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Popular debiased estimation methods for causal inference -- such as augmented inverse propensity weighting and targeted maximum likelihood estimation -- enjoy desirable asymptotic properties like statistical efficiency and double robustness…
This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…
The prototypical Casimir effect arises when a scalar field is confined between parallel Dirichlet boundaries. We study corrections to this when the boundaries themselves have apertures and edges. We consider several geometries: a single…
We found analytical solution for the time evolution of localized electron density in a system of two coupled single-level quantum dots (QDs) connected with continuous spectrum states in the presence of Coulomb interaction. This solution…
A procedure for asymptotic bias reduction of maximum likelihood estimates of generic estimands is developed. The estimator is realized as a plug-in estimator, where the parameter maximizes the penalized likelihood with a penalty function…
A rigorous analytical approach is applied to solve the eigenvalue problem for a pair of circular dielectric cylinders with complex permittivity. This approach relies on field expansion in terms of two sets of orthogonal azimuthal modes,…
We prove two related concentration inequalities concerning the number of rational points of hyperelliptic curves over subsets of a finite field. In particular, we investigate the probability of a large discrepancy between the numbers of…
The reflection spectrum of a probe light in a -type three-level atomic system coupled by an off-resonant standing-wave is investigated experimentally and theoretically. We show that the maximum value of reflection coefficient occurs when…
This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a…
A candidate explanation of the good empirical performance of deep neural networks is the implicit regularization effect of first order optimization methods. Inspired by this, we prove a convergence theorem for nonconvex composite…
We have in earlier papers presented an extension of Mueller's dipole cascade model, which includes subleading effects from energy conservation and running coupling as well as colour suppressed effects from pomeron loops via a ``dipole…
We derive sharp upper and lower bounds for the pointwise concentration function of the maximum statistic of $d$ identically distributed real-valued random variables. Our first main result places no restrictions either on the common marginal…
This is a simplification of our prior work on the existence theory for the Rosseland-type equations. Inspired by the Rosseland equation in the conduction-radiation coupled heat transfer, we use the locally arbitrary growth conditions…
In this paper, several nonlinear elliptic systems are investigated on graphs. One type of the sobolev embedding theorem and a new version of the strong maximum principle are established. Then, by using the variational method, the existence…
This paper examines the stability and distributed stabilization of signed multi-agent networks. Here, positive semidefiniteness is not inherent for signed Laplacians, which renders the stability and consensus of this category of networks…
This paper extends the Concentration-Compactness Principle to Musielak-Orlicz spaces, working in both bounded and unbounded domains. We show that our results include important special cases like classical Orlicz spaces, variable exponent…
It is interesting to study the stress concentration between two adjacent stiff inclusions in composite materials, which can be modeled by the Lam\'e system with partially infinite coefficients. To overcome the difficulty from the lack of…
We develop a deterministic large-time mechanism yielding Ces{\`a}ro asymptotic observability inequalities from moving localized observations for conservative evolutions. On each observation interval, exact convexification on a compact…
We study the limit of D-series minimal models when the central charge tends to a generic irrational value $c\in (-\infty, 1)$. We find that the limit theory's diagonal three-point structure constant differs from that of Liouville theory by…
This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of…