Adaptive Interpolation by Scaled Multiquadrics

We present an adaptive method to extract shape-preserving information from a univariate data sample. The behavior of the signal is obtained by interpolating at adaptively selected few data points by a linear combination of multiquadrics with variable scaling parameters. On the theoretical side, we give a sufficient condition for existence of the scaled multiquadric interpolant. On the practical side, we give various examples to show the applicability of the method.     

Elevation of the glass transition temperature in flexible‐chain semicrystalline polymers

In the idealized two‐phase model of a semicrystalline polymer, the amorphous intercrystalline layers are considered to have the same properties as the fully‐amorphous polymer. In reality, these thin intercrystalline layers can be substantially influenced by the presence of the crystals, as individual polymer molecules traverse both crystalline and amorphous phases. In polymers with rigid backbone units, such as poly(etheretherketone), PEEK, previous work has shown this coupling to be particularly severe; the glass transition temperature (T_g) can be elevated by tens of degrees celsius, with the magnitude of the elevation correlating directly with the thinness of the amorphous layer. However, this connection has not been explored for flexible‐chain polymers, such as those formed from vinyl‐type monomers. Here, we examine T_g in both isotactic polystyrene (iPS) and syndiotactic polystyrene (sPS), crystallized under conditions that produce a range of amorphous layer thicknesses. T_g is indeed shown to be elevated relative to fully‐amorphous iPS and sPS, by an amount that correlates with the thinness of the amorphous layer; the magnitude of the effect is severalfold less than that in PEEK, consistent with the minimum lengths of polymer chain required to make a fold in the different cases. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1198–1204, 2007     

A solution to Schrödinger's problem of non-linear integral equations

A solution of Schrödinger's system of non-linear integral equations determines the rate function of a large deviation principle for kernels with prescribed marginal distributions. This kind of large deviation principle has some meaning in quantum mechanics.Diffusion equations associated with Schrödinger equations have typically transition functions with singular creation and killing. Hence they provide measurable non-negative generally unbounded kernels which may vanish on sets with positive measure and which can possess infinite mass.For Schrödinger systems with such kernels, a solution is proved to exist uniquely in terms of a product measure. It is obtained from a variational principle for the local adjoint of a product measure endomorphism. The generally unbounded factors of the solution are characterized by integrability properties.     

Miscibility of polyester/nitrocellulose blends: A DSC and FTIR study

The miscibility of polyester/nitrocellulose blends was investigated by differential scanning calorimetry and Fourier-transform infrared (FTIR) spectroscopy. Two nitrocelluloses (NC) derived from wood and having different nitrogen contents (12.62 and 13.42%) were used. On the basis of the glass transition temperature criterion, poly(?-caprolactone) (PCL), poly(valerolactone), poly(ethylene adipate), and poly(butylene adipate) are miscible with nitrocellulose, whereas poly(α-methyl α-propyl β-propiolactone) and poly(α-methyl β-proiolactone) are immiscible. The T_g versus composition curves of PCL/NC blends do not follow a monotone function but exhibit a singular point at a critical PCL volume fraction of 0.51 for NC-1342 and 0.45 for NC-1262 in agreement with Kovacs' theory. A shift of 17 cm^-1 of the carbonyl stretching band was observed with PCL/NC blends and is taken as evidence for hydrogen bonding interaction between the PCL carbonyl group and NC hydroxyl group. The frequency difference between the free hydroxyl absorbance and the absorbances of the hydrogen-bonded species was found to be 85 cm^-1 in pure NC and 125 cm^-1 in PCL/NC blends; it indicates that the average strength of this interaction is stronger than the corresponding self-associated hydrogen bonding in pure NC. The presence of a dipole-dipole interaction between the nitrate-ester groups of NC and the carbonyl groups of the polyesters is reported. The relative strength of the hydrogen bonding and dipole-dipole interactions is discussed and correlated with polymer miscibility.     

Pure adaptive search in global optimization

Pure adaptive seach iteratively constructs a sequence of interior points uniformly distributed within the corresponding sequence of nested improving regions of the feasible space. That is, at any iteration, the next point in the sequence is uniformly distributed over the region of feasible space containing all points that are strictly superior in value to the previous points in the sequence. The complexity of this algorithm is measured by the expected number of iterations required to achieve a given accuracy of solution. We show that for global mathematical programs satisfying the Lipschitz condition, its complexity increases at mostlinearly in the dimension of the problem.This work was supported in part by NATO grant 0119/89.     

TGF-β1 induction of the adenine nucleotide translocator 1 in astrocytes occurs through Smads and Sp1 transcription factors

Background  

The adenine nucleotide translocator 1 (Ant1) is an inner mitochondrial membrane protein involved with energy mobilization during oxidative phosphorylation. We recently showed that rodent Ant1 is upregulated by transforming growth factor-beta (TGF-β) in reactive astrocytes following CNS injury. In the present study, we describe the molecular mechanisms by which TGF-β1 regulates Ant1 gene expression in cultured primary rodent astrocytes.