Exploring the Reactivity of a Frustrated Sn/P Lewis Pair: The Highly Selective Complexation of the cis-Azobenzene Photoisomer

The reactivity of the geminal frustrated Lewis pair (FLP) (F₅C₂)₃SnCH₂P(tBu)₂ ( 1 ) was explored by reacting it with a variety of small molecules (PhOCN, PhNCS, PhCCH, tBuCCH, H₃CC(O)CH=CH₂, Ph[C(O)]₂Ph, PhN=NPh and Me₃SiCHN₂), featuring polar or non-polar multiple bonds and/or represent α,β-unsaturated systems. While most adducts are formed readily, the binding of azobenzene requires UV-induced photoisomerization, which results in the highly selective complexation of cis-azobenzene. In the case of benzil, the reaction does not lead to the expected 1,2- or 1,4-addition products, but to the non-stereoselective (tBu)₂PCH₂-transfer to a prochiral keto function of benzil. All adducts of 1 were characterised by means of multinuclear NMR spectroscopy, elemental analyses and X-ray diffraction experiments.     

Stereochemistry of cercosporin

The absolute configuration of the asymmetric carbons and the axial chirality of the natural mold metabolite cercosporin (from $\text{Cercospora sp}$.) have been established on the basis of X-ray analysis and chemical reactions. The results confirm the inherent dissymmetry of the perylenequinone ring, the twisting of which gives rise to the diastereoisomer isocercosporin. The energy barrier for the conversion of cercosporin into isocercosporin has been evaluated.     

Subadditivity of The Entropy and its Relation to Brascamp–Lieb Type Inequalities

We prove a general duality result showing that a Brascamp–Lieb type inequality is equivalent to an inequality expressing subadditivity of the entropy, with a complete correspondence of best constants and cases of equality. This opens a new approach to the proof of Brascamp–Lieb type inequalities, via subadditivity of the entropy. We illustrate the utility of this approach by proving a general inequality expressing the subadditivity property of the entropy on ${\mathbb {R}^n}We prove a general duality result showing that a Brascamp–Lieb type inequality is equivalent to an inequality expressing subadditivity of the entropy, with a complete correspondence of best constants and cases of equality. This opens a new approach to the proof of Brascamp–Lieb type inequalities, via subadditivity of the entropy. We illustrate the utility of this approach by proving a general inequality expressing the subadditivity property of the entropy on \mathbb Rⁿ{\mathbb {R}^n}, and fully determining the cases of equality. As a consequence of the duality mentioned above, we obtain a simple new proof of the classical Brascamp–Lieb inequality, and also a fully explicit determination of all of the cases of equality. We also deduce several other consequences of the general subadditivity inequality, including a generalization of Hadamard’s inequality for determinants. Finally, we also prove a second duality theorem relating superadditivity of the Fisher information and a sharp convolution type inequality for the fundamental eigenvalues of Schr?dinger operators. Though we focus mainly on the case of random variables in \mathbb Rⁿ{\mathbb {R}^n} in this paper, we discuss extensions to other settings as well.     

Existence of proper semihypergroups of type U on the right

We generalize the classical definition of hypergroups of type U on the right to semihypergroups, and we prove some properties of their subsemihypergroups and subhypergroups. In particular, we obtain that a finite proper semihypergroup of type U on the right can exist only if its order is at least 6. We prove that one such semihypergroup of order 6 actually exists. Moreover, we show that there exists a hypergroup of type U on the right of cardinality 9 containing a proper non-trivial subsemihypergroup. In this way, we solve a problem left open in [D. Freni, Sur les hypergroupes de type U et sous-hypergroupes engendrés par un sous-ensemble, Riv. Mat. Univ. Parma 13 (1987) 29-41].     

A combined approach for evaluating papers, authors and scientific journals

An integrated model for ranking scientific publications together with authors and journals recently presented in [Bini, Del Corso, Romani, ETNA 2008] is closely analyzed. The model, which relies on certain adjacency matrices H,K and F obtained from the relations of citation, authorship and publication, provides the ranking by means of the Perron vector of a stochastic matrix obtained by combining H,K and F. Some perturbation theorems concerning the Perron vector previously introduced by the authors are extended to more general cases and a counterexample to a property previously addressed by the authors is presented. The theoretical results confirm the consistency and effectiveness of our model. Some paradigmatic examples are reported together with some results obtained on a real set of data.     

A heuristic algorithm based on multi-assignment procedures for nurse scheduling

This paper tackles a Nurse Scheduling Problem which consists of generating work schedules for a set of nurses while considering their shift preferences and other requirements. The objective is to maximize the satisfaction of nurses’ preferences and minimize the violation of soft constraints. This paper presents a new deterministic heuristic algorithm, called MAPA (multi-assignment problem-based algorithm), which is based on successive resolutions of the assignment problem. The algorithm has two phases: a constructive phase and an improvement phase. The constructive phase builds a full schedule by solving successive assignment problems, one for each day in the planning period. The improvement phase uses a couple of procedures that re-solve assignment problems to produce a better schedule. Given the deterministic nature of this algorithm, the same schedule is obtained each time that the algorithm is applied to the same problem instance. The performance of MAPA is benchmarked against published results for almost 250,000 instances from the NSPLib dataset. In most cases, particularly on large instances of the problem, the results produced by MAPA are better when compared to best-known solutions from the literature. The experiments reported here also show that the MAPA algorithm finds more feasible solutions compared with other algorithms in the literature, which suggest that this proposed approach is effective and robust.     

Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.