Results 91 to 100 of about 302,460 (378)
On the Laplacian eigenvalues of a graph and Laplacian energy
Linear Algebra and its Applications, 2015 Abstract Let G be a simple graph with n vertices, m edges, maximum degree Δ, average degree d ‾ = 2 m n , clique number ω having Laplacian eigenvalues μ 1 , μ 2 , … , μ n − 1 , μ n = 0 . For k ( 1 ≤ k ≤ n ), let S k ( G ) = ∑ i = 1 k μ i and let
S. Pirzada, Hilal A. Ganie
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Stimulated Raman Scattering with Optical Vortex Beams
Advanced Photonics Research, EarlyView.This study presents exact analytical expressions for stimulated Raman scattering with Laguerre‐Gaussian beams, revealing signal dependence on topological and hyperbolic momentum. The results provide a theoretical foundation for coherent Raman imaging and detecting orbital angular momentum of light via structured light in nonlinear optics.
Minhaeng Cho
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Cospectral constructions for several graph matrices using cousin vertices
Special Matrices, 2021 Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum.
Lorenzen Kate
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A nodal domain theorem and a higher-order Cheeger inequality for the graph $p$-Laplacian [PDF]
, 2016 We consider the nonlinear graph $p$-Laplacian and its set of eigenvalues and associated eigenfunctions of this operator defined by a variational principle. We prove a nodal domain theorem for the graph $p$-Laplacian for any $p\geq 1$. While for $p>1$ the
Hein, Matthias, Tudisco, Francesco
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Iterated Conformal Dynamics and Laplacian Growth
, 2001 The method of iterated conformal maps for the study of Diffusion Limited Aggregates (DLA) is generalized to the study of Laplacian Growth Patterns and related processes.
A. Arneódo +27 more
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Determinants of Laplacians [PDF]
Communications in Mathematical Physics, 1987 The determinant of the Laplacian on spinor fields on a Riemann surface is evaluated in terms of the value of the Selberg zeta function at the middle of the critical strip. A key role in deriving this relation is played by the Barnes double gamma function.
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Lower bounds for fractional Laplacian eigenvalues [PDF]
Communications in Contemporary Mathematics, 2014 In this paper, we investigate eigenvalues of fractional Laplacian (–Δ)α/2|D, where α ∈ (0, 2], on a bounded domain in an n-dimensional Euclidean space and obtain a sharper lower bound for the sum of its eigenvalues, which improves some results due to Yildirim Yolcu and Yolcu in [Estimates for the sums of eigenvalues of the fractional Laplacian on a ...
Lingzhong Zeng, He-Jun Sun, Guoxin Wei
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Advanced Science, EarlyView.Utilizing a stereotaxic injection mouse model and a novel mathematical approach, this study uncovers key subnetworks that drive pathological α‐synuclein (α‐Syn) progression in Parkinson's disease (PD). Remarkably, just 2% of the strongest connections in the connectome are sufficient to predict its spread.
Yuanxi Li +16 more
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On the Laplacian and Signless Laplacian Characteristic Polynomials of a Digraph
Symmetry, 2022 Let D be a digraph with n vertices and a arcs. The Laplacian and the signless Laplacian matrices of D are, respectively, defined as L(D)=Deg+(D)−A(D) and Q(D)=Deg+(D)+A(D), where A(D) represents the adjacency matrix and Deg+(D) represents the diagonal matrix whose diagonal elements are the out-degrees of the vertices in D.
Hilal A. Ganie, Yilun Shang
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Reconstructing Three‐Dimensional Optical Anisotropy with Tomographic Müller‐Polarimetric Microscopy
Advanced Science, EarlyView.Tomographic Müller polarimetric microscopy is a novel imaging technique that resolves 3D birefringent properties of bulky samples, unveiling hierarchical nanostructures at microscopic resolution. Based on incoherent visible‐light polarimetry, it achieves experimental simplicity by eliminating phase measurements.
Yang Chen +4 more
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