Synthesis of Novel Monomeric Dyes with Anthraquinone Residue

Two novel polymerizable dyes with anthraquinone residue have been prepared, and their structures were characterized by FTIR, ^1HNMR and EA.     

Moments of an exponential functional of random walks and permutations with given descent sets

The exponential functional of simple, symmetric random walks with negative drift is an infinite polynomial Y = 1 + ξ₁ + ξ₁ξ₂ + ξ₁ξ₂ξ₃ + ⋯ of independent and identically distributed non-negative random variables. It has moments that are rational functions of the variables μ _k = E(ξ ^k ) < 1 with universal coefficients. It turns out that such a coefficient is equal to the number of permutations with descent set defined by the multiindex of the coefficient. A recursion enumerates all numbers of permutations with given descent sets in the form of a Pascal-type triangle. This revised version was published online in August 2006 with corrections to the Cover Date.     

Synthesis of paramagnetic BODIPY dyes as new double (spin and fluorescence) sensors

Paramagnetic pyrroline and 1,2,3,6-tetrahydropyridine derivatives of BODIPY and their diamagnetic analogs have been synthesized and characterized as novel redox double sensor and cation sensitive reagents.     

Non-Trivial t-Intersection in the Function Lattice

The function lattice, or generalized Boolean algebra, is the set of ℓ-tuples with the ith coordinate an integer between 0 and a bound n_i. Two ℓ-tuples t-intersect if they have at least t common nonzero coordinates. We prove a Hilton–Milner type theorem for systems of t-intersecting ℓ-tuples.Received September 29, 2004     

Study of the gas-phase parameters affecting the silicon-oxide film deposition induced by an ArF laser

A study of the gas-phase parameters involved in ArF laser induced chemical vapour deposition of silicon-oxide thin films is presented. A complete set of experiments has been performed showing the influence of the concentration of the precursor gases, N₂O and SiH₄, and their influence on total and partial pressures on film growth and properties. In this paper we demonstrate the ability of this LCVD method to deposit silicon oxide films of different compositions and densities by appropriate control of gas composition and total pressure. Moreover, a material specific calibration plot comprising data obtained using different preparation techniques is presented, allowing determination of the stoichiometry of SiO _x films by using FTIR spectroscopy independently of the deposition method. For the range of processing conditions examined, the experimental results suggest that chemical processes governing deposition take place mainly in the gas phase.     

Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant

Summary. This article contains an elementary constructive proof of resolution of singularities in characteristic zero. Our proof applies in particular to schemes of finite type and to analytic spaces (so we recover the great theorems of Hironaka). We introduce a discrete local invariant whose maximum locus determines a smooth centre of blowing up, leading to desingularization. To define , we need only to work with a category of local-ringed spaces satisfying certain natural conditions. If , then depends only on . More generally, is defined inductively after any sequence of blowings-up whose centres have only normal crossings with respect to the exceptional divisors and lie in the constant loci of . The paper is self-contained and includes detailed examples. One of our goals is that the reader understand the desingularization theorem, rather than simply “know” it is true. Oblatum 27-VII-1995 & 30-V-1996     

Detailed nuclear structure studies far from stability

State-of-the-art spectroscopy of nuclei far from stability has achieved an extraordinary level of sophistication and detail in the last ten years. In principle, if a state can be populated, it can be characterized by its energy, spin, parity, and major decay paths. Sometimes its lifetime can be measured. In practice, one is confronted with enormous complexity. To convert raw spectroscopic data into nuclear structure data involves a complex process of disentangling gamma rays and conversion electrons into decay schemes. Specifically, coincidence techniques, especially coincidence intensities, play a crucial role in this process. Recent examples and methods from work done at UNISOR are presented.     

RANDOM EDGE can be exponential on abstract cubes

We prove that RANDOM EDGE, the simplex algorithm that always chooses a random improving edge to proceed on, can take a mildly exponential number of steps in the model of abstract objective functions (introduced by Williamson Hoke [Completely unimodal numberings of a simple polytope, Discrete Appl. Math. 20 (1988) 69-81.] and by Kalai [A simple way to tell a simple polytope from its graph, J. Combin. Theory Ser. A 49(2) (1988) 381-383.] under different names). We define an abstract objective function on the n-dimensional cube for which the algorithm, started at a random vertex, needs at least exp(const·n^1/3) steps with high probability. The best previous lower bound was quadratic. So in order for RANDOM EDGE to succeed in polynomial time, geometry must help.