On the density of 2‐colorable 3‐graphs in which any four points span at most two edges

Let ex₂(n, K) be the maximum number of edges in a 2‐colorable K‐free 3‐graph (where K={123, 124, 134} ). The 2‐chromatic Turán density of K is $\pi_{2}({K}_{4}^-) =lim_{{n}\to \infty} {ex}_{2}({n}, {K}_{4}^-)/\left(_{3}^{n}\right)Let ex₂(n, K) be the maximum number of edges in a 2‐colorable K‐free 3‐graph (where K={123, 124, 134} ). The 2‐chromatic Turán density of K is $\pi_{2}({K}_{4}^-) =lim_{{n}\to \infty} {ex}_{2}({n}, {K}_{4}^-)/\left(_{3}^{n}\right)$. We improve the previously best known lower and upper bounds of 0.25682 and 3/10?ε, respectively, by showing that This implies the following new upper bound for the Turán density of K In order to establish these results we use a combination of the properties of computer‐generated extremal 3‐graphs for small n and an argument based on “super‐saturation”. Our computer results determine the exact values of ex(n, K) for n≤19 and ex₂(n, K) for n≤17, as well as the sets of extremal 3‐graphs for those n. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 105–114, 2010     

Diminishing blocking interval in particle-conveying channel bundles

We consider a channel bundle consisting of N_c parallel channels conveying a particulate flux. Particles enter these channels according to a homogeneous Poisson process and exit after a fixed transit time, τ. An individual channel blocks if N particles are simultaneously present. When a channel is blocked the flux previously entering it is redistributed evenly over the remaining open channels. We perform event driven simulations to examine the behaviour of an initially empty channel bundle with a total entering flux of intensity Λ. The mean blockage time of the kth channel is denoted by ? t_k ? ,k = 1,...,N_c. For N = 1, as shown previously, the interval between successive blockages is constant, while for N> 1 an accelerating cascade, i.e. one in which the interval between successive blockages decreases, is observed. After an initial transient regime we observe a well-defined universal regime that is characterized by\hbox{$\Delta_k^{(N)} = (-1)^{N-1}\frac{[(N-1)!]^2}{(\Lambda\tau)^N}$}Δk(N)=(?1)N?1[(N?1)!]2(Λτ)Nwhere \hbox{$\Delta_k^{(1)}=\langle t_k \rangle-\langle t_{k-1}\rangle$}Δk(1)=?tk???tk?1? and \hbox{$\Delta_k^{(j)}=\Delta_k^{(j-1)}-\Delta_{k-1}^{(j-1)}$}Δk(j)=Δk(j?1)?Δk?1(j?1) denotes the jth order difference.     

A new biolistic intradermal injector

We present a novel intradermal needle-free drug delivery device which exploits the unsteady high-speed flow produced by a miniature shock tube to entrain drug or vaccine particles onto a skin target. A first clinical study of pain and physiological response of human subjects study is presented, comparing the new injector to intramuscular needle injection. This clinical study, performed according to established pain assessment protocols, demonstrated that every single subject felt noticeably less pain with the needle-free injector than with the needle injection. Regarding local tolerance and skin reaction, bleeding was observed on all volunteers after needle injection, but on none of the subjects following powder injection. An assessment of the pharmacodynamics, via blood pressure, of pure captopril powder using the new device on spontaneously hypertensive rats was also performed. It was found that every animal tested with the needle-free injector exhibited the expected pharmacodynamic response following captopril injection. Finally, the new injector was used to study the delivery of an inactivated influenza vaccine in mice. The needle-free device induced serum antibody response to the influenza vaccine that was comparable to that of subcutaneous needle injection, but without requiring the use of an adjuvant. Although no effort was made to optimize the formulation or the injection parameters in the present study, the novel injector demonstrates great promise for the rapid, safe and painless intradermal delivery of systemic drugs and vaccines.     

Copper-catalyzed functionalization of enynes

The copper-catalyzed functionalization of enyne derivatives has recently emerged as a powerful approach in contemporary synthesis. Enynes are versatile and readily accessible substrates that can undergo a variety of reactions to yield densely functionalized, enantioenriched products. In this perspective, we review copper-catalyzed transformations of enynes, such as boro- and hydrofunctionalizations, copper-mediated radical difunctionalizations, and cyclizations. Particular attention is given to the regiodivergent functionalization of 1,3-enynes, and the current mechanistic understanding of such processes.

The copper-catalyzed functionalization of enynes is a powerful approach to yield densely functionalized products. This review covers various transformations, such as boro- and hydrofunctionalizations, copper-mediated radical difunctionalizations, and cyclizations.     

