Analysis and Mathematical Physics最新文献

Fukaya and Oh studied the correspondence between pseudoholomorphic disks in (T^{*}M) which are bounded by Lagrangian sections ({L_{i}^{epsilon }}) and gradient trees in M which consist of gradient curves of ({f_{i}-f_{j}}). Here, (L_{i}^{epsilon }) is defined by (L_{i}^{epsilon }=) graph((epsilon df_{i})). They constructed approximate pseudoholomorphic disks in the case (epsilon >0) is sufficiently small. When (M=mathbb {R}) and Lagrangian sections are affine, pseudoholomorphic disks (w_{epsilon }) can be constructed explicitly. In this paper, we show that pseudoholomorphic disks (w_{epsilon }) converges to the gradient tree in the limit (epsilon rightarrow +0) when the number of Lagrangian sections is three and four.

In this paper, we define generalized monotonicity concepts related to equilibrium problems generated by trifunctions. We then study the existence of solutions to mixed equilibrium problems described as the sum of a maximal monotone trifunction and a pseudomonotone trifunction in Brézis sense. The main tools for this study are a Thikonov regularization procedure with respect to the generalized duality mapping and recession analysis adapted to trifunctions. An application consists in an existence result for a noncoercive hemivariational inequality.

The aim of this paper is to investigate the right-sided quaternionic free metaplectic transformation (QFMT) and its associated uncertainty principles (UPs) for (mathbb {R}^{2d})-dimensional quaternionic-valued signals. First, we establish the fundamental mathematical properties of the QFMT, including partial derivatives, the inversion formula, Parseval’s theorem, and the Hausdorff–Young inequality. Next, we establish various UPs within this framework, such as the Rènyi and Shannon entropy UPs and Donoho–Stark’s UP in terms of concentration. Finally, we derive (L^a)-bandlimited variant of the Donoho–Stark UP in the QFMT domain.

Conformal geodesics form an invariantly defined family of unparametrized curves in a conformal manifold generalizing unparametrized geodesics/paths of projective connections. The equation describing them is of third order, and it was an open problem whether they are given by an Euler–Lagrange equation. In dimension 3 (the simplest, but most important from the viewpoint of physical applications) we demonstrate that the equation for unparametrized conformal geodesics is variational.

We consider the Schrödinger operator on the quantum graph whose edges connect the points of ({{mathbb {Z}}}). The numbers of the edges connecting two consecutive points n and (n+1) are read along the orbits of a shift of finite type. We prove that the Lyapunov exponent is potitive for energies E that do not belong to a discrete subset of ([0,infty )). The number of points E of this subset in ([(pi (j-1))^2, (pi j)^2]) is the same for all (jin {{mathbb {N}}}).

In this paper, we investigate the existence of multiple weak solutions for a Schrödinger-Kirchhoff type elliptic system involving nonlocal ((alpha _1(cdot ), ldots , alpha _N(cdot )))-Laplacian operator. The system is modeled as follows:

We apply the three critical points theorem to establish sufficient conditions for the existence of at least three weak solutions under appropriate assumptions on the system’s parameters and nonlinearity terms. This work extends the analysis of elliptic systems involving variable exponent spaces and nonlocal operators, offering novel insights into their mathematical structure and solution properties.

We find two Lax representations for the reduced magnetohydrodynamics equations (rmhd) and construct a local variational Poisson structure (a Hamiltonian operator) for them. Its inverse defines a nonlocal symplectic structure for the same equations. We describe the action of both operators on the second-order cosymmetries and on the infinitesimal contact symmetries of rmhd, respectively. The reduction of rmhd by the symmetry of shifts along the z-axis coincides with the equations of two-dimensional ideal magnetohydrodynamics (imhd). Applied to the Lax representations and the variational Poisson structure of rmhd, the reduction provides analogous constructions for imhd.

In this work we introduce a family of conformal flows generalizing the classical Yamabe flow. We prove that for a large class of such flows long-time existence holds, and the arguments are in fact simpler than in the classical case. Moreover, we establish convergence for the case of negative scalar curvature and expect a similar statement for the positive and the flat cases as well.

Let X be a ball quasi-Banach function space, (alpha in mathbb {R}) and (qin (0,infty )). In this article, the authors first introduce the Herz-type Hardy space (mathcal {Hdot{K}}_{X}^{alpha ,,q}({mathbb {R}}^n)), which is defined via the non-tangential grand maximal function. Under some mild assumptions on X, the authors establish the atomic decompositions of (mathcal {Hdot{K}}_{X}^{alpha ,,q}({mathbb {R}}^n)). As an application, the authors obtain the boundedness of certain sublinear operators from (mathcal {Hdot{K}}_{X}^{alpha ,,q}({mathbb {R}}^n)) to (mathcal {dot{K}}_{X}^{alpha ,,q}({mathbb {R}}^n)), where (mathcal {dot{K}}_{X}^{alpha ,,q}({mathbb {R}}^n)) denotes the Herz-type space associated with ball quasi-Banach function space X. Finally, the authors apply these results to three concrete function spaces: Herz-type Hardy spaces with variable exponent, mixed Herz-Hardy spaces and Orlicz-Herz Hardy spaces, which belong to the family of Herz-type Hardy spaces associated with ball quasi-Banach function spaces.