On quadratic convergence of the initial value adjusting method for nonlinear multipoint boundary value problems

A natural interpretation of “maj” and “inv” q-counting of multiset permutations in terms of walks on a lattice with multilane highways is presented. This is applied to give a short combinatorial proof of two theorems of MacMahon and to rederive a recent result of Gessel.     

Multipoint boundary value problems with discontinuities II. Convergence of the initial value adjusting method

In this paper we give a proof for convergence of the initial value adjusting method, described in detail in part I, based on Kantorovich's theorem. Under standard assumptions on the dynamics, boundary conditions, and initial approximations, a quadratic convergence rate is obtained.     

Molecular structure of phosgene as studied by gas electron diffraction and microwave spectroscopy: The rs,rm, and re structures

The microwave spectra of eight isotopic species of COCl₂ have been observed, and the following rotational constants have been obtained: An analysis of the rotational constants has resulted in the r_s and r_m structures. The equilibrium structure, r_e, has been estimated by combining the r_m parameters derived according to Watson's method and the r_e bond distances estimated in our recent electron-diffraction and spectroscopic studies to be $\text{r}{}_{\mathrm{e}}\text{(CO}\text{) = 1.1756 ± 0.0023}\text{A}\text{?}$, $\text{r}{}_{\mathrm{e}}\text{(CCl}\text{) = 1.7381 ± 0.0019}\text{A}\text{?}$, ∠_eClCCl = 111.79 ± 0.24°.     

Novel lactonization of ethenetricarboxylate derivatives: intermolecular trapping of alkenes

A novel cyclization of 1,1-diethyl 2-tert-butyl ethenetricarboxylate (1a) in the presence of a Lewis acid afforded a 5,5-dimethyl-gamma-lactone derivative 2a. The reaction process has been shown to arise from formation by trapping of isobutylene generated in situ. Lewis acid-promoted intermolecular reactions of 1,1-diethyl 2-hydrogen ethenetricarboxylate (5) and various alkenes to afford highly functionalized gamma-lactones were also developed. [reaction: see text]     

Behavior of the Bergman kernel at infinity

We give a precise decay rate of the Bergman kernel and metric at infinity on model domains, characterized in terms of certain convex polyhedron.Supported by JSPS.     

Bilepton production in $ e^-\gamma $ collisions

We study the production of bileptons, new gauge bosons of lepton number two, in the minimal 3-3-1 model in high energy collisions. If the bilepton masses are in the range of 300 GeV the reaction will give observable cross-sections in future colliders.Received: 5 August 2003, Published online: 23 March 2004Dang Van Soa: On leave of absence from Department of Physics, Hanoi University of Education, Hanoi, VietnamHoang Ngoc Long: On leave of absence from Institute of Physics, NCST, P.O. Box 429, Bo Ho, Hanoi 10000, Vietnam     

Reductive electron injection into duplex DNA by aromatic amines

An assay based on photoinduced reaction and subsequent cleavage of duplex DNA containing a bromodeoxyuridine ((Br)U) residue and an abasic site was developed to screen aromatic amines for their ability to initiate charge transfer by reductive electron donation. Two candidates, N,N,N',N'-tetramethyl-1,5-diaminonaphthalene (TMDN) and 1,5-diaminonaphthalene (DAN), expressed the desired activity, and an oligodeoxynucleotide-TMDN conjugate was subsequently prepared to identify additional variables affecting the efficiency of electron injection and transfer into DNA. This system demonstrated only mild sensitivity to molecular oxygen but was strongly inhibited by high concentrations of 2-mercaptoethanol. The nucleobase counter to the attached TMDN strongly modulated charge transfer as evident by a 60-fold decrease in reduction of the distal (Br)U when the counterbase A was substituted for C. An inverse relationship between this reduction and quenching of TMDN fluorescence by the counterbase was also discovered and is consistent with a competition between radical recombination and electron migration away from the initial site of its injection into DNA.