Abstract In this article, we consider the bounded variation capacity (BV capacity) and characterize Sobolev-type inequalities related to BV functions in a general framework of strictly local Dirichlet spaces with doubling measure via capacity. Under weak Bakry-Émery curvature-type condition, give connection between Hausdorff capacity, discover some capacitary Maz’ya-Sobolev for functions. The De Giorgi characterization total is also obtained quasi-Bakry-Émery curvature condition. It should...

This paper focuses on the concentration properties of spectral norm normalized Laplacian matrix for Erd\H{o}s-R\'enyi random graphs. First, We achieve optimal bound that can be attained in further question posed by Le et al. [24] regularized matrix. Beyond that, we also establish a uniform inequality homogeneous case, relying key tool: property degrees, which may independent interest. Additionally, prove after normalizing eigenvector corresponding to largest eigenvalue, concentrates around...

The integration of PV power brings many economic and environmental benefits. However, high penetration challenges for system operations planning, mainly due to its uncertain intermittent characteristics. output is subjected ramping, since dependence on solar irradiance other meteorological factors changes frequently. One the possible solutions balance these forecasting. This paper presents a comprehensive systematic overview existing research works Major that influence generation forecasting...

Let L=−Δ+V be a Schrödinger operator, where the potential V belongs to reverse Hölder class. By subordinative formula, we introduce fractional heat semigroup {e−tLα}t>0, 0<α<1, associated with L. aid of fundamental solution equation: ∂tu+Lu=∂tu−Δu+Vu=0, estimate gradient and time-fractional derivatives kernel Kα,tL(·,·), respectively. This method is independent Fourier transform, can applied second-order differential operators whose kernels satisfy Gaussian upper bounds. As an...

In this paper we introduce a class of generalized Morrey spaces associated with the Schrödinger operator $L=-\Delta+V$ . Via pointwise estimate, obtain boundedness operators $V^{\beta_{2}}(-\Delta +V)^{-\beta_{1}}$ and their dual on these spaces.

Abstract In this paper, we discuss the H 1 L -boundedness of commutators Riesz transforms associated with Schrödinger operator =−△+ V , where ( R n ) is Hardy space . We assume that x a nonzero, nonnegative potential which belongs to B q for some > /2. Let T = )(−△+ −1 2 1/2 (−△+ −1/2 and 3 ∇ prove that, b ∈ BMO commutator [ ] not bounded from as itself. As an alternative, obtain i =1,2,3 are weak -boundedness.

<abstract><p>In this paper, we consider a Schrödinger operator $ L = -\Delta_{\mathbb{H}}+V on the stratified Lie group \mathbb{H} $. First, establish fractional heat kernel estimates related to L^{\beta} $, \beta\in(0, 1) By utilizing estimations and Carleson measure, are able derive characterization of Campanato type space BMO_{L}^{v}(\mathbb{H}) Second, demonstrate that both Littlewood-Paley {\bf g} $-functions area functions bounded BMO^{v}_{L}(\mathbb{H}) Finally, also...

In this paper, we establish the global existence and uniqueness of a mild solution so-called fractional Navier-Stokes equations with small initial data in critical Besov-Q space covering many already known function spaces.

In this paper, we consider the compactness of some commutators Riesz transforms associated to Schrödinger operator L = -+ V on R n , ≥ 3, where is non-zero, nonnegative and belongs reverse Hölder class B q for > 2 .We prove that if

Abstract This article addresses the control issues of underwater manipulator arms in complex marine environments, proposing a composite strategy based on Harris Hawk Optimization (HHO) algorithm and Radial Basis Function (RBF) neural network. Combining global search capability HHO with fast approximation characteristics RBF networks, self-adaptive method for is designed. By automatically optimizing parameters network, performance robustness system are enhanced. Through simulation...