Strong valid inequalities for orthogonal disjunctions and bilinear covering sets

In this paper, we derive a closed-form characterization of the convex hull of a generic nonlinear set, when this convex hull is completely determined by orthogonal restrictions of the original set. Although the tools used in this construction include disjunctive programming and convex extensions, our characterization does not introduce additional variables. We develop and apply a toolbox of results to check the technical assumptions under which this convexification tool can be employed. We demonstrate its applicability in integer programming by providing an alternate derivation of the split cut for mixed-integer polyhedral sets and finding the convex hull of certain mixed/pure-integer bilinear sets. We then extend the utility of the convexification tool to relaxing nonconvex inequalities, which are not naturally disjunctive, by providing sufficient conditions for establishing the convex extension property over the non-negative orthant. We illustrate the utility of this result by deriving the convex hull of a continuous bilinear covering set over the non-negative orthant. Although we illustrate our results primarily on bilinear covering sets, they also apply to more general polynomial covering sets for which they yield new tight relaxations.     

α-Returns to scale and multi-output production technologies

This contribution proposes a specification of strictly increasing and decreasing returns to scale in multi-output technologies. Along this line a notion of α-returns to scale is derived from that of homogeneous multi-output technology. For a large class of technologies we establish necessary and sufficient conditions characterizing strictly increasing and strictly decreasing returns to scale to scale. Furthermore, a relationship between input, output and graph distance functions is established. These connections lead naturally to a link between the various Malmquist indexes and the Chavas–Cox productivity index. Finally, we show that these concepts can be implemented in a DEA context using a piecewise homogeneous constant elasticity substitution–transformation model due to [Färe, R., Grosskopf, S., Njinkeu, D., 1988b. On piecewise reference technologies. Management Science 34, 1507–1511].     

Optical characterization of bubbly flows with a near-critical-angle scattering technique

The newly developed critical angle refractometry and sizing technique (CARS) allows simultaneous and instantaneous characterization of the local size distribution and the relative refractive index (i.e. composition) of a cloud of bubbles. The paper presents the recent improvement of this technique by comparison of different light scattering models and inversion procedures. Experimental results carried in various air/water and air/water-ethanol bubbly flows clearly demonstrate the efficiency and the potential of this technique.     

Comparing theoretical frameworks enacted in experimental research: TELMA experience

In the context of the Kaleidoscope Network of Excellence, six European research teams developed a methodology for integrating their research approaches. In this paper, we present the methodology based on a cross-experimentation, showing how it gave insight to the understanding of each team’s research and on the relationship between theoretical frameworks and experimental research.     

Fat point embeddings in affine space

We show that any fat point (local punctual scheme) has at most one embedding in the affine space up to analytic equivalence. If the algebra of functions of the fat point admits a non-trivial grading over the non-negative integers, we prove that it has at most one embedding up to algebraic equivalence. However, we give an example of a fat point having algebraically non-equivalent embeddings in the affine plane.     

Capra-Convexity,Convex Factorization and Variational Formulations for the ℓ0 Pseudonorm

Set-Valued and Variational Analysis - The so-called ?0 pseudonorm, or cardinality function, counts the number of nonzero components of a vector. In this paper, we analyze the ?0...     

Cambrian Acyclic Domains: Counting c-singletons

Order - We study the size of certain acyclic domains that arise from geometric and combinatorial constructions. These acyclic domains consist of all permutations visited by commuting equivalence...     

Cyanine-based near infra-red organic photoredox catalysis

Direct metal-free near infra-red photoredox catalysis is applied to organic oxidation, photosensitization and reduction, involving cyanines as photocatalysts. This photocatalyst is competitive with conventional reactions catalyzed under visible light. Kinetic and quenching experiments are also reported. Interestingly, these systems are compatible with water media, opening perspective for various applications.

Direct metal-free near infra-red photoredox catalysis is applied to oxidation, reduction and photosensitization, involving cyanines as photocatalysts. Mechanistic insights through kinetic and quenching experiments are also reported.