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Creases are purposely introduced to thin structures for designing deployable origami, artistic geometries, and functional structures with tunable nonlinear mechanics. Modeling the mechanics of creased structures is challenging because creases introduce geometric discontinuity and often have complex mechanical responses due to local material damage. In this work, we propose a continuous description of the sharp geometry of creases and apply it to the study of creased annuli, made by introducing radial creases to annular strips with the creases annealed to behave elastically. We find that creased annuli have generic bistability and can be folded into various compact shapes, depending on the crease pattern and the overcurvature of the flat annulus. We use a regularized Dirac delta function (RDDF) to describe the geometry of a crease, with the finite spike of the RDDF capturing the localized curvature. Together with anisotropic rod theory, we solve the nonlinear mechanics of creased annuli, with its stability determined by the standard conjugate point test. We find excellent agreement between precision tabletop models, numerical predictions from our analytical framework, and modeling results from finite element simulations. We further show that by varying the rest curvature of the thin strip, dynamic switches between different states of creased annuli can be achieved, which could inspire the design of deployable and morphable structures. We believe that our smooth description of discontinuous geometries will benefit the mechanical modeling and design of a wide spectrum of engineering structures that embrace geometric and material discontinuities.

In this paper, based on the charge simulation method, a conformal mapping computational method is proposed to map the unbounded multiply connected regions onto the annulus with spiral slit domains. In addition, for the system of pathological equations generated during the conformal mapping process, it is proposed to solve them by using the GMRES(m) method, which in turn constructs an approximate conformal mapping function with high accuracy. Finally, numerical examples validate the effectiveness of the algorithms in this paper.

We consider a two-dimensional determinantal point process arising in the random normal matrix model and which is a two-parameter generalization of the complex Ginibre point process. In this paper, we prove that the probability that no points lie on any number of annuli centered at 0 satisfies large n asymptotics of the form exp ( C 1 n 2 + C 2 n log n + C 3 n + C 4 n + C 5 log n + C 6 + F n + O ( n - 1 12 ) ) , where n is the number of points of the process. We determine the constants C 1 , … , C 6 explicitly, as well as the oscillatory term F n which is of order 1. We also allow one annulus to be a disk, and one annulus to be unbounded. For the complex Ginibre point process, we improve on the best known results: (i) when the hole region is a disk, only C 1 , … , C 4 were previously known, (ii) when the hole region is an unbounded annulus, only C 1 , C 2 , C 3 were previously known, and (iii) when the hole region is a regular annulus in the bulk, only C 1 was previously known. For general values of our parameters, even C 1 is new. A main discovery of this work is that F n is given in terms of the Jacobi theta function. As far as we know this is the first time this function appears in a large gap problem of a two-dimensional point process.

For affine Coxeter groups of affine types \\(\\tilde D\\) and \\(\\tilde B\\), we model the interval \\([1,c]_T\\) in the absolute order by symmetric noncrossing partitions of an annulus with one or two double points. In type \\(\\tilde B\\) (and \\emph{almost} in type \\(\\tilde D\\)), the diagrams also model the larger lattice defined by McCammond and Sulway.

A metanalysis of available randomized controlled trials and observational studies comparing self-expanding (SE) and balloon-expandable (BE) bioprostheses in patients with small aortic annulus and aortic stenosis for short- and midterm hemodynamic and clinical outcomes was performed. A total of 21 studies with a total 8,647 patients (SE: n = 4,336 patients vs BE: n = 4,311 patients) were included. SE bioprostheses had a lower postoperative mean gradient at 30 days (Mean Difference [MD] −5.16, 95% confidence interval [CI] 4.7 to 5.5, p <0.001) and at 1 year (MD −6.6, 95%CI 6.1 to 7.03, p <0.001), with a larger indexed effective orifice area (0.17, 95% CI 0.13 to 0.22, p <0.001 and 0.17, 95% CI 0.08 to 0.27, p <0.001) at both time intervals. BE bioprostheses had a higher risk of 30-day and 1-year severe prosthesis-patient mismatch (risk ratio [RR] 1.07, 95% CI 1.04 to 1.09, p <0.001; RR 1.07, 95% CI 1.04 to 1.11, p <0.001). The 30-day and 1 year paravalvular leaks (RR 0.99, 95% CI 0.98 to 0.99, p <0.001; RR 0.89, 95% CI 0.82 to 0.95, p <0.001) and permanent pacemaker implantation (RR 0.97, 95% CI 0.94 to 0.99, p 0.01, I2 = 40%,) were lower in the BE group. BE bioprostheses were associated with a lower risk of in-hospital stroke (RR 0.99, 95% CI 0.98 to 1, p = 0.01). In conclusion, in patients with small aortic annulus and aortic stenosis, SE bioprostheses have superior hemodynamic performance but higher rates of paravalvular leak, permanent pacemaker implantation, and in-hospital stroke. BE bioprostheses were associated with a higher risk of severe prosthesis-patient mismatch. [Display omitted] Self-expandable bioprostheses have superior hemodynamic performance but higher rates of paravalvular leak, permanent pacemaker implantation, and in-hospital stroke. Balloon-expandable bioprostheses were associated with a higher risk of severe prosthesis-patient mismatch.

