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

The geometric algebra of Fierz identities in arbitrary dimensions and signatures

We use geometric algebra techniques to give a synthetic and computationally efficient approach to Fierz identities in arbitrary dimensions and signatures, thus generalizing previous work. Our approach leads to a formulation which displays the underlying real, complex or quaternionic structure in an explicit and conceptually clear manner and is amenable to implementation in various symbolic computation systems. We illustrate our methods and results with a few examples which display the basic features of the three classes of pin representations governing the structure of such identities in various dimensions and signatures.Comment: 77 pages; version published in JHEP in 201

Laparoscopic re-interventions for bile duct injuries

Clinica Chirurgie II, Timișoara, România, Al XI-lea Congres al Asociației Chirurgilor „Nicolae Anestiadi” din Republica Moldova și cea de-a XXXIII-a Reuniune a Chirurgilor din Moldova „Iacomi-Răzeșu” 27-30 septembrie 2011Lucrarea prezintă 2 cazuri exemplificate cu filme video în care intervenţia chirurgicală laparoscopică a fost indicată pentru rezolvarea unor suferinţe biliare postcolecistectomie pe cale clasică. Primul caz a fost o pacientă cu colecistectomie clasică incompletă la care s-a efectuat totalizarea colecistectomiei pe cale laparoscopică la două luni după intervenţia clasică. Acest caz susţine ideea din literatura actuală conform căreia vechiul termen de neocolecist corespundea unor colecistectomii incomplete. Abordul laparoscopic este posibil, dar recomandabil în centre cu multă experienţă în chirurgia laparoscopică. Al doilea caz a fost o pacientă cu o leziune de coledoc după o colecistectomie clasică. Această leziune a fost reparată laparoscopic în urgenţă la 8 zile după prima intervenţie. Evoluţia ambelor paciente a fost simplă, dovedind că în unele cazuri reintervenţia pe cale laparoscopică este fezabilă, sigură şi benefică pentru pacient.This paper presents 2 case reports illustrated by surgical video. In both cases laparoscopic intervention was indicated for repair of bile duct injuries produced during open cholecystectomy. The first case describes a female patient who underwent an incomplete open cholecystectomy. Two months after the first intervention cholecystectomy was completed by the laparoscopic approach. This case supports the idea circulating in the actual medical literature that postoperative dilatation of cystic duct (neocholecyst) is the consequence of the incomplete cholecystectomy. Laparoscopic approach is possible but can be recommended only in centers with experience in minimally invasive surgery. The second case was a patient with bile duct injury after classic cholecystectomy. This lesion was repaired in emergency by laparoscopic approach 8 days after the first operation. The evolution of both patients was uneventful, therefore proving that in selected cases laparoscopic re- intervention is a safe and feasible treatment option

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

In vitro evaluation on HeLa cells of protective mechanisms of probiotic lactobacilli against Candida clinical isolates

Aims: To characterize in vitro the ability of human Lactobacillus strains to inhibit the adhesion, to displace and to compete with clinically isolated Candida strains. Methods and Results: Three types of assays were performed to determine the inhibitory effect of Lactobacillus plantarum 319, Lactobacillus rhamnosus IMC 501, Lactobacillus paracasei IMC 502 and a specific probiotic combination (SYNBIO) on adhesion of Candida pathogens to HeLa cells: blockage by exclusion (lactobacilli and HeLa followed by pathogens), competition (lactobacilli, HeLa and pathogens together) and displacement (pathogens and HeLa followed by the addition of lactobacilli). Bacterial adhesion to HeLa was quantified by microscopy after May-Grunwald/Giemsa stain. The inhibition results highlight a significant (P < 0.05) competition of the considered probiotics against all the Candida strains. The results suggest that the probiotic strains used in this study could prevent colonization of the urogenital tract by relevant pathogens such as Candida strains through barrier and interference mechanisms (mainly displacement and competition), but the degree of inhibition of adhesion was bacterial strain-dependent. Conclusions: The results support the potential of these Lactobacillus probiotic strains as anti-infective agents in the vagina and encourage further studies about their capacity to prevent and manage urogenital tract infections in females. Significance and Impact of the Study: To optimize the defensive properties of the vaginal microbiota, improving the health of many women by probiotic intervention

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