Results 151 to 160 of about 302,460 (378)

First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet

Communications on Pure and Applied Mathematics, EarlyView.
Abstract For any p∈(1,∞)$p \in (1,\infty)$, we construct p$p$‐energies and the corresponding p$p$‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular ...
Mathav Murugan, Ryosuke Shimizu
wiley   +1 more source

Considering spatiotemporal evolutionary information in dynamic multi‐objective optimisation

CAAI Transactions on Intelligence Technology, EarlyView., 2023
Abstract Preserving population diversity and providing knowledge, which are two core tasks in the dynamic multi‐objective optimisation (DMO), are challenging since the sampling space is time‐ and space‐varying. Therefore, the spatiotemporal property of evolutionary information needs to be considered in the DMO.
Qinqin Fan, Min Jiang, Wentao Huang, Qingchao Jiang   +3 more
wiley   +1 more source

New constructions of nonregular cospectral graphs

Special Matrices
We consider two types of joins of graphs G1{G}_{1} and G2{G}_{2}, G1⊻G2{G}_{1}\hspace{0.33em}⊻\hspace{0.33em}{G}_{2} – the neighbors splitting join and G1∨=G2{G}_{1}\mathop{\vee }\limits_{=}{G}_{2} – the nonneighbors splitting join, and compute ...
Hamud Suleiman, Berman Abraham
doaj   +1 more source

Bounds for eigenvalue ratios of the Laplacian [PDF]

arXiv, 2011
For a bounded domain $\Omega$ with a piecewise smooth boundary in an $n$-dimensional Euclidean space $\mathbf{R}^{n}$, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. First we give a general inequality for eigenvalues of the Laplacian.
arxiv  

Bochner Laplacian and Bergman kernel expansion of semi-positive line bundles on a Riemann surface

, 2018
We generalize the results of Montgomery for the Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann surfaces, this leads to the Bergman kernel expansion and geometric quantization results for semi-positive line bundles ...
Marinescu, George, Savale, Nikhil
core  

Uniqueness on average of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature

Communications on Pure and Applied Mathematics, EarlyView.
Abstract Let (Mn,g)$(M^n,g)$ be a complete Riemannian manifold which is not isometric to Rn$\mathbb {R}^n$, has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature decay. We prove that there exists a set G⊂(0,∞)$\mathcal {G}\subset (0,\infty)$ with density 1 at infinity such that for every V∈G$V\in \mathcal {G}$ there ...
Gioacchino Antonelli, Marco Pozzetta, Daniele Semola   +2 more
wiley   +1 more source

Inequalities for eigenvalues of the weighted Hodge Laplacian [PDF]

arXiv, 2013
In this paper, we obtain "universal" inequalities for eigenvalues of the weighted Hodge Laplacian on a compact self-shrinker of Euclidean space. These inequalities generalize the Yang-type and Levitin-Parnovski inequalities for eigenvalues of the Laplacian and Laplacian.
arxiv  

Plane nets periodic of period 3 under the laplacian transformation [PDF]

, 1915
J. O. Hassler
openalex   +1 more source

On classification of global dynamics for energy‐critical equivariant harmonic map heat flows and radial nonlinear heat equation

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
wiley   +1 more source

The Laplacian spectrum of weighted composite networks and the applications

AIP Advances
The topological properties of the networks can be described by the Laplacian spectra, but resolving the Laplacian spectra of networks poses difficulties. In this study, a novel approach for solving the Laplacian spectrum of weighted composite networks is
Jian Zhu, Da Huang, Haiping Gao, Xianyong Li   +3 more
doaj   +1 more source