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First Passage Density of Brownian Motion with Two-sided Piecewise Linear Boundaries
The first passage time has many applications in fields like finance, econometrics, statistics, and biology. However, explicit formulas for the first...
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The Visible-Volume Function of a Set of Cameras is Continuous, Piecewise Rational, Locally Lipschitz, and Semi-Algebraic in All Dimensions
The visible-volume function assigns to a configuration of cameras and a flexible environment in a convex room the volume that can be supervised by...
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Convergence and stability of spectral collocation method for hyperbolic partial differential equation with piecewise continuous arguments
This paper deals with the convergence and stability of the spectral collocation method for a hyperbolic partial differential equation with piecewise...
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Nonparametric Bayesian Inference for Stochastic Processes with Piecewise Constant Priors
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is...
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Variable Piecewise Interpolation Solution of the Transport Equation
In this paper, we construct a piecewise interpolation method of approximate solution of the transport equation based on the Newton interpolation...
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Time Distribution from Zero up to Beginning: of the Final Stop of Semi-Markov Diffusion Process on Interval with Unattainable Boundaries
AbstractA one-dimensional process with continuous trajectories on a non-negative semiaxis is considered. The process has the Markov property with...
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Continuous/Discontinuous Galerkin Difference Discretizations of High-Order Differential Operators
We develop continuous/discontinuous discretizations for high-order differential operators using the Galerkin Difference approach. Grid dispersion...
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Cascade Synthesis of Differentiators with Piecewise Linear Correction Signals
AbstractBased on the state observer theory of dynamic plants operating under uncertainty, we propose a method for reconstructing high-order...
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Subdivision and G-Spline Hybrid Constructions for High-Quality Geometric and Analysis-Suitable Surfaces
This survey of piecewise polynomial surface constructions for filling multi-sided holes in a smooth spline complex focusses on a class of hybrid...
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Rayleigh Waves for Elliptic Systems in Domains with Periodic Boundaries
AbstractWe consider formally self-adjoint elliptic systems of partial differential equations generating formally positive operators and having the...
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Convergent adaptive hybrid higher-order schemes for convex minimization
This paper proposes two convergent adaptive mesh-refining algorithms for the hybrid high-order method in convex minimization problems with two-sided p ...
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A regularization–correction approach for adapting subdivision schemes to the presence of discontinuities
Linear approximation methods suffer from Gibbs oscillations when approximating functions with jumps. Essentially non oscillatory subcell-resolution...
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An energy-based discontinuous Galerkin method with tame CFL numbers for the wave equation
We extend and analyze the energy-based discontinuous Galerkin method for second order wave equations on staggered and structured meshes. By combining...
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Optimally Convergent Isoparametric \(P^2\) Mesh Generation
This paper describes a framework for the generation of \(P^2\)...
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Finite Element Approximation of the Levi-Civita Connection and Its Curvature in Two Dimensions
We construct finite element approximations of the Levi-Civita connection and its curvature on triangulations of oriented two-dimensional manifolds....
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A Unified Theory of Non-overlap** Robin–Schwarz Methods: Continuous and Discrete, Including Cross Points
Non-overlap** Schwarz methods with generalized Robin transmission conditions were originally introduced by B. Després for time-harmonic wave...
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Geometry of Real Hypersurfaces: Analytic Continuation
In this chapter we discuss analytic continuation of germs of biholomorphic maps between real analytic strictly pseudoconvex hypersurfaces along paths...