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In this paper we study removable singularities for solutions of the fractional heat equation in the spacial-time space. We introduce associated capacities and we study some of its metric and geometric properties. [ABSTRACT FROM AUTHOR]

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]

In this paper we study removable singularities for regular (1, 1/2)-Lipschitz solutions of the heat equation in time varying domains. We introduce an associated Lipschitz caloric capacity and we study its metric and geometric properties and the connection with the L2 boundedness of the singular integral whose kernel is given by the gradient of the fundamental solution of the heat equation. [ABSTRACT FROM AUTHOR]

This paper aims to study time periodic solutions for 3D inviscid quasi-geostrophic model. We show the existence of non trivial rotating patches by suitable perturbation of stationary solutions given by generic revolution shapes around the vertical axis. The construction of those special solutions are done through bifurcation theory. In general, the spectral problem is very delicate and strongly depends on the shape of the initial stationary solutions. More specifically, the spectral study can be related to an eigenvalue problem of a self-adjoint compact operator. We are able to implement the bifurcation only from the largest eigenvalues of the operator, which are simple. Additional difficulties generated by the singularities of the poles are solved through the use of suitable function spaces with Dirichlet boundary condition type and refined potential theory with anisotropic kernels. [ABSTRACT FROM AUTHOR]

Copyright of Archivos de Cardiología de México is the property of Publicidad Permanyer SLU and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We study the behaviour of singular integral operators T k t of convolution type on C associated with the parametric kernels k t (z) : = (Re z) 3 | z | 4 + t · Re z | z | 2 , t ∈ R , k ∞ (z) : = Re z | z | 2 ≡ Re 1 z , z ∈ C \ { 0 }. It is shown that for any positive locally finite Borel measure with linear growth the corresponding L 2 -norm of T k 0 controls the L 2 -norm of T k ∞ and thus of the Cauchy transform. As a corollary, we prove that the L 2 ( H 1 ⌊ E) -boundedness of T k t with a fixed t ∈ (- t 0 , 0) , where t 0 > 0 is an absolute constant, implies that E is rectifiable. This is so in spite of the fact that the usual curvature method fails to be applicable in this case. Moreover, as a corollary of our techniques, we provide an alternative and simpler proof of the bi-Lipschitz invariance of the L 2 -boundedness of the Cauchy transform, which is the key ingredient for the bilipschitz invariance of analytic capacity. [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]

We show that the boundary of a rotating vortex patch (or V-state, in the terminology of Deem and Zabusky) is C, provided the patch is close to the bifurcation circle in the Lipschitz norm. The rotating patch is also convex if it is close to the bifurcation circle in the C norm. Our proof is based on Burbea's approach to V-states. [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]

In this paper, we study the existence of corotating and counter-rotating pairs of simply connected patches for Euler equations and the $${{\rm (SQG)}_{\alpha}}$$ equations with $${\alpha \in (0,1)}$$ . From the numerical experiments implemented for Euler equations in Deem and Zabusky (Phys Rev Lett 40(13):859-862, 1978), Pierrehumbert (J Fluid Mech 99:129-144, 1980), Saffman and Szeto (Phys Fluids 23(12):2339-2342, 1980) it is conjectured the existence of a curve of steady vortex pairs passing through the point vortex pairs. There are some analytical proofs based on variational principle (Keady in J Aust Math Soc Ser B 26:487-502, 1985; Turkington in Nonlinear Anal Theory Methods Appl 9(4):351-369, 1985); however, they do not give enough information about the pairs, such as the uniqueness or the topological structure of each single vortex. We intend in this paper to give direct proofs confirming the numerical experiments and extend these results for the $${{\rm (SQG)}_{\alpha}}$$ equation when $${\alpha \in (0,1)}$$ . The proofs rely on the contour dynamics equations combined with a desingularization of the point vortex pairs and the application of the implicit function theorem. [ABSTRACT FROM AUTHOR]

In this paper we present a new characterization of Sobolev spaces on $${\mathbb{R}^n}$$ . Our characterizing condition is obtained via a quadratic multiscale expression which exploits the particular symmetry properties of Euclidean space. An interesting feature of our condition is that depends only on the metric of $${\mathbb{R}^n}$$ and the Lebesgue measure, so that one can define Sobolev spaces of any order of smoothness on any metric measure space. [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]

Analytic capacity is associated with the Cauchy kernel 1/ z and the L-norm. For n ∈ ℕ, one has likewise capacities related to the kernels $K_i(x)=x_i^{2n-1}/|x|^{2n}$, 1 ≤ i ≤ 2, $x=(x_1,x_2)\in{\mathbb R}^2$. The main result of this paper states that the capacities associated with the vectorial kernel ( K, K) are comparable to analytic capacity. [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]

Copyright of Water & Landscape (WAL) / Agua & Territorio (AYT) is the property of Editorial de la Universidad de Jaen and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

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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]

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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.

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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]