Spherical models with a Gates-Penrose-type phase transition

Gates and Penrose have given criteria under which classical gases with weak long-range interactions fail to be described by the van der Waals equation with Maxwell's rule. Unfortunately, examples of equations of state for such systems have not yet been produced. This paper examines the Gates-Penrose class of interactions-i.e.,U (r)=q(r)+(r), in the limit0, where the Fourier transform (p) has a minimum at a nonzero value ofp-for the spherical model on a one-dimensional lattice. Free energy and magnetization isotherms are computed; it is seen that there is a phase transition, but that the zero-field spontaneous magnetization is always zero (a parahelicoidal phase). However, the pair-correlation function may exhibit either long-range order or the appearance of oscillation.     

Synthesis and characterization of an azobenzene‐ and acrylamide‐based photoresponsive copolymer and gel

This article reports the synthesis and characterization of a new type of copolymer consisting of acrylamide and trans‐4‐methacroyloxyazobenzene and their gel. Free‐radical polymerization initiated with 2,2′‐azobisisobutyronitrile was used to conduct the synthesis although N,N′‐methylene bisacrylamide was used as a crosslinking agent for the gel synthesis. Despite the insolubility of the different monomers in a single solvent, a certain ratio of water/tetrahydrofuran (THF) enabled the propagating species to stay in the solution and thus to facilitate chain growth. The solubility, Fourier transform infrared spectra, and solid‐state ¹³C NMR investigations revealed that two monomers in the copolymer were chemically bonded. The compositions of the incorporated acrylamide and azobenzene in the copolymer and the gel were determined by NMR spectroscopy. Because the potential actuating behavior of such materials was due to the volume change involved in reversible solvent uptake, the sorption and evaporation of the gel were also investigated and showed that the gel could absorb about 460% water, which corresponded to a polymer content of the weight gel of 18% and was compatible with thermogravimetric analysis of a saturated gel that revealed about 83 wt % of a swollen gel was lost within 12 h. Finally, photoinduced trans–cis isomerization kinetics of the copolymer was investigated in a 30:70 mixture of water and THF against irradiation time. A photostationary state was reached within 5.5 min with a corresponding conversion of 70% of the trans isomer to the cis form. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2886–2896, 2004     

Characteristic fragmentation of bacteriohopanepolyols during atmospheric pressure chemical ionisation liquid chromatography/ion trap mass spectrometry

Bacteriohopanepolyols (BHPs) fragment via characteristic pathways during atmospheric pressure chemical ionisation liquid chromatography/ion trap mass spectrometry (APCI-LC/MS(n)). Comparison of the MS(2) spectra of bacteriohopane-32,33,34,35-tetrol (BHT) and 2 beta-methylbacteriohopane-32,33,34,35-tetrol has confirmed the previously proposed ring-C cleavage occurring between C-9 and 11 and C-8 and 14. This fragmentation, diagnostic of all hopanoids, also occurs in BHPs containing an amino group (-NH(2)) at C-35 although the higher relative stability of the ion limits this fragmentation to a minor process after protonation of the basic nitrogen function. Studies of a number of cell cultures including a prochlorophyte (Prochlorothrix hollandica) and a cyanobacterium (Chlorogloeopsis LA) demonstrate the power of this technique to detect composite BHPs with a complex biological functionality at C-35. We also report the first observation of intact pentafunctionalised bacteriohopanepolyols using this method.     

Development of a two-color laser fluorescence detector. On-line detection of internal standards and unknowns by capillary electrophoresis within the same sample

A two-laser, two-color detector has been developed for the simultaneous detection of naturally occurring and recombinant (internal standards) cytokines within the same biological sample. The internal standards were labeled with Bimane and detected with a 408 nm laser while the natural cytokines were labeled with AlexaFluor633 and detected with a 633 nm laser. The two resulting electropherograms were plotted as overlaid traces and quantification of the natural materials determined by comparison with the standards. Using this system, recovery of all four cytokine standards was greater than 94% in both saline and cytokine-depleted plasma. These recoveries could be achieved with intra- and inter-assay coefficients of variance (c.v.) of less than 4.5 and 5.6, respectively. Application of this system to the examination of clinical samples demonstrated that measurement of the four pro-inflammatory cytokines could distinguish between normals, sub-clinical and clinical inflammation. An advantage of this approach is that direct calculation of unknowns by comparison to identical internal standards can shorten analytical time by eliminating the need for additional standard or calibration runs.