Optimal regularity of robustness for parameterized perturbations

For exponential dichotomies defined by nonautonomous linear equations, we show that sufficiently small C¹-parameterized perturbations originate a family of exponential dichotomies of class C¹ in the parameter. We consider the general case of nonuniform exponential dichotomies, and also the general case of arbitrary growth rates of the form eλρ(t) where ρ is an arbitrary function. This includes the usual exponential behavior as a very special case when ρ(t)=t.     

Hydrolysis of Cutin by PET-Hydrolases

Functionalisation of synthetic polymers by using enzymes has been recently demonstrated. The major advantage of enzymes over chemical processes lies in their surface specific and endo-wise mode of action. Surface hydrophilisation of PET with lipases and cutinases leads to a dramatic increase of the surfacial acid and hydroxyl group content while conventional chemical treatment does not cause any change. However, this PET-hydrolysing activity by enzymes from distinct classes has not yet been correlated to activity on natural polyesters. Here, we show that lipases, cutinases and a PHA-depolymerase are all capable of hydrolysing PET, while only lipases and cutinases also hydrolysed cutin to various degrees. Lipases showed a higher specificity for terminal fatty acids while the cutinases preferred hydroxy fatty acids during cutin hydrolysis.     

Representation fields for quaternionic skew-hermitian forms

Classes of indefinite quadratic forms in a genus are in correspondence with the Galois group of an abelian extension called the spinor class field (Estes and Hsia, Japanese J. Math. 16, 341–350 (1990)). Hsia has proved (Hsia et al., J. Reine Angew. Math. 494, 129–140 (1998)) the existence of a representation field F with the property that a lattice in the genus represents a fixed given lattice if and only if the corresponding element of the Galois group is trivial on F. This far, the corresponding result for skew-hermitian forms was known only in some special cases, e.g., when the ideal (2) is square free over the base field. In this work we prove the existence of representation fields for quaternionic skew-hermitian forms in complete generality.     

Performance appraisal based on distance function methods

Performance appraisal is a process used by some firms to evaluate their employees’ efficiency and productivity in order to plan their promotion policy, salary policy, layoffs policy, etc. Initially this process was just carried out by the executive staff, but recently it has evolved into an evaluation process based on the opinion of different reviewers, supervisors, collaborators, customers and the employees themselves (360-degree method). In such an evaluation process the reviewers evaluate some indicators related to employees performance appraisal. In this paper we propose an evaluation framework where there are different sets of reviewers taking part in the evaluation process. Since reviewers have a different knowledge about the evaluated employee, it seems suitable to offer a flexible framework in which different reviewers can express their assessments in different finite scales according to their knowledge. The final aim is to compute a global evaluation for each employee, that can be used by the management team to make their decisions regarding their human resources policy. In this way, to obtain a global evaluation for each employee, we propose a methodology able to aggregate individual valuation in a metric L_p framework. In this context, the associated optimization problems can be reduced to an Extended Goal Programming formulation that is very easy to compute.     

Extensions of the prudence principle to exploit a valued outranking relation

In many outranking methods, the alternatives are first compared pairwise to build a valued outranking relation, which is then exploited to derive a recommendation for the decision maker. This paper proposes extensions of Arrow and Raynaud’s prudence principle to exploit a valued outranking relation, even in cases where the outranking values have an ordinal interpretation. The idea is to build a ranking that maximizes the weakest support for its implicit pairwise comparisons. We present a family of exploitation models providing three types of solutions, depending on the decision maker’s request: a linear order, a weak order, or a partial preorder. An algorithm is provided which solves the exploitation models. Relations between these models and some of their properties are also discussed.     

Role of sequence and conformation on the photochemistry and the photophysics of A-T DNA dimers: an experimental and computational approach

The role of base sequence and conformation on the photochemistry and photophysics of thymidylyl (3'-5')-2'-deoxyadenosine sodium salt (TpdA) and 2-deoxyadenylyl (3'-5')-thymidine ammonium salt (dApT) was studied. To this end, nanosecond transient absorption at 266 nm, steady-state irradiation at 254 nm, and quantum chemical calculations were used. The transient absorption spectra show the solvated electron broad band in the visible region for each dinucleotide. In addition, low-intensity absorption bands are observed in the UV region, which are attributed to the deprotonated and protonated neutral radicals of adenine and thymine bases. Photoionization (PI) occurs by one- and two-photon pathways; the latter accounting for approximately 70% of the net PI yield. A diffusion-limited rate constant of 2.0 x 10(10) M(-1) s(-1) was obtained for the reaction of the neutral molecule with the photoejected electron in both sequences. The photodestruction yield, measured from the chromophore loss at 260 nm, decreases in the presence of well-known electron scavengers. This suggests the participation of base radical anions as one of the photodegradation pathways, which is higher in TpdA than in dApT. The intermediacy of a radical ion pair (charge separated state) between the adjacent adenine and thymine bases is proposed in the formation of the [2 + 2] cycloadduct intermediate. The [2 + 2] cycloadduct intermediate is known to be the precursor of the thymine-adenine eight-member ring photoproduct (TA*). Conformational constrains in the radical ion pair are suggested to explain the absence of the TA* photoproduct in dApT. This hypothesis is supported by semiempirical calculations performed on all relevant reactive intermediates proposed to participate in the mechanism of formation of TA*. Altogether, the results show that sequence and conformation profoundly influence the photochemistry and the photophysics of these DNA model systems.     

Geometric phase induced by a cyclically evolving squeezed vacuum reservoir

We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by adiabatically manipulating the environment with which it interacts. As a specific scheme, we analyze a multilevel atom interacting with a broadband squeezed vacuum bosonic bath. As the squeezing parameters are smoothly changed in time along a closed loop, the ground state of the system acquires a geometric phase. We also propose a scheme to measure such a geometric phase by means of a suitable polarization detection.     

An efficient synthesis of new C-2 aryl substituted quinolines based on three component imino Diels-Alder reaction

New effective approach to the synthesis of a wide variety of C-2 nitro or aminophenyl substituted quinolines was reported using diverse intermediate 4-(2-oxopyrrolinidyl-1)-tetrahydroquinolines that were prepared by a three component imino Diels-Alder reaction was reported. The key aromatisation process occurs cleanly with the loss of the 2-oxopyrrolinidyl-1 fragment.     

Linear precision for parametric patches

We give a precise mathematical formulation for the notions of a parametric patch and linear precision, and establish their elementary properties. We relate linear precision to the geometry of a particular linear projection, giving necessary (and quite restrictive) conditions for a patch to possess linear precision. A main focus is on linear precision for Krasauskas’ toric patches, which we show is equivalent to a certain rational map on \mathbb C\mathbb P^d{\mathbb C}{\mathbb P}^d being a birational isomorphism. Lastly, we establish the connection between linear precision for toric surface patches and maximum likelihood degree for discrete exponential families in algebraic statistics, and show how iterative proportional fitting may be used to compute toric patches.