Results 21 to 30 of about 271 (172)
Asymptotic properties of cross‐classified sampling designs
Canadian Journal of Statistics, EarlyView.Abstract We investigate the family of cross‐classified sampling designs across an arbitrary number of dimensions. We introduce a variance decomposition that enables the derivation of general asymptotic properties for these designs and the development of straightforward and asymptotically unbiased variance estimators.
Jean Rubin, Guillaume Chauvet
wiley +1 more source
Power spectral density and the brain
Canadian Journal of Statistics, EarlyView.Abstract Time series from M/EEG (magneto/electroencephalography) and ECoG (electrocorticography) recordings are common sources of information about brain function. The power spectral density (PSD) preserves much of this information, up to second order. In the current decade, a burst of brain diagnostics using the slope of log(PSD) has appeared.
Priscilla E. Greenwood +2 more
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JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2022 Cauchy's residue theorem gives a relatively general form for a complex integral along a simple closed contour. With the help of Cauchy's residue theorem, an appropriate closed contour can be chosen to calculate some abnormal definite integrals that might be very complicated and difficult to solve by conventional methods.
openaire +2 more sources
Front Propagation Through a Perforated Wall
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki +2 more
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A Geometric Characterization of Steady Laminar Flow
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We study the steady states of the Euler equations on the periodic channel or annulus. We show that if these flows are laminar (layered by closed non‐contractible streamlines which foliate the domain), then they must be either parallel or circular flows.
Theodore D. Drivas, Marc Nualart
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Modeling proppant transport and settling in a 3D propagating fracture
Deep Underground Science and Engineering, EarlyView.A versatile multiphysics tool is presented for simulating the complex processes involved in hydraulic fracturing treatments. The model couples fracture opening and propagation, variable‐density slurry flow, and proppant particle transport within the multiphysics object‐oriented simulation environment framework, based on two‐phase mixture equations and ...
Robert Egert +2 more
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A New Implementation of Network GARCH Model for Stock Volatility and Co‐Volatility Forecasting
Journal of Forecasting, EarlyView.ABSTRACT Volatility clustering and spillovers are key features of financial time series with many cross‐sectional assets. While network analysis links similar or correlated stocks and helps trace volatility spillovers, contemporary multivariate ARCH‐GARCH formulations struggle to represent structured network dependence and remain parsimonious.
Peiyi Zhou
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Trigonometric integrals evaluated in terms of Riemann zeta and Dirichlet beta functions
Open MathematicsThree classes of trigonometric integrals involving an integer parameter are evaluated by the contour integration and the residue theorem. The resulting formulae are expressed in terms of Riemann zeta function and Dirichlet beta function.
Li Jing, Chu Wenchang
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Amenability Constants for Unconditional Sums of Banach Algebras
Mathematische Nachrichten, EarlyView.ABSTRACT We study Johnson amenability for unconditional direct sums of Banach algebras. Given a family (Ai)i∈I$(A_i)_{i\in I}$ of Banach algebras and a Banach sequence lattice E$E$ on I$I$, the E$E$‐sum ⨁i∈IAiE${\bigl (\bigoplus _{i\in I} A_i\bigr)}_{\!E}$ carries a natural Banach algebra structure via coordinatewise multiplication.
Tomasz Kania, Jerzy Ka̧kol
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Mathematical and Computational ApplicationsIn this paper we develop an approach for obtaining the solutions to systems of linear retarded and neutral delay differential equations. Our analytical approach is based on the Laplace transform, inverse Laplace transform and the Cauchy residue theorem ...
Gilbert Kerr +2 more
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