Space-time analytic smoothing effect for the pseudo-conformally invariant Schrödinger equations

We study the global Cauchy problem for the mass critical nonlinear Schrödinger equations. We prove the global existence of analytic solutions in both space and time variables for sufficiently small and exponentially decaying Cauchy data. The method of proof depends on the Leibniz rule for the generator of pseudo-conformal transforms at the L ² critical level.     

Covering vertices of a graph by k disjoint cycles

Let d, k and n be three integers with k3, d4k−1 and n3k. We show that if d(x)+d(y)d for each pair of nonadjacent vertices x and y of a graph G of order n, then G contains k vertex-disjoint cycles converting at least min{d,n} vertices of G.     

Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations

We study the nonrelativistic limit of the Cauchy problem for the nonlinear Klein-Gordon equation and prove that any finite energy solution converges to the corresponding solution of the nonlinear Schr?dinger equation in the energy space, after the infinite oscillation in time is removed. We also derive the optimal rate of convergence in . Received: 13 July 2000 / Published online: 1 February 2002     

Absolute configurations of endoperoxides determined by vibrational circular dichroism (VCD)

Diastereomeric mixture on the peroxide portion of an endoperoxide acetylmajapolene A (1) was efficiently separated by HPLC on a chiral column, submitting to vibrational circular dichroism (VCD) investigation. The ab initio theoretical VCD and IR calculations of 1a and 1b were performed by density functional theory (DFT) using the B3PW91/6-31G(d,p) level of theory. Focusing on an isolated characteristic peroxide vibrational band, absolute configurations of 1a and 1b were unambiguously determined as (1R,4R,7S,10S) and (1S,4S,7S,10S), respectively. This is the first VCD application to endoperoxides which exist abundantly in nature.     

Evaluation of efficiency of reference potential spatial warping algorithm in conformational sampling of peptides

Molecular dynamics (MD) simulation using the reference potential spatial warping algorithm (REPSWA) is a promising method for computing the conformational equilibrium of a system with a rugged energy surface. Its effectiveness has previously been demonstrated using only a simplified model system of a hydrocarbon chain omitting nonbonded interaction terms from the potential energy function. To evaluate the applicability of REPSWA MD simulation to more realistic problems, we applied it to small peptide systems in an aqueous environment. Difficulties were encountered, however, forcing us to devise several modifications. We investigated their effectiveness in comparison to conventional constant-temperature and multicanonical MD simulations. We found that the sampling efficiency of the modified REPSWA MD after a careful optimization of its parameters was better than that of the constant-temperature MD and comparable to that of the multicanonical MD in several cases.     

Total synthesis of (-)-kainic acid via intramolecular Michael addition: a second-generation route

A total synthesis of (-)-kainic acid starting from the commercially available 2-azetidinone is described. The key delta-lactone intermediate was concisely prepared from the commercially available azetidinone through the Reformatsky-type reaction and an introduction of a glycine moiety. The construction of the functionalized pyrrolidine ring was executed by a one-pot sequential elimination-Michael addition protocol of a beta-amino-delta-lactone intermediate with high diastereoselectivity.     

Synthesis of maremycins A and D1 via cycloaddition of a nitrone with (E)-3-ethylidene-1-methylindolin-2-one

A concise synthesis of maremycins A and D1 has been accomplished via cycloaddition of a chiral cyclic nitrone with ( E)-3-ethylidene-1-methylindolin-2-one as a key step. This synthesis clarifies the stereochemistry of the maremycins and is suitable for large-scale synthesis for biological screening.     

Scanning electrochemical microscope observation of defects in a hexadecanethiol monolayer on gold with shear force-based tip-substrate positioning

Scanning electrochemical microscopy (SECM) was used for imaging of n-hexadecanethiol-modified Au surfaces. In these studies, small defects were observed in the monolayer when a submicrometer electrode was used as an SECM tip, although a cyclic voltammogram of a Au disk electrode showed that the surface of the Au was completely covered with n-hexadecanethiol. The dependence of the SECM images on the potential of the Au electrode was also examined. A comparison of the current at the Au electrode and the tip current in the SECM images showed that direct electron transfer through the monolayer was dominant, rather than electron transfer at the defects. The size of the defects was estimated from the tip current to be 1-100 nm, under the assumption that the defects were small compared to the SECM probe.     

Total synthesis of borrelidin

The total synthesis of borrelidin has been achieved. The best feature of our synthetic route is macrocyclization at C11-C12 for the construction of an 18-membered ring after esterification between two segments. A detailed examination of the macrocyclization led us to the samarium(II) iodide-mediated intramolecular Reformatsky-type reaction as the most efficient synthetic approach. The two key segments were synthesized through regioselective methylation, directed hydrogenation, stereoselective Reformatsky-type reaction, and MgBr2.Et2O-mediated chelation-controlled allylation.     

Effects of Bis(aromatic) Pendants on Recognition of Nucleobase Thymine by Zn2+ -1,4,7,10-tetraazacyclododecane (Zn2+ -cyclen)

We have previously shown that the nucleobase thymine binding to Zn²⁺ -cyclen (cyclen=1,4,7,10-tetraazacyclododecane) complex became stronger by appending acridine, naphthalene, or quinoline rings to the cyclen. Amongst these, the pendant bis((1-naphthyl)methyl) or bis((4-quinolyl)methyl) groups yielded the most effective thymine-recognizing Zn²⁺ -cyclen complexes [J. Am. Chem. Soc., 121 (1999) 5426]. The present study was undertaken to find causes of the bis(aromatic) ring effect by X-ray crystal structure analysis and NMR studies. The crystal structure of the Zn²⁺ -bis((1-naphthyl)methyl)-cyclen complex with a deprotonated 1-methylthymine (1-MeT) failed to show the anticipated evidence for the double ~ - ~ stacking interactions between the two naphthalenes and the Zn 2+ -bound 1-MeT m (1-MeT m =N(3')-deprotonated 1-MeT). Crystal data: formula C₃₆ H₄₇ N₇ O₇ Zn, M r =755.19, monoclinic, space group P2₁/ c (No. 14), a =15.438(2) Å, b =14.093(3) Å, c =16.726(2) Å, g =90.53(1) V =3638.7(8) Å 3 Z =4, R =0.035, R _w =0.049. However, the ¹H NMR studies of Zn²⁼ -bis((4-quinolyl)methyl)-cyclen with 1-MeT in varying H₂O/CH₃ CN solution showed increasing upfield shifts of Me(5') and H(6') of the Zn²⁺ -bound 1-MeT in more aqueous media, indicating that the double intercalation with the two quinolines became more significant in more protic environments. We conclude that the double ~ - ~ stacking effect accounts for the enhanced recognition of thymine base by the appended bis((1-naphthyl)methyl) or bis((4-quinolinyl)methyl) groups.