Algorithms for Approximate Shortest Path Queries on Weighted Polyhedral Surfaces

We consider the well-known geometric problem of determining shortest paths between pairs of points on a polyhedral surface P, where P consists of triangular faces with positive weights assigned to them. The cost of a path in P is defined to be the weighted sum of Euclidean lengths of the sub-paths within each face of P.     

Self‐immolative dendrimers as novel drug delivery platforms

Self‐immolative dendrimers were recently developed and introduced as a potential platform for a single‐triggered multi‐prodrug. These unique structural dendrimers can release all of their tail units through domino‐like chain fragmentation, which is initiated by a single cleavage at the dendrimer core. The incorporation of drug molecules as the tail units and an enzyme substrate as the trigger generates a multi‐prodrug unit that is activated with a single enzymatic cleavage. We have demonstrated several examples of self‐immolative dendritic prodrug systems and have shown significant advantages with respect to the appropriate monomeric prodrug. We anticipate that single‐triggered, dendritic prodrugs will be exploited to further improve selective chemotherapeutic approaches in cancer therapy. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1569–1578, 2006     

Antibody-catalyzed asymmetric intramolecular Michael addition of aldehydes and ketones to yield the disfavored cis-product

The development of new catalytic asymmetric reactions continues to be a major goal in organic chemistry. Here we report a novel antibody-catalyzed intramolecular Michael addition of aldehydes and ketones to enones. The reaction is enantioselective and diastereoselective with a high ee value and cis/trans ratio. This is the first example of asymmetric intramolecular Michael addition of ketones. Antibody 38C2 is the only catalyst to date capable of generating this selectivity in Michael addition products.     

A Combinatorial Proof of Bass's Evaluations of the Ihara-Selberg Zeta Function for Graphs

We derive combinatorial proofs of the main two evaluations of the Ihara-Selberg zeta function associated with a graph. We give three proofs of the first evaluation all based on the algebra of Lyndon words. In the third proof it is shown that the first evaluation is an immediate consequence of Amitsur's identity on the characteristic polynomial of a sum of matrices. The second evaluation of the Ihara-Selberg zeta function is first derived by means of a sign-changing involution technique. Our second approach makes use of a short matrix-algebra argument.

     

On Burgers-type equations with nonmonotonic dissipative fluxes

We study a formation of patterns in Burgers-type equations endowed with a bounded but nonmonotonic dissipative flux: u_t + f(u)_x = ± νQ(u_x)_x, Q(s) = s/(1 + s²). Issues of uniqueness, existence, and smoothness of a solution are addressed. Asymptotic regions of a solution are discussed; in particular, classical and nonclassical traveling waves with an embedded subshock are constructed. © 1998 John Wiley & Sons, Inc.     

Kronecker type theorems,normality and continuity of the multivariate Padé operator

Summary. For univariate functions the Kronecker theorem, stating the equivalence between the existence of an infinite block in the table of Padé approximants and the approximated function being rational, is well-known. In [Lubi88] Lubinsky proved that if is not rational, then its Padé table is normal almost everywhere: for an at most countable set of points the Taylor series expansion of is such that it generates a non-normal Padé table. This implies that the Padé operator is an almost always continuous operator because it is continuous when computing a normal Padé approximant [Wuyt81]. In this paper we generalize the above results to the case of multivariate Padé approximation. We distinguish between two different approaches for the definition of multivariate Padé approximants: the general order one introduced in [Levi76, CuVe84] and the so-called homogeneous one discussed in [Cuyt84]. Received December 19, 1994     

Two-step enantio-selective optical switch

We present an optical "enantio-selective switch" that, in two steps, turns a ("racemic") mixture of left-handed and right-handed chiral molecules into the enantiomerically pure state of interest. The optical switch is composed of an "enantio-discriminator" and an "enantio-converter" acting in tandem. The method is robust, insensitive to decay processes, and does not require molecular preorientation. We demonstrate the method on the purification of a racemate of (transiently chiral) D2S2 molecules, performed on the nanosecond time scale.