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In this paper, we construct time periodic doubly connected solutions for the threedimensional quasi-geostrophic model in the patch setting. More specifically, we prove the existence of nontrivial m-fold doubly connected rotating patches bifurcating from a generic doubly connected revolution shape domain with higher symmetry m > mo and mo large enough. The linearized matrix operator at the equilibrium state has variable and singular coefficients and its spectral analysis is performed via the approach devised in [C. Garcia, T. Hmidi, and J. Mateu, Comm. Math. Phys., 390 (2022), pp. 617--756], where a suitable symmetrization was introduced. New difficulties emerge due to the interaction between the surfaces making the spectral problem richer and involved. [ABSTRACT FROM AUTHOR]

In this paper we characterize the minimizer for a class of nonlocal perturbations of the Coulomb energy. We show that the minimizer is the normalized characteristic function of an ellipsoid, under the assumption that the perturbation kernel has the same homogeneity as the Coulomb potential, is even, is smooth off the origin, and is sufficiently small. This result can be seen as the stability of ellipsoids as energy minimizers, since the minimizer of the Coulomb energy is the normalized characteristic function of a ball. [ABSTRACT FROM AUTHOR]

Background: One-catheter strategy, based in multipurpose catheters, allows exploring both coronary arteries with a single catheter. This strategy could simplify coronary catheterization and reduce the volume of contrast administration, by reducing radial spasm. To date, observational studies showed greater benefits regarding contrast consumption and catheterization performance than controlled trials. The aim of this work is to perform the first systematic review and meta-analysis of randomized clinical trials (RCT) to adequately quantify the benefits of one-catheter strategy, with multipurpose catheters, over conventional two-catheter strategy on contrast consumption, and catheterization performance. Methods: A search in PubMed, CINALH, and CENTRAL databases was conducted to identify randomized trials comparing one-catheter and two-catheter strategies. The primary outcome was volume of iodinated contrast administrated. Secondary endpoints, evaluating coronary catheterization performance included: arterial spasm, fluoroscopy time, and procedural time. Results: Five RCT were included for the final analysis, with a total of 1599 patients (802 patients with one-catheter strategy and 797 patients with two-catheter strategy). One-catheter strategy required less administration of radiological contrast (difference in means [DiM] [95% confidence interval (CI)]; -3.831 mL [-6.165 mL to-1.496 mL], p = 0.001) as compared to two-catheter strategy. Furthermore, less radial spasm (odds ratio [95% CI], 0.484 [0.363 to 0.644], p < 0.001) and less procedural time (DiM [95% CI], -72.471 s [-99.694 s to -45.249 s], p < 0.001) were observed in one-catheter strategy. No differences on fluoroscopy time were observed. Conclusions: One-catheter strategy induces a minimal reduction on radiological contrast administration but improves coronary catheterization performance by reducing arterial spasm and procedural time as compared to conventional two-catheter strategy. [ABSTRACT FROM AUTHOR]

The well-known curvature method initiated in works of Melnikov and Verdera is now commonly used to relate the L2(μ)-boundedness of certain singular integral operators to the geometric properties of the support of measure μ, e.g., rectifiability. It can be applied, however, only if Menger curvature-like permutations directly associated with the kernel of the operator are non-negative. We give an example of an operator in the plane whose corresponding permutations change sign but the L2(μ)-boundedness of the operator still implies that the support of μ is rectifiable. To the best of our knowledge, it is the first example of this type. We also obtain several related results with Ahlfors–David regularity conditions. [ABSTRACT FROM AUTHOR]

In this note, we study the well-posedness of the Cauchy problem for the transport equation in the BMO space and certain Triebel–Lizorkin spaces. [ABSTRACT FROM AUTHOR]

We prove existence of doubly connected V -states for the planar Euler equations which are not annuli. The proof proceeds by bifurcation from annuli at simple eigenvalues. The bifurcated V -states we obtain enjoy an m-fold symmetry for some m ≥ 3. [ABSTRACT FROM AUTHOR]

This paper continues the study, initiated in [MOV] and [MOPV], of the problem of controlling the maximal singular integral T* f by the singular integral Tf. Here, T is a smooth homogeneous Calderón-Zygmund singular integral operator of convolution type. We consider two forms of control, namely, in the weighted L( ω) norm and via pointwise estimates of T* f by M( Tf ) or M( Tf), where M is the Hardy-Littlewood maximal operator and M = M po M its iteration. The novelty with respect to the aforementioned works lies in the fact that here p is different from 2 and the L space is weighted. [ABSTRACT FROM AUTHOR]