New methods for constructing two Dulac–Cherkas functions are developed using which a better, depending on the parameter , inner boundary of the Poincaré–Bendixson annulus is found for the Rayleigh system. A procedure is proposed for directly finding a polynomial whose zero level set contains a transversal oval used as the outer boundary of . An interval for is specified with which the best outer boundary of the annulus is a closed contour composed of two arcs of the constructed oval and two arcs of unclosed curves of the zero level set of one of the Dulac–Cherkas functions. Thus, a refined global Poincaré–Bendixson annulus for the limit cycle of the Rayleigh system is presented.

Let \\(A\\) be an annulus in the plane \\(\\mathbb R^2\\) and \\(g:A\\rightarrow A\\) be a boundary components preserving homeomorphism which is distal and has no periodic points. Then there is a continuous decomposition of \\(A\\) into \\(g\\)-invariant circles such that all the restrictions of \\(g\\) on them share a common irrational rotation number and all these circles are linearly ordered by the inclusion relation on the sets of bounded components of their complements in \\(\\mathbb R^2\\).

Prosthesis-patient mismatch (PPM) is a common phenomenon after transcatheter aortic valve implantation (TAVI), especially in patients with small aortic annuli. Whether factors during implantation, such as the implantation depth, have an impact on the occurrence of PPM is currently unclear. The objectives of our study were to (1) investigate the influence of procedure planning- and implantation-related factors on the occurrence of PPM and (2) evaluate the impact of PPM on long-term mortality after TAVI. Data from 315 patients with small aortic annuli, defined as multidetector computed tomography-derived annulus area <400 mm2, treated with transfemoral TAVI between 2014 and 2021 were retrospectively analyzed. TAVI was performed with ballon-expandable valves (BEVs) in 113 and self-expanding valves (SEVs) in 202 cases. PPM was defined according to Valve Academic Research Consortium 3 and follow-up was obtained within 5 years after TAVI. Overall, PPM occurred in 121 patients (38.4%) and was significantly more frequent in patients treated with BEVs (54.9%) than with SEVs (29.2%, p <0.001). Evaluation of planning- and implantation-related factors found that deeper implantation of BEVs significantly increased the risk of PPM (p = 0.014), whereas no association was observed in SEVs. The overall mortality rates at 3 and 5 years were 25.5% and 43.1%, respectively, without significant differences between patients with and without PPM. In conclusion, PPM occurred frequently, especially after BEV implantation. In these patients, implantation depth was identified as a predictor of PPM, whereas no association was found for SEV implantation. In addition, there was no difference in longer-term mortality between patients with and without PPM.

•We pooled data from 2 randomized controlled trials, including 620 women with small annuli.•Women underwent self-expanding, supra-annular transcatheter aortic valve replacement (TAVR) or surgery.•All-cause mortality or disabling stroke was similar with TAVR versus surgery.•Hemodynamic outcomes were significantly better with TAVR than surgery. There are limited data from randomized controlled trials assessing the impact of transcatheter aortic valve replacement (TAVR) or surgery in women with aortic stenosis and small aortic annuli. We evaluated 2-year clinical and hemodynamic outcomes after aortic valve replacement to understand acute valve performance and early and midterm clinical outcomes. This post hoc analysis pooled women enrolled in the randomized, prospective, multicenter Evolut Low Risk and Surgical Replacement and Transcatheter Aortic Valve Implantation (SURTAVI) intermediate risk trials. Women with severe aortic stenosis at low or intermediate surgical risk who had a computed tomography–measured annular perimeter of ≤72.3 mm were included and underwent self-expanding, supra-annular TAVR or surgery. The primary end point was 2-year all-cause mortality or disabling stroke rate. The study included 620 women (323 TAVR, 297 surgery) with a mean age of 78 years. At 2 years, the all-cause mortality or disabling stroke was 6.5% for TAVR and 8.0% for surgery, p = 0.47. Pacemaker rates were 20.0% for TAVR and 8.3% for surgery, p <0.001. The mean effective orifice area at 2 years was 1.9 ± 0.5 cm2 for TAVR and 1.6 ± 0.5 cm2 for surgery and the mean gradient was 8.0 ± 4.1 versus 12.7 ± 6.0 mm Hg, respectively (both p <0.001). Moderate or severe patient-prothesis mismatch at discharge occurred in 10.9% of patients who underwent TAVR and 33.2% of patients who underwent surgery, p <0.001. In conclusion, in women with small annuli, the clinical outcomes to 2 years were similar between self-expanding, supra-annular TAVR and surgery, with better hemodynamics in the TAVR group and fewer pacemakers in the surgical group.

Motivated by the well-known phase-space portrait of the nonlinear pendulum, the purpose of this paper is to obtain convergence rates in the ergodic theorem for flows in the plane that have arbitrarily slow trajectories. Considering bounded periodic trajectories near the heteroclinic orbits, it is shown that despite lacking a spectral gap, there exists a functional space (which is a strict subset of \\(L^2\\)) on which time averages converge uniformly to spatial averages (with an explicit rate). The main ingredient of the proof is an estimate of the density of the spectrum of the generator of the flow near zero.