On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities

Weakly clamped uniformly stretched thin elastic plates can experience edge buckling when subjected to a transverse pressure. This situation is revisited here for a circular plate, under the assumption of finite rotations and negligible bending stiffness in the pre-buckling range. The eigenproblem describing this instability is formulated in terms of two singularly perturbed fourth-order differential equations involving the non-dimensional bending stiffness ε>0. By using an extension of the asymptotic reduction technique proposed by Coman and Haughton (Acta Mech 55:179–200, 2006), these equations are formally reduced to a simple second-order ordinary differential equation in the limit ε→0+. It is further shown that the predictions of this reduced problem are in excellent agreement with the direct numerical simulations of the original bifurcation equations

Convergence and multiplicities for the Lempert function

Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space Hol (\D,\Omega) of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii's work) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for Matemati

Pluricomplex Green and Lempert functions for equally weighted poles

For $\Omega$ a domain in $\mathbb C^n$, the pluricomplex Green function with poles $a_1, ...,a_N \in \Omega$ is defined as $G(z):=\sup \{u(z): u\in PSH_-(\Omega), u(x)\le \log \|x-a_j\|+C_j \text{when} x \to a_j, j=1,...,N \}$. When there is only one pole, or two poles in the unit ball, it turns out to be equal to the Lempert function defined from analytic disks into $\Omega$ by $L_S (z) :=\inf \{\sum^N_{j=1}\nu_j\log|\zeta_j|: \exists \phi\in \mathcal {O}(\mathbb D,\Omega), \phi(0)=z, \phi(\zeta_j)=a_j, j=1,...,N \}$. It is known that we always have $L_S (z) \ge G_S(z)$. In the more general case where we allow weighted poles, there is a counterexample to equality due to Carlehed and Wiegerinck, with $\Omega$ equal to the bidisk. Here we exhibit a counterexample using only four distinct equally weighted poles in the bidisk. In order to do so, we first define a more general notion of Lempert function "with multiplicities", analogous to the generalized Green functions of Lelong and Rashkovskii, then we show how in some examples this can be realized as a limit of regular Lempert functions when the poles tend to each other. Finally, from an example where $L_S (z) > G_S(z)$ in the case of multiple poles, we deduce that distinct (but close enough) equally weighted poles will provide an example of the same inequality. Open questions are pointed out about the limits of Green and Lempert functions when poles tend to each other.Comment: 25 page

Flexible uretero- renoscopy for intrarenal calculi. Initial experience of a single centre. Outcome analysis

Clinica Endoplus, Cluj Napoca, Romania, Al VI-lea Congres de Urologie, Dializă şi Transplant Renal din Republica Moldova cu participare internaţională (21-23 octombrie 2015)INTRODUCERE cu privire la rata de succes (stone free rate-SFR) şi rata Scopul acestui studiu a fost să evaluăm rezultatele clinicii complicaţiilor (RC). noastre în uretero-renoscopia flexibila pentru calculii renali.Introduction Aim of this study was to evaluate the outcome of flexible uretero- renoscopy treatment for renal stones of a single surgeon, with regard to primary stone-free rates (SFR) and complication rates (CR) in a single center

Characterization of the GGPP synthase gene family in Arabidopsis thaliana

Geranylgeranyl diphosphate (GGPP) is a key precursor of various isoprenoids that have diverse functions in plant metabolism and development. The annotation of the Arabidopsis thaliana genome predicts 12 genes to encode geranylgeranyl diphosphate synthases (GGPPS). In this study we analyzed GGPPS activity as well as the subcellular localization and tissue-specific expression of the entire protein family in A. thaliana. GGPPS2 (At2g18620), GGPPS3 (At2g18640), GGPPS6 (At3g14530), GGPPS7 (At3g14550), GGPPS8 (At3g20160), GGPPS9 (At3g29430), GGPPS10 (At3g32040) and GGPPS11 (At4g36810) showed GGPPS activity in Escherichia coli, similar to activities reported earlier for GGPPS1 (At1g49530) and GGPPS4 (At2g23800) (Zhu et al. in Plant Cell Physiol 38(3):357-361, 1997a; Plant Mol Biol 35(3):331-341, b). GGPPS12 (At4g38460) did not produce GGPP in E. coli. Based on DNA sequence analysis we propose that GGPPS5 (At3g14510) is a pseudogene. GGPPS-GFP (green fluorescent protein) fusion proteins of the ten functional GGPP synthases localized to plastids, mitochondria and the endoplasmic reticulum, with the majority of the enzymes located in plastids. Gene expression analysis using quantitative real time-PCR, GGPPS promoter-GUS (β-glucuronidase) assays and publicly available microarray data revealed a differential spatio-temporal expression of GGPPS genes. The results suggest that plastids and mitochondria are key subcellular compartments for the synthesis of ubiquitous GGPP-derived isoprenoid species. GGPPS11 and GGPPS1 are the major isozymes responsible for their biosynthesis. All remaining paralogs, encoding six plastidial isozymes and two cytosolic isozymes, were expressed in specific tissues and/or at specific developmental stages, suggesting their role in developmentally regulated isoprenoid biosynthesis. Our results show that of the 12 predicted GGPPS encoded in the A. thaliana genome 10 are functional proteins that can synthesize GGPP. Their specific subcellular location and differential expression pattern suggest subfunctionalization in providing GGPP to specific tissues, developmental stages, or metabolic pathway