C(alpha)-Tetrasubstituted alpha-amino acids are important building blocks for the synthesis of peptidemimetics with stabilized secondary structure, because of their ability to rigidify the peptide backbone. Recently our group reported a new class of cyclic C(alpha)-tetrasubstituted tetrahydrofuran alpha-amino acids prepared from methionine and aromatic aldehydes. We now report the extension of ...

The assignment of secondary structure elements in proteins is a key step in the analysis of their structures and functions. We have developed an algorithm, SACF (secondary structure assignment based on Cα fragments), for secondary structure element (SSE) assignment based on the alignment of Cα backbone fragments with central poses derived by clustering known SSE fragments. The assignment algori...

The congruence coefficient was first introduced by Burt (1948) under the name of unadjusted correlation as a measure of the similarity of two factorial configurations. The name congruence coefficient was later tailored by Tucker (1951, see also Harman, 1976). The congruence coefficient is also sometimes called a monotonicity coefficient (Borg & Groenen, 1997, p. 203). The congruence coefficient...

The congruence between two configurations of points quantifies their similarity. The configurations to be compared are, in general, produced by factor analytic methods which decompose an “observations by variables” data matrix and produce one set of factor scores for the observations and one set of factor scores (i.e., the “loadings”) for the variables. The congruence between two sets of factor...

In the title compound, C17H21N2O6P·CH3OH, the planes of the 4-nitro-aniline and 2-hy-droxy-phenyl groups form a dihedral angle of 84.04 (8)°. The P atom exhibits tetra-hedral geometry involving two O-ethyl groups, a Cα atom and a double-bonded O atom. In the crystal, O-H⋯O, N-H⋯O and C-H⋯O hydrogen bonds link the α-amino-phospho-nic acid and methanol mol-ecules into chains that propagate parall...

In this article we analyze the exact boundary behavior of solutions to the singular nonlinear Dirichlet problem −∆u = b(x)g(u) + λa(x)f(u), u > 0, x ∈ Ω, u|∂Ω = 0, where Ω is a bounded domain with smooth boundary in RN , λ > 0, g ∈ C1((0,∞), (0,∞)), lims→0+ g(s) = ∞, b, a ∈ Cα loc(Ω), are positive, but may vanish or be singular on the boundary, and f ∈ C([0,∞), [0,∞)).

In this paper, we study the following elliptic problem   ∆u+K(x)u p = 0 in R u > 0 in R (∗) where K(x) is a given function in Cα(R \ 0) for some fixed α ∈ (0, 1), p > 1 is a constant. Some existence, monotonicity and asymptotic expansion at infinity of solutions of (∗) are discussed. ∗Research supported in part by the Natural Science Foundation of China and NSFC †Research supported in part b...

By using a mixture model for the density distribution of the three pseudobond angles formed by Cα atoms of four consecutive residues, the local structural states are discretized as 17 conformational letters of a protein structural alphabet. This coarse-graining procedure converts a 3D structure to a 1D code sequence. A substitution matrix between these letters is constructed based on the struct...

We consider the 3D incompressible Euler equations in vorticity form following fundamental domain for octahedral symmetry group: {(x1,x2,x3):0<x3<x2<x1}. In this domain, we prove local well-posedness Cα vorticities not necessarily vanishing on boundary with any 0<α<1, and establish finite-time singularity formation within same class smooth compactly supported initial data. The solutions can be e...

The aim of this paper is to study local configurations issued from discrete rotations. The algorithm of discrete rotations that we consider is the discretized rotation. It simply consists in the composition of a Euclidean rotation with a rounding operation, as studied in [B. Nouvel, E. Rémila, On colorations induced by discrete rotations, in: DGCI, in: LNCS, vol. 2886, 2003, pp. 174–183; B. Nou...