The nonparametric integral of the Calculus of Variations as a Weierstrass integral: Existence and representation

The definition and properties of an abstract and very general nonparametric integral of the Calculus of Variations is presented. In harmony with the Lewy-McShane approach, the nonparametric integral ∝ f, for set functions ? taking their values in a Banach space E, is defined in terms of its associated parametric integral. For the latter use is made of the abstract parametric integral proposed by Cesari in Rⁿ and then extended to Banach spaces by Breckenridge, Warner, and the authors. A condition (c) is shown to be relevant for the existence of the integral, and is preserved by the nonlinear operation f. Also, for f nonnegative, a Tonelli-type theorem is proved in the sense that the so defined Weierstrass integral ∝ f is always larger than or equal to the corresponding Lebesgue integral, and equality holds if and only if absolute continuity conditions hold. In the proof a suitable martingale is associated and a convergence theorem for martingales is applied. Applications to the calculus of variations will follow.     

Una generalizzazione di alcuni teoremi di Matrosov

Sunto Si generalizzano condizioni sufficienti per la stabilità uniformemente asintotica e per l'instabilità espresse da alcuni teoremi di Matrosov. I risultati ottenuti sono utilizzabili anche nel caso che i secondi membri delle equazioni del moto siano funzioni non limitate. A Bruno Finzi nel suo 70^mo compleanno. Lavoro eseguito nell'ambito dei Gruppi di ricerca matematica del C.N.R. Entrato in Redazione il 24 gennaio 1970.     

Sulla quasi additività per raffinamenti

We introduce two new sufficient conditions for the existence of Burkill-Cesari integral: the «quasi additivity by refinement» and the «almost quasi additivity by refinement», that are intermediate between the well-known concepts of quasi additivity; moreover we study the behavior of these concepts in relation to subsets.     

Boundary displacements in membranes of revolution under symmetrical loads

Summary Boundary displacements in a large variety of membranes of revolution under live and dead loads are explicitely given. The boundary rotation is proved to be independent of the meridional shape for the dead load and identically zero for live loads under conditions often encountered in structural domes. To Mauro Picone on his 70^th birth day.     

Antisense-mediated isoform switching of steroid receptor coactivator-1 in the central nucleus of the amygdala of the mouse brain

Background

Antisense oligonucleotide (AON)-mediated exon skipping is a powerful tool to manipulate gene expression. In the present study we investigated the potential of exon skipping by local injection in the central nucleus of the amygdala (CeA) of the mouse brain. As proof of principle we targeted the splicing of steroid receptor coactivator-1 (SRC-1), a protein involved in nuclear receptor function. This nuclear receptor coregulator exists in two splice variants (SRC-1a and SRC-1e) which display differential distribution and opposing activities in the brain, and whose mRNAs differ in a single SRC-1e specific exon.

Methods

For proof of principle of feasibility, we used immunofluorescent stainings to study uptake by different cell types, translocation to the nucleus and potential immunostimulatory effects at different time points after a local injection in the CeA of the mouse brain of a control AON targeting human dystrophin with no targets in the murine brain. To evaluate efficacy we designed an AON targeting the SRC-1e-specific exon and with qPCR analysis we measured the expression ratio of the two splice variants.

Results

We found that AONs were taken up by corticotropin releasing hormone expressing neurons and other cells in the CeA, and translocated into the cell nucleus. Immune responses after AON injection were comparable to those after sterile saline injection. A successful shift of the naturally occurring SRC-1a:SRC-1e expression ratio in favor of SRC-1a was observed, without changes in total SRC-1 expression.

Conclusions

We provide a proof of concept for local neuropharmacological use of exon skipping by manipulating the expression ratio of the two splice variants of SRC-1, which may be used to study nuclear receptor function in specific brain circuits. We established that exon skipping after local injection in the brain is a versatile and useful tool for the manipulation of splice variants for numerous genes that are relevant for brain function.     

Stereochemistry of atropisomeric 9,10-dihydrophenanthrene dimers from Pholidota chinensis

Nine bis-9,10-dihydrophenanthrene and 9,10-dihydrophenanthrene/(dihydro)stilbene derivatives, including the new phochinenins G-L 1–6, were isolated from the whole plant of Pholidota chinensis. Their structures were elucidated on the basis of extensive spectroscopic investigations (1D, 2D NMR, and HR-EIMS). Owing to the sterically hindered rotation around the biaryl axis, some of these biaryl compounds can exist as a pair of enantiomers, but were isolated as racemates. Computed inversion barriers of selected atropisomeric derivatives suggested that phochinenins K 5, gymconpin C 7, and flavanthrin 9 have stable atropisomers. Their racemates were separated by HPLC on an optically active stationary phase, and were stereochemically characterized on-line by circular dichroism (CD) spectroscopy (LC-CD coupling), in conjunction with quantum-mechanics CD calculations.     

Transfer measurements for the Ti+Ni systems at near barrier energies

Large enhancements have been observed in the sub-barrier fusion cross sections for Ti+Ni systems in our previous studies. Coupled channel calculations incorporating couplings to 2⁺ and 3⁻ states failed to explain these enhancements completely. A possibilty of transfer channels contributing to the residual enhancements had been suggested. In order to investigate the role of relevant transfer channels, measurements of one- and two-nucleon transfer were carried out for ^46,48Ti+⁶¹Ni systems. The present paper gives the results of these studies.