It is known that the improved Cotlar's inequality B∗f(z)≤CM(Bf)(z), z∈C, holds for the Beurling transform B, the maximal Beurling transform B∗f(z)= supε>0∣∫|w|>εf(z−w)1/w²dw∣, z∈C, and the Hardy-Littlewood maximal operator M. In this note we consider the maximal Beurling transform associated with squares, namely, B*Sf(z)=supε>0∣∫w∉Q(0,ε) f(z−w)1/w²dw∣∣∣, z∈C, Q(0,ε) being the square with sides parallel to the coordinate axis of side length ε. We prove that B*Sf(z)≤CM²(Bf)(z), z∈C, where M²=M ○ M is the iteration of the Hardy-Littlewood maximal operator, and M² cannot be replaced by M. [ABSTRACT FROM AUTHOR]

In this paper, we pursue the study of the problem of controlling the maximal singular integral T∗f by the singular integral Tf. Here T is a smooth homogeneous Calderón–Zygmund singular integral of convolution type. We consider two forms of control, namely, in the norm and via pointwise estimates of T∗f by M(Tf) or M2(Tf), where M is the Hardy–Littlewood maximal operator and its iteration. It is known that the parity of the kernel plays an essential role in this question. In a previous article, we considered the case of even kernels and here we deal with the odd case. Along the way, the question of estimating composition operators of the type arises. It turns out that, again, there is a remarkable difference between even and odd kernels. For even kernels we obtain, quite unexpectedly, weak (1,1) estimates, which are no longer true for odd kernels. For odd kernels, we obtain sharp weaker inequalities involving a weak L1 estimate for functions in L log L. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper we discuss a special class of Beltrami coefficients whose associated quasiconformal mapping is bilipschitz. A particular example are those of the form , where Ω is a bounded domain with boundary of class and f a function in satisfying . An important point is that there is no restriction whatsoever on the norm of f besides the requirement on Beltrami coefficients that the supremum norm be less than 1. The crucial fact in the proof is the extra cancellation enjoyed by even homogeneous Calderón–Zygmund kernels, namely that they have zero integral on half the unit ball. This property is expressed in a particularly suggestive way and is shown to have far reaching consequences. An application to a Lipschitz regularity result for solutions of second order elliptic equations in divergence form in the plane is presented. [Copyright &y& Elsevier]

This article explores the idea that learning can be best understood as a life project. This entails recognition that socio-experiential (being), cognitive (knowing) and behavioural (doing) dimension are crucial, and that the future is of central importance – more than the past – in teaching and learning processes. Based on the concepts of "affinity space" and "activity ecology", it is also suggested that teaching and learning processes are across settings and time. This proposition is illustrated through two worked examples linked to biographical processes of identity construction in the field of art and the acquisition of English as a foreign language. The article concludes considering the need to recontextualize the school within the perspective outlined here. [ABSTRACT FROM AUTHOR]

This document is a bibliography of various books and articles related to cartography and maps. It includes topics such as the history of mapmaking, the use of maps in different disciplines, and specific maps from different regions and time periods. The sources cover a range of perspectives and approaches to studying maps, providing valuable resources for researchers interested in this field. [Extracted from the article]

In this paper, the authors show that a function b ∈ BMO(ℝn) is in CMO(ℝn) if and only if the Riesz transform commutator [b, Ri] is compact on Lwp(ℝn)for i ∈ {1, 2, ..., n}, p ∈ (1, ∞), and w ∈ Ap(ℝn), and if and only if the fractional integral commutator [b, Iα] is compact from ... (ℝn) to ...(ℝn), where α ∈ (0, n), p, q ∈ (1, ∞) with 1/p = 1/q + α/n and w ∈ Ap, q(ℝn). [ABSTRACT FROM AUTHOR]

The article offers information on miscellaneous topics including list of editorial board members such as Bernard Dacorogna, Gianni Dal Maso, and Hitoshi Ishii; table of contents; and information on journal's manager.

Let $ E \subset \mathbb{C} $ be a compact set, $ g:\mathbb{C} \to \mathbb{C} $ be a K-quasiconformal map, and let 0 < t < 2. Let $ {\mathcal{H}^t} $ denote t-dimensional Hausdorff measure. Then This is a refinement of a set of inequalities on the distortion of Hausdorff dimensions by quasiconformal maps proved by K. Astala in [] and answers in the positive a conjecture of K. Astala in op. cit. [ABSTRACT FROM AUTHOR]