Large Time Decay for the Magnetohydrodynamics System in $\dot{\boldsymbol{H}^{s}}(\mathbb{R}^{n})$
Sign Up to like & getrecommendations! Published in 2019 at "Acta Applicandae Mathematicae"
DOI: 10.1007/s10440-019-00276-y
Abstract: We show that $t^{s/2} \| (\boldsymbol{u},\boldsymbol{b})(t) \|_{{\dot{H}^{s}(\mathbb{R}^{n})}} \to0 $ as $t \to\infty$ for global Leray solutions $(\boldsymbol{u},\boldsymbol{b})(t)$ of the incompressible MHD equations, where $2 \leq n \leq4$ and $s \geq0$ (real). We also provide some… read more here.
Keywords: large time; boldsymbol; magnetohydrodynamics; time decay ... See more keywords
How Far Does the Influence of the Free Surface Extend in Turbulent Open Channel Flow?
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DOI: 10.1007/s10494-025-00665-4
Abstract: Turbulent open channel flow is known to feature a multi-layer structure near the free surface. In the present work we employ direct numerical simulations considering Reynolds numbers up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}… read more here.
Keywords: 12pt minimal; boldsymbol; document; documentclass 12pt ... See more keywords
Structural, magnetic and photocatalytic characterization of Bi1−xLaxFeO3 nanoparticles synthesized by thermal decomposition method
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DOI: 10.1007/s12034-016-1346-0
Abstract: Single-phase La-substituted bismuth ferrite (Bi1−x$_{\boldsymbol {1-x}}$Lax$_{\boldsymbol {x}}$FeO3$_{\mathbf {3}}$) nanoparticles have been synthesized by thermal decomposition of a glyoxylate precursor. The crystal structure transition of BiFeO3$_{\mathbf {3}}$ from the rhombohedral (R3c) to the cubic Pm3̄m$\boldsymbol {Pm}\bar… read more here.
Keywords: bi1; synthesized thermal; nanoparticles synthesized; boldsymbol ... See more keywords
The 2-Rainbow Domination Numbers of $${\boldsymbol{C}}_4\Box {\boldsymbol{C}}_n$$C4□Cn and $${\boldsymbol{C}}_8\Box {\boldsymbol{C}}_n$$C8□Cn
Sign Up to like & getrecommendations! Published in 2019 at "National Academy Science Letters"
DOI: 10.1007/s40009-018-0779-y
Abstract: A k-rainbow dominating function (kRDF) of G is a function $$f:V(G)\rightarrow {\mathcal {P}}(\{1,2,\ldots ,k\})$$f:V(G)→P({1,2,…,k}) for which $$f(v)=\emptyset $$f(v)=∅ we have $$\bigcup \nolimits _{u\in N(v)}f(u)=\{1,2,\ldots ,k\}$$⋃u∈N(v)f(u)={1,2,…,k}. The weightw(f) of a function f is defined as $$w(f)=\sum… read more here.
Keywords: boldsymbol box; box boldsymbol; boldsymbol; rainbow domination ... See more keywords
Polarized orbifolds associated to quantized Hamiltonian torus actions
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DOI: 10.1016/j.geomphys.2021.104363
Abstract: Suppose given an holomorphic and Hamiltonian action of a compact torus $T$ on a polarized Hodge manifold $M$. Assume that the action lifts to the quantizing line bundle, so that there is an induced unitary… read more here.
Keywords: orbifolds associated; polarized orbifolds; associated quantized; boldsymbol ... See more keywords
Exact solutions to the Erdős-Rothschild problem
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DOI: 10.1017/fms.2023.117
Abstract: Abstract Let $\boldsymbol {k} := (k_1,\ldots ,k_s)$ be a sequence of natural numbers. For a graph G, let $F(G;\boldsymbol {k})$ denote the number of colourings of the edges of G with colours $1,\dots ,s$ such… read more here.
Keywords: boldsymbol; erd rothschild; problem; extremal graph ... See more keywords
On the spatial segregation of helicity by inertial waves in dynamo simulations and planetary cores
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DOI: 10.1017/jfm.2018.497
Abstract: The distribution of kinetic helicity in a dipolar planetary dynamo is central to the success of that dynamo. Motivated by the helicity distributions observed in numerical simulations of the Earth’s dynamo, we consider the relationship… read more here.
Keywords: inertial waves; boldsymbol; unicode stix; helicity ... See more keywords
Scale-space energy density function transport equation for compressible inhomogeneous turbulent flows
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DOI: 10.1017/jfm.2021.468
Abstract: Abstract The scale-space energy density function $E(\boldsymbol {x},\boldsymbol {r})$ is defined as the derivative of the two-point velocity correlation $Q_{ii}(\boldsymbol {x},\boldsymbol {r})$ as $E(\boldsymbol {x},r_\alpha ) = -(\partial Q_{ii}(\boldsymbol {x},\boldsymbol {r})/\partial r_\alpha )/{2}$, where $\boldsymbol… read more here.
Keywords: energy; scale space; density; boldsymbol ... See more keywords
Measurement Error and the Specification of the Weights Matrix in Spatial Regression Models
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DOI: 10.1017/pan.2019.35
Abstract: While the spatial weights matrix $\boldsymbol{W}$ is at the core of spatial regression models, there is a scarcity of techniques for validating a given specification of $\boldsymbol{W}$. I approach this problem from a measurement error… read more here.
Keywords: spatial regression; regression; weights matrix; regression models ... See more keywords
COPRIME COMMUTATORS IN THE SUZUKI GROUPS $^{\textbf{2}}{\boldsymbol{B}}_{\textbf{2}}\boldsymbol{(q)}$
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DOI: 10.1017/s0004972720001537
Abstract: Abstract In this note we show that every element of a simple Suzuki group $^2B_2(q)$ is a commutator of elements of coprime orders. read more here.
Keywords: coprime commutators; boldsymbol; textbf boldsymbol; suzuki groups ... See more keywords
Godbillon-Vey helicity and magnetic helicity in magnetohydrodynamics
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DOI: 10.1017/s0022377819000679
Abstract: The Godbillon–Vey invariant occurs in homology theory, and algebraic topology, when conditions for a co-dimension 1, foliation of a three-dimensional manifold are satisfied. The magnetic Godbillon–Vey helicity invariant in magnetohydrodynamics (MHD) is a higher-order helicity… read more here.
Keywords: godbillon vey; boldsymbol; magnetohydrodynamics; helicity ... See more keywords