Finite fermion mass effects in pseudoscalar Higgs production via gluon–gluon fusion

We compute the leading logarithmic behaviour of the cross-section for the production of a pseudoscalar Higgs boson in gluon–gluon fusion to all-orders in perturbation theory, in the limit of large partonic centre of mass energy. We also calculate the Higgs rapidity distribution to the same accuracy. We include the contributions of top and bottom quarks, together with their interference. Our results are given in terms of single and double integrals, evaluated explicitly up to next-to next-to leading order (NNLO). We use our results to improve the known NNLO inclusive cross-section computed in the effective theory where the fermions in the loop are integrated out. The size of finite fermion mass effects on the inclusive cross-section is found to be small, reaching a few percent only for large values of the pseudoscalar mass.     

On the Pythagoras numbers of real analytic curves

We show that the Pythagoras number of a real analytic curve is the supremum of the Pythagoras numbers of its singularities, or that supremum plus 1. This includes cases when the Pythagoras number is infinite.      

Capacitated lot sizing and scheduling with parallel machines and shared buffers: A case study in a packaging company

The aim of this work is to propose a solution approach for a capacitated lot sizing and scheduling real problem with parallel machines and shared buffers, arising in a packaging company producing yoghurt. The problem has been formulated as a hybrid Continuous Set-up and Capacitated Lot Sizing Problem (CSLP–CLSP). A new effective two stage optimisation heuristic based on the decomposition of the problem into a lot sizing problem and a scheduling problem has been developed. An assignment of mixture to buffers is made in the first stage, and therefore the corresponding orders are scheduled on the production lines by performing a local search. Computational tests have been performed on the real data provided by the company. The heuristic exhibits near-optimal solutions, all obtained in a very short computational time.     

Improving the bounds of the multiplicity conjecture: The codimension 3 level case

The Multiplicity Conjecture (MC) of Huneke and Srinivasan provides upper and lower bounds for the multiplicity of a Cohen-Macaulay algebra A in terms of the shifts appearing in the modules of the minimal free resolution (MFR) of A. All the examples studied so far have lead to conjecture (see [J. Herzog, X. Zheng, Notes on the multiplicity conjecture. Collect. Math. 57 (2006) 211-226] and [J. Migliore, U. Nagel, T. Römer, Extensions of the multiplicity conjecture, Trans. Amer. Math. Soc. (preprint: math.AC/0505229) (in press)]) that, moreover, the bounds of the MC are sharp if and only if A has a pure MFR. Therefore, it seems a reasonable-and useful-idea to seek better, if possibly ad hoc, bounds for particular classes of Cohen-Macaulay algebras.In this work we will only consider the codimension 3 case. In the first part we will stick to the bounds of the MC, and show that they hold for those algebras whose h-vector is that of a compressed algebra.In the second part, we will (mainly) focus on the level case: we will construct new conjectural upper and lower bounds for the multiplicity of a codimension 3 level algebra A, which can be expressed exclusively in terms of the h-vector of A, and which are better than (or equal to) those provided by the MC. Also, our bounds can be sharp even when the MFR of A is not pure.Even though proving our bounds still appears too difficult a task in general, we are already able to show them for some interesting classes of codimension 3 level algebras A: namely, when A is compressed, or when its h-vector h(A) ends with (…,3,2). Also, we will prove our lower bound when h(A) begins with (1,3,h₂,…), where h₂≤4, and our upper bound when h(A) ends with (…,h_c−1,h_c), where h_c−1≤h_c+1.     

Skin Cleansing without or with Compromise: Soaps and Syndets

Products designed to cleanse the skin commonly do so through surfactant action, which leads to the lowering of the surface tension of the skin to facilitate the removal of dirt from its surface. Skin cleansers generally come in one of two types: soap-based and synthetic detergents, or syndets. While the latter can effectively maintain the native skin structure, function and integrity, the former tends to negatively affect the skin by causing barrier disruption, lipid dissolution and pH alteration. Despite this, soap is still often preferred, possibly due to the negative connotations around anything that is not perceived as ‘natural’. It is, therefore, important that the science behind cleansers, especially those designed for the maintenance of healthy skin and the management of common skin conditions such as eczema, be understood by both formulators and end-users. Here, we carefully weigh the advantages and disadvantages of the different types of surfactant—the key ingredient(s) in skin cleansers—and provide insight into surfactants’ physicochemical properties, biological activity and potential effects. Fine-tuning of the complex characteristics of surfactants can successfully lead to an ‘optimal’ skin cleanser that can simultaneously be milder in nature, highly effective and beneficial, and offer minimal skin interference and environmental impact.     

A Selective HIV‐Protease Assay Based on a Chromogenic Amino Acid

(2S,3S)‐2‐Amino‐3‐hydroxy‐5‐(4‐nitrophenoxy)pentanoic acid ( 5 ) was prepared stereoselectively as the N‐Fmoc, O‐(tert‐butyl)‐protected derivative 5a in eleven steps from ethyl (E)‐4‐benzyloxypent‐2‐enoate ( 6 ). This protected amino acid was used for the solid‐phase peptide synthesis of oligopeptides, which serve as sequence‐specific chromogenic protease substrates when used in the presence of NaIO₄ and bovine serum albumin. The peptide 1 (KRAVNle 5  EANleNH₂ (Nle=norleucine)) allows detection of HIV‐protease activity spectrophotometrically at 405 nm.     

Search for supermassive magnetic monopoles with the MACRO detector at the gran sasso laboratory

We present the results of the search for supermassive magnetic monopoles with the MACRO experiment. Our detector is equipped with three independent subdetectors (liquid scintillation counters, limited streamer tubes and nuclear track detectors), operating in different ranges of monopole velocity. In several years of data taking no candidates were found; the present flux upper limits are the level of half the Parker Bound for β > 10⁻⁴; for 10⁻⁴ < β < 5 × 10⁻² the limit is the best existing.     

A new selective fluorescence chemosensor for Cu(II) in water

A new chemosensor for the Cu(II) ion has been realized by connecting via an amido bond an anthracenyl residue to the all cis 2,4,6-triamino-1,3,5-trihydroxycyclohexane ligand (TACI). This sensor is able to detect micromolar concentrations of Cu(II) ions in water at pH 7 without interference with many other divalent transition metal ions.