Nonlinear Double-well Schrödinger Equations in the Semiclassical Limit

We consider time-dependent Schrödinger equations with a double well potential and an external nonlinear, both local and non-local, perturbation. In the semiclassical limit, the finite dimensional eigenspace associated to the lowest eigenvalues of the linear operator is almost invariant for times of the order of the beating period and the dominant term of the wavefunction is given by means of the solutions of a finite dimensional dynamical system. In the case of local nonlinear perturbation, we assume the spatial dimension d=1 or d=2.     

Hermitian matrices and cohomology of Kähler varieties

We give some upper bounds on the dimension of the kernel of the cup product map $H^{1}(X,\mathbb{C}) \otimes H^{1}(X,\mathbb{C}) \to H^{2}(X,\mathbb{C})We give some upper bounds on the dimension of the kernel of the cup product map , where X is a compact K?hler variety without Albanese fibrations.     

Cortical disinhibition occurs in chronic neuropathic,but not in chronic nociceptive pain

Background  

The aim of this study was to examine the relationship between chronic neuropathic pain after incomplete peripheral nerve lesion, chronic nociceptive pain due to osteoarthritis, and the excitability of the motor cortex assessed by transcranial magnetic stimulation (TMS). Hence in 26 patients with neuropathic pain resulting from an isolated incomplete lesion of the median or ulnar nerve (neuralgia), 20 patients with painful osteoarthritis of the hand, and 14 healthy control subjects, the excitability of the motor cortex was tested using paired-pulse TMS to assess intracortical inhibition and facilitation. These excitability parameters were compared between groups, and the relationship between excitability parameters and clinical parameters was examined.     

Is breaking of ensemble equivalence monotone in the number of constraints?

Breaking of ensemble equivalence between the microcanonical ensemble and the canonical ensemble may occur for random graphs whose size tends to infinity, and is signaled by a non-zero specific relative entropy between the two ensembles. In Garlaschelli et al. (2017) and Garlaschelli et al. (0000) it was shown that breaking occurs when the constraint is put on the degree sequence (configuration model). It is not known what is the effect on the relative entropy when the number of constraints is reduced, i.e., when only part of the nodes are constrained in their degree (and the remaining nodes are left unconstrained). Intuitively, the relative entropy is expected to decrease. However, this is not a trivial issue because when constraints are removed both the microcanonical ensemble and the canonical ensemble change. In this paper a formula for the relative entropy valid for generic discrete random structures, recently formulated by Squartini and Garlaschelli, is used to prove that the relative entropy is monotone in the number of constraints when the constraint is on the degrees of the nodes. It is further shown that the expression for the relative entropy corresponds, in the dense regime, to the degrees in the microcanonical ensemble being asymptotically multivariate Dirac and in the canonical ensemble being asymptotically Gaussian.     

Patterning of cantilevers with inverted dip-pen nanolithography: efforts toward combinatorial AFM

We report patterning of AFM cantilevers by inverted dip-pen nanolithography, thereby markedly enhancing the development of combinatorial AFM as a high-throughput force-measuring instrument capable of determining interactions between opposing libraries of biomolecules.     

A new selective fluorogenic probe for trivalent cations

A new selective chromo-fluorogenic probe for Fe(3+), Cr(3+) and Al(3+) is reported. Detection limits are in the μM range and the fluorogenic sensing ability could be observed by the naked eye when illuminated with UV-light. No response is observed with divalent cations.     

Secondary Metabolites,including a New 5,6-Dihydropyran-2-One,Produced by the Fungus Diplodia corticola. Aphicidal Activity of the Main Metabolite,Sphaeropsidin A

An undescribed 5,6-dihydropyran-2-one, namely diplopyrone C, was isolated and characterized from the cultures of an isolate of the fungus Diplodia corticola recovered from Quercus suber in Algeria. The structure and relative stereostructure of (5S,6S,7Z,9S,10S)-5-hydroxy-6-(2-(3-methyloxiran-2-yl)vinyl)-5,6-dihydro-2H-pyran-2-one were assigned essentially based on NMR and MS data. Furthermore, ten known compounds were isolated and identified in the same cultures. The most abundant product, the tetracyclic pimarane diterpene sphaeropsidin A, was tested for insecticidal effects against the model sucking aphid, Acyrthosiphon pisum. Results showed a toxic dose-dependent oral activity of sphaeropsidin A, with an LC₅₀ of 9.64 mM.