Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting

In this paper we discuss Sobolev bounds on functions that vanish at scattered points in a bounded, Lipschitz domain that satisfies a uniform interior cone condition. The Sobolev spaces involved may have fractional as well as integer order. We then apply these results to obtain estimates for continuous and discrete least squares surface fits via radial basis functions (RBFs). These estimates include situations in which the target function does not belong to the native space of the RBF.

     

PDE with Random Coefficients and Euclidean Field Theory

In this paper a new proof of an identity of Giacomin, Olla, and Spohn is given. The identity relates the 2 point correlation function of a Euclidean field theory to the expectation of the Green's function for a pde with random coefficients. The Euclidean field theory is assumed to have convex potential. An inequality of Brascamp and Lieb therefore implies Gaussian bounds on the Fourier transform of the 2 point correlation function. By an application of results from random pde, the previously mentioned identity implies pointwise Gaussian bounds on the 2 point correlation function.     

A Bitangential Interpolation Problem on the Closed Unit Ball for Multipliers of the Arveson Space

We solve a bitangential interpolation problem for contractive multipliers on the Arveson space with an arbitrary interpolating set in the closed unit ball . The solvability criterion is established in terms of positive kernels. The set of all solutions is parametrized by a Redheffer transform. Submitted: February 2, 2002.     

Enhanced visualization methods for interpretation of wind tunnel data

Journal of Visualization -     

Increased Photosensitivity in HL60 Cells Expressing Wild-Type p53

Loss of p53 function has been correlated with decreased sensitivity to chemotherapy and radiation therapy in a variety of human tumors. Comparable analysis of p53 status with sensitivity to oxidative stress induced by pho-todynamic therapy has not been reported. In the current study we examined photosensitivity in human promye-locytic leukemia HL60 cells exhibiting either wild-type p53, mutated p53 or deleted p53 expression. Experiments were performed using a purpurin, tin ethyl etiopurpurin (SnET2)-, or a porphyrin, Photofrin (PH)-based photo-sensitizer. Total SnET2 accumulation was comparable in all three cell lines. Uptake of PH was highest in cells expressing wild-type p53 but incubation conditions could be adjusted to achieve equivalent cellular PH levels during experiments that analyzed photosensitivity. Survival measurements demonstrated that HL60 cells expressing wild-type p53 were more sensitive to PH- and SnET2-mediated photosensitization, as well as to UVC irradiation, when compared to HL60 cells exhibiting deleted or mutated p53 phenotypes. A rapid apoptotic response was observed following purpurin- and porphyrin-induced photosensitization in all cell lines. Results of this study indicate that photosensitivity is increased in HL60 cells expressing wild-type p53 and that photosensitizer-medi-ated oxidative stress can induce apoptosis through a p53-independent mechanism in HL60 cells .     

Access to Paullone Analogues by Intramolecular Heck Reaction

The syntheses of paullone ( 1a ) and three paullone derivatives, including a sulfur analogue ( 2a ), a tricyclic derivative ( 2b ), and a ring‐enlarged variant ( 2c ), are described, Pd‐catalyzed intramolecular Heck reaction being the key step. The kinase‐inhibitory properties of the novel paullone analogues were investigated.     

An Interval-Parameter Fuzzy Approach for Multiobjective Linear Programming Under Uncertainty

An interval-parameter fuzzy linear programming method (IFMOLP) is proposed in this study for multiple objective decision-making under uncertainty. As a hybrid of interval-parameter and fuzzy methodologies, the IFMOLP incorporates interval-parameter linear programming and fuzzy multiobjective programming approaches to form an integrated optimization system. The method inherits advantages of interval-parameter programming, and allows uncertainties and decision-makers’ aspirations to be effectively communicated into its programming processes and resulting solutions. Membership functions for both objectives and constraints are formulated to reflect uncertainties in different system components and their interrelationships. An interactive solution procedure has been developed based on solution approaches of the interval-parameter and fuzzy programming techniques, plus necessary measures for handling the multiobjective feature. A didactic example is provided in the paper to illustrate the detailed solution process. Possibilities of further improvements by seeking Pareto optimum and incorporating flexible preference within constraints are also discussed.