calculations at the second-order level of M?ller-Plesset perturbation theory, using the 6-31G* basis set. All three structures feature a B⋯O electron donor-acceptor interaction. One of the structures, in which the carbon dioxide axis eclipses one of the BF bonds, was found to be a genuine minimum, one (the corresponding staggered form) a first-order saddle point and the third (a linearly bonded B⋯OCO species) a second-order transition state. The computed infrared spectrum of the preferred conformer has been used to predict the appearance of the spectrum of boron trifluoride and carbon dioxide co-deposited in cryogenic matrices, which will be reported in a forthcoming publication. Received: 18 November 1996 / Accepted: 11 March 1997     

Simultaneous determination of udenafil and its active metabolite, DA-8164, in human plasma and urine using ultra-performance liquid chromatography-tandem mass spectrometry: application to a pharmacokinetic study

A rapid, sensitive, and simple ultra-performance liquid chromatography-tandem mass spectrometry (UPLC/MS/MS) method for the determination of udenafil and its active metabolite, DA-8164, in human plasma and urine using sildenafil as an internal standard (IS) was developed and validated. Udenafil, DA-8164 and IS from a 100 microL aliquot of biological samples were extracted by protein precipitation using acetonitrile. Chromatographic separation was carried on an Acquity UPLC BEH C(18) column (50 x 2.1 mm, i.d., 1.7 microm) with an isocratic mobile phase consisting of acetonitrile and containing 0.1% formic acid (75:25, v/v) at flow rate of 0.4 mL/min, and total run time was within 1 min. Detection and quantification was performed by the mass spectrometer using multiple reaction-monitoring mode at m/z 517 --> 283 for udenafil, m/z 406 --> 364 for DA-8164 and m/z 475 --> 100 for IS. The assay was linear over a concentration range of 1-600 ng/mL with a lower limit of quantification of 1 ng/mL in both human plasma and urine. The coefficient of variation of this assay precision was less than 13.7%, and the accuracy exceeded 92.0%. This method was successfully applied for pharmacokinetic study after oral administration of udenafil 100 mg to healthy Korean male volunteers.     

Surface vibration induced spatial ordering of periodic polymer patterns on a substrate

We demonstrate the possibility of producing regular, long-range, spatially ordered polymer patterns without requiring the use of physical or chemical templating through the interfacial destabilization of a thin polymer film driven by surface acoustic waves (SAWs). The periodicity and spot size of the pattern are observed to be dependent on a single parameter, that is, the SAW frequency (or wavelength), therefore offering a rapid, simple, yet novel method for self-organized regular spatial polymer pattern formation that is far more tunable than conventional polymer patterning procedures.     

Determination of kinetic parameters for interfacial enzymatic reactions on self-assembled monolayers

This paper reports a method to characterize the kinetic constants for the action of enzymes on immobilized substrates. This example uses cutinase, a serine esterase that hydrolyzes 4-hydroxyphenyl valerate moieties that are immobilized on a self-assembled monolayer of alkanethiolates on gold. The product of the enzyme reaction is a hydroquinone, which is redox active and therefore permits the use of cyclic voltammetry to monitor the extent of reaction in situ. A kinetic model based on the Michaelis-Menten formalism is used to analyze the dependence of initial rates of reaction on both the substrate density and the enzyme concentration. The resulting value of k(cat)/K(M) for the interfacial reaction is comparable to that for a homogeneous phase reaction with a substrate of similar structure. This strategy of using monolayers presenting substrates for the enzyme and cyclic voltammetry to measure reaction rates provides quantitative and real-time information on reaction rates and permits a level of analysis of interfacial enzyme reactions that to date has been difficult to realize.