Enhancement in the rate of conversion of peptide Cys-Pro esters to peptide thioesters by structural modification

We previously reported that the peptide containing a Cys-Pro ester (CPE) moiety is spontaneously transformed into a peptide thioester via an N to S acyl shift followed by diketopiperazine formation. In an attempt to identify more reactive structures for the formation of a peptide thioester, we modified the CPE structure, in which the Pro residue in the CPE moiety was replaced with N-substituted glycine derivatives. These peptides were transformed into a peptide thioester more rapidly. Alternatively, the addition of an amino acid residue at the C-terminus of the CPE moiety also accelerated thioester formation.     

Viscous Shock Wave and Boundary Layer Solution to an Inflow Problem for Compressible Viscous Gas

The inflow problem for a one-dimensional compressible viscous gas on the half line (0,+) is investigated. The asymptotic stability on both the viscous shock wave and a superposition of the viscous shock wave and the boundary layer solution is established under some smallness conditions. The proofs are given by an elementary energy method.     

Stability properties and the KMS condition

First we derive stability properties of KMS states and subsequently we derive the KMS condition from stability properties. New results include a convergent perturbation expansion for perturbed KMS states in terms of appropriate truncated functions and stability properties of ground states. Finally we extend the results of Haag, Kastler, Trych-Pohlmeyer by proving that stable states ofL ¹-asymptotically abelian systems which satisfy a weak three point cluster property are automatically KMS states. This last theorem gives an almost complete characterization of KMS states, ofL ¹-asymptotic abelian systems, by stability and cluster properties (a slight discrepancy can occur for infinite temperature states).Supported during this research by the Norwegian Research Council for Science and Humanities     

Asymptotic behavior toward nonlinear waves for radially symmetric solutions of the multi-dimensional Burgers equation

The present paper is concerned with the asymptotic behaviors of radially symmetric solutions for the multi-dimensional Burgers equation on the exterior domain in ${\mathbb{R}}^n,n\ge 3$, where the boundary and far field conditions are prescribed. We show that in some case where the corresponding 1-D Riemann problem for the non-viscous part admits a shock wave, the solution tends toward a linear superposition of stationary and rarefaction waves as time goes to infinity, and also show the decay rate estimates. Furthermore, we improve the results on the asymptotic stability of the stationary waves which are treated in the previous papers [2], [3]. Finally, for the case of $n=3$, we give the complete classification of the asymptotic behaviors, which includes even a linear superposition of stationary and viscous shock waves.     

Homotopy of a Pair of Approximately Commuting Unitaries in a Simple C*-Algebra

It is shown that, for a class of unital C*-algebras including purely infinite simple C*-algebras, real rank zero simple A algebras, and AF algebras, ifuandvare almost commuting unitaries whereuhas trivialK₁-class,vhas full spectrum, and a certainK₀-valued obstruction associated to the pairu,vis trivial, thenucan be deformed to 1 through a path of unitaries in the algebra almost commuting withv, and the length of the path can be estimated by a universal constant. This result is used to identify the obstruction with Loring's Bott element associated to the pairu,vand also to prove the more universal statement that if (u_i, v_i),i=1, 2, are two pairs of almost commuting unitaries with [u_i]₁, [v_i]₁, and Bott (u_i, v_i) each independent ofi, then one pair can be deformed into the other along a path of pairs of almost commuting unitaries in the algebra, the length of the path being bounded by a universal constant.     

The Ext class of an approximately inner automorphism

Let be a simple unital algebra of real rank zero. It is shown below that the range of the natural map from the approximately inner automorphism group to coincides with the kernel of the map .

     

Dalitz plot analysis of Coulomb exploding O3 in ultrashort intense laser fields

The three-body Coulomb explosion of O3, O3(3+)-->O++O++O+, in ultrashort intense laser fields (2x10(15) W/cm2) is studied with two different pulse durations (9 and 40 fs) by the coincidence momentum imaging method. In addition to a decrease in the total kinetic energy release, a broadening in the Dalitz plot distribution [Philos. Mag. 44, 1068 (1953)] is observed when the pulse duration is increased from 9 to 40 fs. The analysis based on a simple Coulomb explosion model shows that the geometrical structure of O3 remains almost unchanged during the interaction with the few-cycle intense laser fields, while a significant structural deformation along all the three vibrational coordinates, including the antisymmetric stretching coordinate, is identified in the 40 fs intense laser fields. The observed nuclear dynamics are discussed in terms of the population transfer to the excited states of O3.