A Preorganized Hydrogen-Bonding Motif for the Molecular Recognition of Carbohydrates

The choice between adaptive and preorganized architectures, or of the most effective hydrogen bonding groups to be selected, are dilemmas that supramolecular chemists must address in designing synthetic receptors for such a challenging guest as carbohydrates. In this paper, structurally related architectures featuring two alternative hydrogen bonding motifs were compared to ascertain the structural and functional origin of their binding differences and the advantages that can be expected in monosaccharide recognition. A set of structurally related macrocyclic receptors were prepared, and their binding properties were measured by NMR and ITC techniques in chloroform vs a common saccharidic target, namely, the β-octyl glycoside of D-glucose. Results showed that the diaminocarbazolic motif, recently reported as the constituting unit of highly effective receptors for saccharides in water, is a superior hydrogen bonding motif compared to the previously described diaminopyrrolic motif, which was successfully employed in molecular recognition of carbohydrates in polar organic solvents, due to intrinsic structural and functional factors, rather than to hydrophobic contributions. In addition, the occurrence of a rare example of a thermodynamic template effect exerted by the beta-glucoside has been ascertained, enhancing the synthesis outcome of the otherwise low yielding preparation of the described macrocyclic receptors.     

Prescriptions for gravitational initial data as judged by a simple radiating model

Several methods of prescribing initial data for gravitational and matter fields, which are intended to eliminate extraneous radiation that is not produced by the matter source, are analysed in a simple exactly soluble radiating model. The model consists of an harmonic oscillator coupled to a scalar field along future light cones of Minkowski space time. In particular we analyze the asymptotic regime of the oscillator and find it is characterized essentially by two distinct decay modes. They differ in the way they behave both in the limit of small coupling constant and in a certain Newtonian limit. As a criterion to select initial data for the field with no extra radiation, we require that these initial data sets should put the oscillator from the start into the asymptotic regime. The underlying hypothesis here is that initial transients result from excitation of the oscillator by incoming radiation. We then see that the requirement of a uniform Newtonian limit leads to unique data for the scalar field for each arbitrary data set for the oscillator. We further find that this unique data set indeed satisfies our criterion.     

Quotient normed cones

Given a normed cone (X, p) and a subconeY, we construct and study the quotient normed cone (X/Y,p) generated byY. In particular we characterize the bicompleteness of (X/Y, ‖·‖ ^p ,p) in terms of the bicompleteness of (X, p), and prove that the dual quotient cone ((X/Y)^*, || · ‖·‖^p,p) can be identified as a distinguished subcone of the dual cone (X ^*, || · ||_{p, u}). Furthermore, some parts of the theory are presented in the general setting of the spaceCL(X, Y) of all continuous linear mappings from a normed cone (X, p) to a normed cone (Y, q), extending several well-known results related to open continuous linear mappings between normed linear spaces.     

Commutators of singular integrals on spaces of homogeneous type

In this work we prove some sharp weighted inequalities on spaces of homogeneous type for the higher order commutators of singular integrals introduced by R. Coifman, R. Rochberg and G. Weiss in Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (1976), 611–635. As a corollary, we obtain that these operators are bounded on L ^p (w) when w belongs to the Muckenhoupt’s class A _p , p > 1. In addition, as an important tool in order to get our main result, we prove a weighted Fefferman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature.     

Solute-diffusion-controlled dislocation creep in pure aluminium containing 0.026 at.% Fe

Pure aluminium containing about 200?at.ppm Fe in solution is shown to creep about 10⁶ times slower at 200°C than the same aluminium containing a negligible amount of iron in solution. The high creep resistance of the Al–200?at.ppm?Fe alloy is attributed to the presence of subgrain boundaries containing iron solute atoms. It is proposed that the opposing stress fields from subgrain boundaries and from the piled-up dislocations during creep are cyclically relaxed, by iron solute diffusion, to allow climb of the lead dislocation in the pile-up. The mechanism is a form of mechanical ratcheting. The model is applied to Al–Fe alloys and correctly predicts that the creep rate is controlled by the rate of iron solute diffusion and by a temperature dependence equal to the activation energy for iron diffusion, namely Q _c?=?221?kJ?mol^?1. Basic creep studies on solid-solution alloying with solute atoms that diffuse slowly in the lattice of aluminium (e.g. manganese, chromium, titanium and vanadium) appear worthy of study as a way of enhancing creep strength and of understanding creep mechanisms involving solute-atom-containing subgrain boundaries.     

Line graph eigenvalues and line energy of caterpillars

The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. A caterpillar is a tree in which the removal of all pendant vertices makes it a path. Let d?3 and n?2(d-1). Let p=[p₁,p₂,…,p_d-1] with p₁?1,p₂?1,…,p_d-1?1 such that

p₁+p₂+?+p_d-1=n-d+1.     

Complete rotation hypersurfaces with Hk constant in space forms

In this paper we classify all complete rotation hypersurfaces withH _k constant in ⁿ⁺¹ andH ⁿ⁺¹, is the normalizedk-th symmetric function of the principal curvatures. Partial results are also given forH ⁿ⁺¹.Partially supported by DGAPA-UNAM, México, CONACYT, México, under Project 1068P, and CNPp, Brazil.     

A generalization of the fast LUP matrix decomposition algorithm and applications

We show that any m × n matrix A, over any field, can be written as a product, LSP, of three matrices, where L is a lower triangular matrix with l's on the main diagonal, S is an m × n matrix which reduces to an upper triangular matrix with nonzero diagonal elements when the zero rows are deleted, and P is an n × n permutation matrix. Moreover, L, S, and P can be found in O(m^α?1n) time, where the complexity of matrix multiplication is O(m^α). We use the LSP decomposition to construct fast algorithms for some important matrix problems. In particular, we develop O(m^α?1n) algorithms for the following problems, where A is any m × n matrix: (1) Determine if the system of equations $\text{A}\text{x}\text{=}\text{b}$ (where $\text{b}$ is a column vector) has a solution, and if so, find one such solution. (2) Find a generalized inverse, $\text{A}{}^1$, of A (i.e., $\text{AA}{}^1\text{A = A}$). (3) Find simultaneously a maximal independent set of rows and a maximal independent set of columns of A.