Carbon-13 nuclear magnetic resonance spectra of some heterocyclic D-homoandrostanes

The ¹³C chemical shift data of several D-homoandrostanes with heteroatoms (N,O) in the 17a-position are reported. Heteroatom effects on the shieldings of the carbons of rings C and D are discussed.     

A classification theorem for essentially binormal operators

An essentially binormal operator on Hilbert space is an operator which is unitarily equivalent to a 2 × 2 matrix of essentially commuting, essentially normal operators. A natural invariant of essentially binormal operators up to unitary equivalence in the Calkin Algebra is the reducing essential 2 × 2 matricial spectrum. A nonempty compact subset X of the set of 2 × 2 matrices is called hypoconvex, if it is the reducing essential 2 × 2 matricial spectrum of an operator on Hilbert space. The set EN₂(X) is then defined to be the set of all equivalence classes (up to unitary equivalence in the Calkin algebra) of essentially binormal operators whose reducing essential 2 × 2 matricial spectrum coincides with X. The aim of this paper is to prove a result that enables one to compute EN₂(X) in terms of the topological structure of the space $\text{X}\text{?}$ of unitary orbits of X. Indeed, it is shown that for every hypoconvex subset X of the set of 2 × 2 matrices, there exists a natural homomorphism from $\text{Ext}\text{(}\text{X}\text{?}\text{)}$ onto EN₂(X). Also, a six term cyclic exact sequence is obtained, which produces a characterization of the kernel of the above-mentioned homomorphism.     

Elimination of spectral interferences in the reaction of 2-thiobarbituric acid with malonaldehyde, 2-furfuraldehyde and 5-hydroxymethyl-2-furfuraldehyde by partial least squares multivariate calibration (PLS)

Summary The spectral resolution of ternary mixtures of malonaldehyde (MLD), 2-furfuraldehyde (FUR) and 5-hydroxymethyl-2-furfuraldehyde (HMF) in the presence of glyoxal and biliverdine is achieved by partial least squares multivariate calibration (PLS). The spectrophotometric method is based on the reaction of these substances with 2-thiobarbituric acid (TBA). A calibration set of standard samples has been statistically designed in the presence of adequate amounts of both interferent compounds in several degrees of concentration. The possibility of a spectrophotometric determination of mixtures of MLD, FUR and HMF in the presence of glyoxal and biliverdine is demonstrated. A comparative study of the results found by application of PLS-1 and PLS-2 methods is presented.     

On the mean-field Ising model in a random external field

We use a method developed by van Hemmen to obtain the free energy of the mean-field Ising model in a random external magnetic field. Some results of previous mean-field calculations are confirmed and generalized. The tricritical point in the global phase diagram is discussed in detail. We also consider different probability distributions of the random fields and provide some proofs regarding the conditions for the existence of a tricritical point.     

On geometric properties of the generating function for the Ramanujan sequence

The Ramanujan sequence \(\{\theta _{n}\}_{n \ge 0}\), defined as \(\theta _{0}= {1}/{2}\), \({n^{n}} \theta _{n}/{n !} = {e^{n}}/{2} - \sum _{k=0}^{n-1} {n^{k}}/{k !}\, \), \(n \ge 1\), has been studied on many occasions and in many different contexts. Adell and Jodrá (Ramanujan J 16:1–5, 2008) and Koumandos (Ramanujan J 30:447–459, 2013) showed, respectively, that the sequences \(\{\theta _{n}\}_{n \ge 0}\) and \(\{4/135 - n \cdot (\theta _{n}- 1/3 )\}_{n \ge 0}\) are completely monotone. In the present paper, we establish that the sequence \(\{(n+1) (\theta _{n}- 1/3 )\}_{n \ge 0}\) is also completely monotone. Furthermore, we prove that the analytic function \((\theta _{1}- 1/3 )^{-1}\sum _{n=1}^{\infty } (\theta _{n}- 1/3 ) z^{n} / n^{\alpha }\) is universally starlike for every \(\alpha \ge 1\) in the slit domain \(\mathbb {C}\setminus [1,\infty )\). This seems to be the first result putting the Ramanujan sequence into the context of analytic univalent functions and is a step towards a previous stronger conjecture, proposed by Ruscheweyh et al. (Israel J Math 171:285–304, 2009), namely that the function \((\theta _{1}- 1/3 )^{-1}\sum _{n=1}^{\infty } (\theta _{n}- 1/3 ) z^{n} \) is universally convex.     

Limit cycles and update digraphs in Boolean networks

Boolean networks have been used as models of gene regulation and other biological networks, as well as for other kinds of distributed dynamical systems. One key element in these models is the update schedule, which indicates the order in which states have to be updated. In Salinas (2008) [22] and Aracena et al. (2009) [1], equivalence classes of deterministic update schedules according to the labeled digraph associated to a Boolean network (update digraph) were defined and it was proved that two schedules in the same class yield the same dynamical behavior. In this paper, we study the relations between the update digraphs and the preservation of limit cycles of Boolean networks iterated under non-equivalent update schedules. We show that the related problems lie in the class of NP-hard problems and we prove that the information provided by the update digraphs is not sufficient to determine whether two Boolean networks share limit cycles or not. Besides, we exhibit a polynomial algorithm that works as a necessary condition for two Boolean networks to share limit cycles. Finally, we construct some update schedule classes whose elements share a given limit cycle under certain conditions on the frozen nodes of it.     

Luminescence Spectroscopy of Rhodamine Homodimer Dications in Vacuo Reveals Strong Dye-Dye Interactions

Being alone or together makes a difference for the photophysics of dyes but for ionic dyes it is difficult to quantify the interactions due to solvent screening and nearby counter ions. Gas-phase luminescence experiments are desirable and now possible based on recent developments in mass spectrometry. Here we present results on tailor-made rhodamine homodimers where two dye cations are separated by methylene linkers, (CH₂)_n. In solution the fluorescence is almost identical to that from the monomer whereas the emission from bare cation dimers redshifts with decreasing n. In the absence of screening, the electric field from the charge on one dye is strong enough to polarize the other dye, both in the ground state and in the excited state. An electrostatic model based on symmetric dye responses (equal induced-dipole moments in ground state) captures the underlying physics and demonstrates interaction even at large distances. Our results have possible implications for gas-phase Förster Resonance Energy Transfer.