Results 11 to 20 of about 67,630 (266)
International Journal of Robust and Nonlinear Control, EarlyView., 2023 Abstract We propose a hierarchical energy management scheme for aggregating Distributed Energy Resources (DERs) for grid flexibility services. To prevent a direct participation of numerous prosumers in the wholesale electricity market, aggregators, as self‐interest agents in our scheme, incentivize prosumers to provide flexibility. We firstly model the
Xiupeng Chen +3 more
wiley +1 more source
On Laplacian Equienergetic Signed Graphs
Journal of Mathematics, 2021 The Laplacian energy of a signed graph is defined as the sum of the distance of its Laplacian eigenvalues from its average degree. Two signed graphs of the same order are said to be Laplacian equienergetic if their Laplacian energies are equal.
Qingyun Tao, Lixin Tao
doaj +1 more source
Small eigenvalues of the conformal Laplacian [PDF]
Geometric And Functional Analysis, 2003 We introduce a differential topological invariant for compact differentiable manifolds by counting the small eigenvalues of the Conformal Laplace operator. This invariant vanishes if and only if the manifold has a metric of positive scalar curvature. We show that the invariant does not increase under surgery of codimension at least three and we give ...
Bär, Christian, Dahl, Matthias
openaire +4 more sources
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 +3 more
wiley +1 more source
Boundary Value Problems, 2021 We investigate the multiplicity of solutions for problems involving the fractional N-Laplacian. We obtain three theorems depending on the source terms in which the nonlinearities cross some eigenvalues. We obtain these results by direct computations with
Q-Heung Choi, Tacksun Jung
doaj +1 more source
Communications in Advanced Mathematical Sciences, 2018 The signless Laplacian eigenvalues of a graph $G$ are eigenvalues of the matrix $Q(G) = D(G) + A(G)$, where $D(G)$ is the diagonal matrix of the degrees of the vertices in $G$ and $A(G)$ is the adjacency matrix of $G$.
Rao Li
doaj +1 more source
Network Coherence in a Family of Book Graphs
Frontiers in Physics, 2020 In this paper, we study network coherence characterizing the consensus behaviors with additive noise in a family of book graphs. It is shown that the network coherence is determined by the eigenvalues of the Laplacian matrix.
Jing Chen, Yifan Li, Weigang Sun
doaj +1 more source
Spectral threshold dominance, Brouwer's conjecture and maximality of Laplacian energy [PDF]
, 2015 The Laplacian energy of a graph is the sum of the distances of the eigenvalues of the Laplacian matrix of the graph to the graph's average degree. The maximum Laplacian energy over all graphs on $n$ nodes and $m$ edges is conjectured to be attained for ...
Helmberg, Christoph, Trevisan, Vilmar
core +3 more sources
Integer Laplacian eigenvalues of chordal graphs
Linear Algebra and its Applications, 2021 15 pages, 5 ...
Nair Abreu +2 more
openaire +2 more sources
Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
europepmc +2 more sources