Regulating Hartshorne’s connectedness theorem

The tensor square conjecture states that for \(n \ge 10\), there is an irreducible representation V of the symmetric group \(S_n\) such that \(V \otimes V\) contains every irreducible representation of \(S_n\). Our main result is that for large enough n, there exists an irreducible representation V such that \(V^{\otimes 4}\) contains every irreducible representation. We also show that tensor squares of certain irreducible representations contain \((1-o(1))\)-fraction of irreducible representations with respect to two natural probability distributions. Our main tool is the semigroup property, which allows us to break partitions down into smaller ones.     

Electron impact mass spectrometry of some geminal bis-sulphones

The behaviour under electron impact of six 1,1-bis(benzenesulphonyl)cyclioalkanes and of 1-phenyl-1-(benzensesulphaonyl)cyclopropane has been studied in detail with the aid of exact mass measurements, linked scans for metastable ion analysis, collisional spectroscopy and kinetic energy release measurements. The molecular ions of these compounds undergo a sulphone-sulphinate rearrangement with alkyl group migration on oxygen, in analogy with what is found for simple monosulphones and, in general, their fragmentation resembles that of mono-sulphonyl compounds. Loss of SO₂ from the molecular ion is observed for all substrates, but only in the case of 1, 1-bis(benzenesulphonyl)cyclopropane is this followed by loss of the second SO₂ unit; the first loss of SO₂ is probably accompanied by rearrangement since the fragmentation pattern of [M ? SO₂]⁺˙ ions from this compound is different than that of the isobaric molecular ions of 1-phenyl-1-(benzenesulphonyl)cyclopropane.     

Aldolase activity of serum albumins

Bovine and human serum albumins catalyze the aldol reaction of aromatic aldehyedes and acetone, with saturation kinetics and moderate and opposite enantioselectivity. The reaction occurs at the binding site in domain IIa, and is inhibited by warfarin. Kinetic data are consistent with an enamine mechanism. The activity is conserved in a 103 aminoacid peptide derived from the albumin sequence.     

Modulation of drug activation profiles through carboxylate ligand modification in cytotoxic trans-platinum planar amine compounds

Transplatinum planaramine (TPA) compounds possessing carboxylate ligands in the trans position have been shown to be potential antitumor drugs in a variety of cell types, including cisplatin and oxaliplatin-resistant cell lines. In this work, we ask whether the nature and stability of the carboxylate ligand can be tuned in an attempt to manipulate the extent of serum protein binding; and consequently influence cytotoxicity, cellular drug accumulation and DNA adduct formation. Monitoring the interactions of selected TPAs with N-acetyl-methionine (NAM) by (1)H and (195)Pt NMR spectroscopy shows significant differences in the rate of sulfur binding. TPA-containing acetate ligands show a much lower sulfur binding rate than those possessing formate leaving groups. The same trend was seen when acetate and formate TPA compounds were incubated with human serum albumin and the reaction monitored for 24 h. To understand whether these results could be translated into a cellular medium, MTT cytotoxicity assays were conducted for each compound, before and after incubation with whole serum. Both the formate and acetate compounds, t-[Pt(4-pic)NH(3)(OFm)(2)] and t-[Pt(4-pic)NH(3)(OAc)(2)], showed minimal losses in cytotoxic efficacy and outperformed cisplatin after pre-incubation with serum. The same trends were seen when monitoring the effects of protein binding on cellular uptake and DNA platination. The rate of protein binding/drug deactivation was shown to be directly related to the stability of the leaving group (OAc(-) > OFm(-) > Cl(-)). Thus, our results suggest that utilization of the 'carboxylate strategy' substantially enhances the cellular efficacy of TPA compounds over cisplatin by allowing for an optimal balance between cytotoxic and metabolic efficiency.     

On maximum likelihood estimation of a Pareto mixture

In this paper we deal with maximum likelihood estimation (MLE) of the parameters of a Pareto mixture. Standard MLE procedures are difficult to apply in this setup, because the distributions of the observations do not have common support. We study the properties of the estimators under different hypotheses; in particular, we show that, when all the parameters are unknown, the estimators can be found maximizing the profile likelihood function. Then we turn to the computational aspects of the problem, and develop three alternative procedures: an EM-type algorithm, a Simulated Annealing and an algorithm based on Cross-Entropy minimization. The work is motivated by an application in the operational risk measurement field: we fit a Pareto mixture to operational losses recorded by a bank in two different business lines. Under the assumption that each population follows a Pareto distribution, the appropriate model is a mixture of Pareto distributions where all the parameters have to be estimated.     

Two-point b.v.p. for multivalued equations with weakly regular r.h.s.

A two-point boundary value problem associated to a semilinear multivalued evolution equation is investigated, in reflexive and separable Banach spaces. To this aim, an original method is proposed based on the use of weak topologies and on a suitable continuation principle in Fréchet spaces. Lyapunov-like functions are introduced, for proving the required transversality condition. The linear part can also depend on the state variable x and the discussion comprises the cases of a nonlinearity with sublinear growth in x or of a noncompact valued one. Some applications are given, to the study of periodic and Floquet boundary value problems of partial integro-differential equations and inclusions appearing in dispersal population models. Comparisons are included, with recent related achievements.     

Dynamical models of molecular chains and efficient integration algorithms

Chains of point masses and chains of rigid bodies are used to model biological polymers. To investigate their dynamics we propose a method which allows an efficient realization of the constraints jointly with a simple and accurate integration of the free rigid body motion. The method is quite effective to evolute the geodesic flow of a rigid body chain and the global performance depends on the computational complexity of the algorithms used to compute the interaction forces. Our approach is suitable to describe a chain of rigid bodies immersed in a thermal bath. In the method we propose, the constraints are realized by hard springs whose elastic constant is set to maximize the energy dissipation rate of a Runge–Kutta integrator scheme. Moreover the use of local Lagrangian coordinates is introduced using the possibility of a continuous change of chart, such that the distance from the coordinate singularities is the highest possible. For a chain of point masses the numerical results are checked with another method where the constraints are exactly realized by means of Lagrangian coordinates. When the chain is subject to regular interactions potentials plus a thermal bath the exact and approximate constraints realization provide comparable results.     

Solid-state Reactions of Mercury with Pure Noble Metals Part 2. Mercury–iridium system

Thermogravimetry, cyclic voltammetry and other analytical techniques were used to study the reactions of mercury with pure iridium. The results allowed to suggest when subjected to heat or anodic stripping voltammetry an electrodeposited mercury film reacts with Ir substrate and at least three mass loss steps and three peaks appear in the mercury desorption process. The first two were attributed to Hg(0)species removal like a mercury bulk and a mercury monolayer. The last can be ascribed to the mercury removal from a solid solution with iridium. This revised version was published online in July 2006 with corrections to the Cover Date.     

Molecular interactions in the poly(vinyl chloride)-di-n-butylphthalate system determined by infrared spectroscopy

Infrared studies of the poly(vinyl chloride) (PVC)/di-n-butylphthalate (DBP) system are reported. Spectra of DBP in different solvents seem to be indicative of the ability of DBP to interact with PVC chains in the same way as with polyesters and of competitive interactions between DBP molecules and DBP with PVC. Plots of the width at half-height of the carbonyl stretching vibration, measured at 25 and at ?180°C, as a function of composition, show a sudden change of slope at about 60% PVC concentration by weight, indicating that above this polymer composition interaction between DBP and PVC dominates that between DBP molecules. This change corresponds to a “singularity” observed in the dependence of the glass transition temperature on composition.