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Large-eddy simulation developments and validations are presented for an improved simulation of turbulent internal flows. Numerical methods are proposed according to two competing criteria: numerical qualities (precision and spectral…
Virtually all questions that one can ask about the behavioral and structural complexity of a stochastic process reduce to a linear algebraic framing of a time evolution governed by an appropriate hidden-Markov process generator. Each type…
We introduce a general algorithm for the computation of the scale functions of a spectrally negative L\'evy process $X$, based on a natural weak approximation of $X$ via upwards skip-free continuous-time Markov chains with stationary…
We construct intrinsic on-and off-diagonal upper and lower estimates for the transition probability density of a L\'evy process in small time. By intrinsic we mean that such estimates reflect the structure of the characteristic exponent of…
We present a method for constructing numerical schemes with up to 3rd strong convergence order for solution of a class of stochastic differential equations, including equations of the Langevin type. The construction proceeds in two stages.…
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
The z-transform of a sequence is a classical tool used within signal processing, control theory, computer science, and electrical engineering. It allows for studying sequences from their generating functions, with many operations that can…
We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…
Stable inverse systems for periodically time-varying plants are essential for feedforward control and iterative learning control of multirate and periodic systems, yet existing approaches either require complex-valued Floquet factors and…
In this paper we address the problem of rare-event simulation for heavy-tailed L\'evy processes with infinite activities. We propose a strongly efficient importance sampling algorithm that builds upon the sample path large deviations for…
This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
We propose certain conditions which are sufficient for the functional law of the iterated logarithm (the Strassen invariance principle) for some general class of non-stationary Markov-Feller chains. This class may be briefly specified by…
Using the shift-operator technique, a compact formula for the Fourier transform of a product of two Slater-type orbitals located on different atomic centers is derived. The result is valid for arbitrary quantum numbers and was found to be…
The theory of symmetric, non-selfadjoint operators has several deep applications to the complex function theory of certain reproducing kernel Hilbert spaces of analytic functions, as well as to the study of ordinary differential operators…
Iterative Fast Fourier Transform methods are useful for calculating the fields in composite materials and their macroscopic response. By iterating back and forth until convergence, the differential constraints are satisfied in Fourier…
This work investigates the strong and weak convergence orders of numerical methods for SDEs driven by time-changed L\'{e}vy noise under the globally Lipschitz conditions. Based on the duality theorem, we prove that the numerical…
This paper presents a non-minimal order dynamics model for many analysis, simulation, and control problems of constrained mechanical systems with switching topology by making use of linear projection operator. The distinct features of this…
We find necessary and sufficient conditions for almost sure finiteness of integral functionals of spectrally positive L\'evy processes. Via Lamperti type transforms, these results can be applied to obtain new integral tests on extinction…
Variational inequalities play a key role in machine learning research, such as generative adversarial networks, reinforcement learning, adversarial training, and generative models. This paper is devoted to the constrained variational…