Escape times for branching processes with random mutational fitness effects

We consider a large declining population of cells under an external selection pressure, modeled as a subcritical branching process. This population has genetic variation introduced at a low rate which leads to the production of exponentially expanding mutant populations, enabling population escape from extinction. Here we consider two possible settings for the effects of the mutation: Case (I) a deterministic mutational fitness advance and Case (II) a random mutational fitness advance. We first establish a functional central limit theorem for the renormalized and sped up version of the mutant cell process. We establish that in Case (I) the limiting process is a trivial constant stochastic process, while in Case (II) the limit process is a continuous Gaussian process for which we identify the covariance kernel. Lastly we apply the functional central limit theorem and some other auxiliary results to establish a central limit theorem (in the large initial population limit) of the first time at which the mutant cell population dominates the population. We find that the limiting distribution is Gaussian in both Cases (I) and (II), but a logarithmic correction is needed in the scaling for Case (II). This problem is motivated by the question of optimal timing for switching therapies to effectively control drug resistance in biomedical applications.     

A new xanthone from Garcinia nitida

A detailed chemical study on the stem bark of Garcinia nitida has led to the isolation of five xanthones. They are 1,6-dihydroxy-5-methoxy-6,6-dimethylpyrano[2',3':2,3]-xanthone (1), inophyllin B (2), osajaxanthone (3), 3-isomangostin (4) and rubraxanthone (5). The structures of these compounds were established using mainly 1-D and 2-D NMR spectroscopy ((1)H, (13)C, DEPT, COSY, HMBC and HMQC) while molecular masses were determined via MS techniques; 1 is a new compound.     

Unimolecular ligand-initiator dual functional systems (ULIS) for low copper ATRP of vinyl monomers including acrylic/methacrylic acids

A novel approach for ATRP has been developed which enables the polymerization of vinyl monomers including those bearing carboxylic acid groups such as acrylic/methacrylic acid in the free acid form with ppm amounts of copper. The quantity of copper used in the polymerization is comparable to those left in purified polymers obtained by a conventional ATRP process.     

Superconductivity in three-layer Na0.3CoO2·1.3H2O

The observation of superconductivity at 4.3 K in a new crystalline form of Na_0.3CoO₂·1.3H₂O is reported. The new superconductor has three layers of CoO₆ octahedral per crystallographic unit cell, in contrast to the previously reported two-layer superconductor. The three-layer cell occurs because the relative orientations of neighboring CoO₂ layers are distinctly different from what is seen in the two-layer superconducting phase. This type of structural difference in materials that are otherwise chemically and structurally identical is not possible to attain on the layered copper oxide superconductors. The synthesis and stability of the new phase are described.     

Synthesis and characterization of a 1-D porous barium carboxylate coordination polymer, [Ba(HBTB)] (H3BTB = benzene-1,3,5-trisbenzoic acid)

The synthesis and characterization of [Ba(HBTB)] is reported. This is the first porous framework synthesized with barium using carboxylate ligands. The framework has robust microporous character (Langmuir surface area of 879 m(2) g(-1)) and possesses unsaturated metal sites when fully desolvated.     

Forced convective heat transfer enhancement with perforated pin fins

Increasing miniaturization of high speed multi-functional electronics demands ever more stringent thermal management. The present work investigates experimentally and numerically the use of staggered perforated pin fins to enhance the rate of heat transfer in these devices. In particular, the effects of the number of perforations and the diameter of perforation on each pin are studied. The results show that the Nusselt number for the perforated pins is 45 % higher than that for the conventional solid pins and it increases with the number of perforation. Pressure drop with perforated pins is also reduced by 18 % when compared with that for solid pins. Perforations produce recirculations in the x–y as well as the x–z planes downstream of the pins which effectively increase convective heat transfer. However, thermal dissipation decreases significantly when the ratio of pin diameter to perforation diameter exceeds 0.375. This is due to both a reduction in the number of perforation per pin and the decrease in the axial heat conduction along the pin.     

Parametric CR-umbilical locus of ellipsoids in C2

For every real numbers $a?1$, $b?1$ with $(a,b)\ne (1,1)$, the curve parametrized by $\theta \in \mathbb{R}$ valued in ${\mathbb{C}}^2?{\mathbb{R}}^4$

$\gamma :\theta ?(x(\theta )+\sqrt{?1}y(\theta ),u(\theta )+\sqrt{?1}v(\theta ))$

with components:

$\begin{array}{c}x(\theta ):=\sqrt{\frac{a?1}{a(ab?1)}}\cos ?\theta ,y(\theta ):=\sqrt{\frac{b(a?1)}{ab?1}}\sin ?\theta ,\hfill \\ u(\theta ):=\sqrt{\frac{b?1}{b(ab?1)}}\sin ?\theta ,v(\theta ):=?\sqrt{\frac{a(b?1)}{ab?1}}\cos ?\theta ,\hfill \end{array}$

has image contained in the CR-umbilical locus:

$\gamma (\mathbb{R})?\mathsf{UmbCR}\left({\mathsf{E}}_{a,b}\right)?{\mathsf{E}}_{a,b}$

of the ellipsoid ${\mathsf{E}}_{a,b}?{\mathbb{C}}^2$ of equation $a{x}^2+y^2+b{u}^2+v^2=1$, where the CR-umbilical locus of a Levi nondegenerate hypersurface $M^3?{\mathbb{C}}^2$ is the set of points at which the Cartan curvature of M vanishes.     

Mesomorphic behaviors of a series of heterocyclic benzothiazole-imine-ester-based liquid crystals

A series of new calamitic liquid crystals, 2-[4-(4-alkoxybenzoyloxy)benzylidenamino]benzothiazoles comprising a heterocyclic (benzothiazole) and two phenyl rings core system, terminal alkoxy chain, imine and ester linkers were prepared and characterized. This series comprises eight members wherein the members vary by the length of alkoxy chain (C_nH_2n+1O-, where n?=?4, 6, 8, 10, 12, 14, 16, 18). Spectral analysis results were in conformity with the expected structure. Their thermotropic behaviors were studied by using differential scanning calorimetry, optical polarizing microscopy and powder X-ray diffraction techniques. A single mesophase (nematic) was observed for the first member of the series (n?=?4). As the alkoxy chain increased to n?=?6, 8, 10, 12, 14, the nematic phase appeared together with an additional SmA phase. When moving from n?=?16 until the highest member (n?=?18), the nematic phase disappeared and these compounds only exhibited a single mesophase (SmA).