Localization of compact invariant sets and global stability in analysis of one tumor growth model

In this paper, we study some features of global behavior of the four‐dimensional superficial bladder cancer model with Bacillus Calmette‐Guérin (BCG) immunotherapy described by Bunimovich‐Mendrazitsky et al. in 2007 with the help of localization analysis of its compact invariant sets. Its dynamics is defined by the BCG treatment and by densities of three cells populations: effector cells, tumor infected cells by BCG, and tumor uninfected cells. We find upper bounds for ultimate dynamics of the whole state vector in the positive orthant and also under condition that there are no uninfected tumor cells. Further, we prove the existence of the bounded positively invariant domain in both of these two situations. Finally, by using these assertions, we derive our main result: sufficient conditions of global asymptotic stability of the tumor‐free equilibrium point in the positive orthant. Copyright © 2013 John Wiley & Sons, Ltd.     

Performance of columns packed with the new shell particles,Kinetex-C18

The performance of the new Kinetex-C₁₈ column was investigated. Packed with a new brand of porous shell particles, this column has an outstanding efficiency. Once corrected for the contribution of the instrument extra column volume, the minimum values of the reduced plate heights for a number of low molecular weight compounds (e.g., anthracene and naphtho[2,3-a]pyrene) were between 1.0 and 1.3, breaking the legendary record set 3 years ago by Halo-C₁₈ packed columns. The liquid-solid mass transfer of proteins (e.g., insulin and lyzozyme) is exceptionally fast on Kinetex-C₁₈ much faster than on the Halo-C₁₈ column. The different contributions of dispersion and mass transfer resistances to the column efficiency were determined and discussed. The possible reasons for this extremely high column efficiency are discussed.     

Simulation of non-Gaussian multivariate stationary processes

Mathematical justifications are given for a simulation technique of multivariate non-Gaussian random processes and fields based on Rosenblatt's transformation of Gaussian processes. Different types of convergences are given for the approaching sequence. Moreover an original numerical method is proposed in order to solve the functional equation yielding the underlying Gaussian process autocorrelation function.     

FRET detection of Octamer-4 on a protein nanoarray made by size-dependent self-assembly

An alternative approach for fabricating a protein array at nanoscale is suggested with a capability of characterization and/or localization of multiple components on a nanoarray. Fluorescent micro- and nanobeads each conjugated with different antibodies are assembled by size-dependent self-assembly (SDSA) onto nanometer wells that were created on a polymethyl methacrylate (PMMA) substrate by electron beam lithography (EBL). Antibody-conjugated beads of different diameters are added serially and electrostatically attached to corresponding wells through electrostatic attraction between the charged beads (confirmed by zeta potential analysis) and exposed p-doped silicon substrate underneath the PMMA layer. This SDSA method is enhanced by vibrated-wire-guide manipulation of droplets on the PMMA surface containing nanometer wells. Saturation rates of antibody-conjugated beads to the nanometer patterns are up to 97% under one component and 58–70% under two components nanoarrays. High-density arrays (up to 40,000 wells) could be fabricated, which can also be multi-component. Target detection utilizes fluorescence resonance energy transfer (FRET) from fluorescent beads to fluorescent-tagged secondary antibodies to Octamer-4 (Oct4), which eliminates the need for multiple steps of rinsing. The 100 nm green beads are covalently conjugated with anti-Oct4 to capture Oct4 peptides (39 kDa); where the secondary anti-Oct4 and F(ab)₂ fragment of anti-gIgG tagged with phycoerythrin are then added to function as an indicator of Oct4 detection. FRET signals are detected through confocal microscopes, and further confirmed by Fluorolog3 spectrofluorometer. The success rates of detecting Oct4 are 32% and 14% of the beads in right place under one and two component nanoarrays, respectively. Ratiometric FRET is used to quantify the amount of Oct4 peptides per each bead, which is estimated about 2 molecules per bead.     

Allenylzincs and tert-butylsulfinylimines: a fruitful marriage for synthesis

The stereoselective synthesis of alkynyl 1,2-amino alcohols by the addition of 3-chloro- and 3-methoxymethoxy- allenylzincs to chiral tert-butylsulfinylimines is described. The methodology is applicable to the preparation of alkynyl 2-amino-1,3-diols (O,N,O stereotriads) using α-alkoxy tert-butylsulfinylimines as chiral starting materials. The scope and limitations of the methodology along with recent applications to the efficient asymmetric syntheses of natural and/or bioactive alkaloids and polyhydroxylated alkaloids are presented.     

Polynomial and regular images of ℝ n

We obtain new necessary conditions for ann-dimensional semialgebraic subset of ℝ ⁿ to be a polynomial image of ℝ ⁿ . Moreover, we prove that a large family of planar bidimensional semialgebraic sets with piecewise linear boundary are images of polynomial or regular maps, and we estimate in both cases the dimension of their generic fibers. Supported by Spanish GAAR BFM2002-04797 and European RAAG HPRN-CT-2001-00271.     

Skew-product decompositions of Brownian motions on manifolds: A probabilistic aspect of the Lichnerowicz-Szabo theorem

We show that the only compact simply connected manifolds for which the radial part of Brownian motion enjoys the Markov property are compact two points homogeneous spaces, i.e. rank one symmetric spaces.     

An algorithm to compute odd orders and ramification indices of cyclic actions on compact surfaces

In this paper we get an effective algorithm to compute all odd orders and ramification indices of homeomorphisms acting on compact surfaces, orientable or not. E. Bujalance and A. F. Costa were partially supported by DGICYT PB 89-201 and Science Plan N SC1-CT91-0716, J. M. Gamboa was partially supported by DGICYT PB 89-379 and Science Plan N SC1-CT91-0716, and J. Lafuente was partially supported by Science Plan N SC1-CT91-0716.