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61.
In this paper the problem of the regularity, i.e. fractal behaviour, of the minima of the branched transport problem is addressed. We show that, under suitable conditions on the irrigated measure, the minima present a fractal regularity, that is on a given branch of length l the number of branches bifurcating from it whose length is comparable with ε can be estimated both from above and below by l/ε. 相似文献
62.
In this paper we consider an isotropic variant of the BMO‐type norm recently introduced (Bourgain, Brezis, and Mironescu, 2015). We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions.© 2016 Wiley Periodicals, Inc. 相似文献
63.
Luigi Ambrosio Jean Bourgain Haïm Brezis Alessio Figalli 《Comptes Rendus Mathematique》2014,352(9):697-698
The aim of this note is to announce some recent results showing that an isotropic variant of the BMO-type norm introduced in [3] can be related via a precise formula to the perimeter of sets. 相似文献
64.
Alessio Figalli 《Mathematische Annalen》2010,347(1):43-57
In this paper we study the regularity of flow maps of H 3/2-vector fields on the circle in terms of fractional Sobolev spaces. This problem is motivated by the understanding of the geometry of Bers’s universal Teichmüller space. 相似文献
65.
Francesca Alessio Piero Montecchiari 《Calculus of Variations and Partial Differential Equations》2013,46(3-4):591-622
We consider a class of semilinear elliptic equations of the form $$ \label{eq:abs}-\Delta u(x,y,z)+a(x)W'(u(x,y,z))=0,\quad (x,y,z)\in\mathbb {R}^{3},$$ where ${a:\mathbb {R} \to \mathbb {R}}$ is a periodic, positive, even function and, in the simplest case, ${W : \mathbb {R} \to \mathbb {R}}$ is a double well even potential. Under non degeneracy conditions on the set of minimal solutions to the one dimensional heteroclinic problem $$-\ddot q(x)+a(x)W^{\prime}(q(x))=0,\ x\in\mathbb {R},\quad q(x)\to\pm1\,{\rm as}\, x\to \pm\infty,$$ we show, via variational methods the existence of infinitely many geometrically distinct solutions u of (0.1) verifying u(x, y, z) → ± 1 as x → ± ∞ uniformly with respect to ${(y, z) \in \mathbb {R}^{2}}$ and such that ${\partial_{y}u \not \equiv0, \partial_{z}u \not\equiv 0}$ in ${\mathbb {R}^{3}}$ . 相似文献
66.
A group is called extended residually finite (ERF) if every subgroup is closed in the profinite topology. The ERF-property is studied for nilpotent groups, soluble groups, locally finite groups and FC-groups. A complete characterization is given of FC-groups which are ERF. 相似文献
67.
Alessio Martini 《Journal of Functional Analysis》2011,260(9):2767-2814
The joint spectral theory of a system of pairwise commuting self-adjoint left-invariant differential operators L1,…,Ln on a connected Lie group G is studied, under the hypothesis that the algebra generated by them contains a “weighted subcoercive operator” of ter Elst and Robinson (1998) [52]. The joint spectrum of L1,…,Ln in every unitary representation of G is characterized as the set of the eigenvalues corresponding to a particular class of (generalized) joint eigenfunctions of positive type of L1,…,Ln. Connections with the theory of Gelfand pairs are established in the case L1,…,Ln generate the algebra of K-invariant left-invariant differential operators on G for some compact subgroup K of Aut(G). 相似文献
68.
Alessio Porta 《Tetrahedron》2007,63(19):3989-3994
A highly enantioselective synthesis of the (8S,12S)-enantiomer of preclavulone A and its methyl ester is described featuring the Julia protocol for installing the (Z)-double bond in the lower chain. This procedure is suitable for the preparation of labeled preclavulone analogues for biosynthetic studies on marine clavulones. 相似文献
69.
Licchelli M Linati L Orbelli Biroli A Perani E Poggi A Sacchi D 《Chemistry (Weinheim an der Bergstrasse, Germany)》2002,8(22):5161-5169
The new quadridentate bischelating ligands 2 and 3 display in solution the typical absorption and emission properties expected for naphthalenediimide derivatives. Spectrophotometric studies show that systems 2 and 3 interact with Zn(II), Cd(II) and Cu(I) in CHCl3 or MeCN according to an apparent 1:1 stoichiometry. Molecular modelling, ESI-MS and 1H NMR experiments indicate that the complex species formed in the presence of stoichiometric amounts of metal ion are nonhelical [2 + 2] adducts. The metal-induced self-assembling process is signalled by an intense excimer-type emission caused by the intramolecular interaction of two naphthalenediimide subunits that face each other in the [2 + 2] adduct, as shown by molecular modelling studies. In the presence of excess metal ion, a disassembling process takes place, leading to a dinuclear complex with a 2:1 metal/ligand stoichiometry, in which the intramolecular excimer is no longer allowed to form because the interaction between the naphthalenediimide subunits has been lost. Thus, the overall metal-induced assembling/disassembling process is signalled by the appearance and disappearance of the excimer band in the emission spectrum. 相似文献
70.
We consider a set of macroscopic (classical) degrees of freedom coupled to an arbitrary many-particle Hamiltonian system, quantum or classical. These degrees of freedom can represent positions of objects in space, their angles, shape distortions, magnetization, currents and so on. Expanding their dynamics near the adiabatic limit we find the emergent Newton’s second law (force is equal to the mass times acceleration) with an extra dissipative term. In systems with broken time reversal symmetry there is an additional Coriolis type force proportional to the Berry curvature. We give the microscopic definition of the mass tensor. The mass tensor is related to the non-equal time correlation functions in equilibrium and describes the dressing of the slow degree of freedom by virtual excitations in the system. In the classical (high-temperature) limit the mass tensor is given by the product of the inverse temperature and the Fubini–Study metric tensor determining the natural distance between the eigenstates of the Hamiltonian. For free particles this result reduces to the conventional definition of mass. This finding shows that any mass, at least in the classical limit, emerges from the distortions of the Hilbert space highlighting deep connections between any motion (not necessarily in space) and geometry. We illustrate our findings with four simple examples. 相似文献