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Analogs of the Pólya–Szegő and Makai Inequalities for the Euclidean Moment of Inertia of a Convex Domain
In this paper, we obtain two-sided estimates for the Euclidean moment of inertia I 2 ( G ) of a convex domain G on the plane in terms of geometric...
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The hyperbolic Anderson model: moment estimates of the Malliavin derivatives and applications
In this article, we study the hyperbolic Anderson model driven by a space-time colored Gaussian homogeneous noise with spatial dimension
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Multisummability of Formal Solutions for a Family of Generalized Singularly Perturbed Moment Differential Equations
The notion of moment differentiation is extended to the set of generalized multisums of formal power series via an appropriate integral...
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Asymptotic expansions in the CLT containing the last known moment in the main part
This paper proposes new asymptotic expansions in the central limit theorem which permit us to approximate distributions of normalized sums of...
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Waves in a Random Medium: Endpoint Strichartz Estimates and Number Estimates
In this article we reconsider the problem of the propagation of waves in a random medium in a kinetic regime. The final aim of this program would be...
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Moment-SoS methods for optimal transport problems
Most common optimal transport (OT) solvers are currently based on an approximation of underlying measures by discrete measures. However, it is...
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Moment Estimates of the Cloud of a Planar Measure
With a proper function theoretic definition of the cloud of a positive measure with compact support in the real plane, a computational scheme of...
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Local limit theorems without assuming finite third moment
One of the most fundamental probabilities is the probability at a particular point. The local limit theorem is the well-known theorem that estimates...
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The first moment of quadratic Dirichlet L-functions at central values
We obtain an asymptotic formula for the smoothly weighted first moment of quadratic Dirichlet L -functions at central values, with explicit main terms...
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Estimates of the Rate of Convergence in the Limit Theorem for Negative Binomial Random Sums
New practically applicable estimates are constructed for the accuracy of approximation to the distributions of negative binomial random sums in the...
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Exact Estimates of the Probability of a Random Variable Falling Into a Specified Interval in One Class of Unimodal Distributions
The authors consider a class A of unimodal distribution functions F μ ( x ) for which only two first moments and mode m that coincides with the first...
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The cubic moment of Hecke–Maass cusp forms and moments of L-functions
In this paper, we prove that the smooth cubic moments dissipate for the Hecke–Maass cusp forms, which gives a new case of the random wave conjecture....
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A distributional Farkas’ lemma and moment optimization problems with no-gap dual semi-definite programs
We present a generalized Farkas’ Lemma for an inequality system involving distributions. This lemma establishes an equivalence between an...
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Standard Error Adaptive Moment Estimation for Mean-Value-at-Risk Portfolio Optimization Problems by Sampling
In this paper, an improvement of the adaptive moment estimation (Adam) method equipped with standard error (SE), namely the AdamSE algorithm, is...
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Constructing Estimates of Reachability Sets in Crowd Flows Modeling
AbstractMathematical modeling of crowd flows in a building is studied. The study is based on a modification of the discrete CTM macromodel built on...
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The Mertens Estimates
We need estimates for the number of primes in the initial interval. Such estimates are long known. Efforts to make them explicit started in the...
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Sharp norm estimates for functional dual affine quermassintegrals
This paper presents refined estimates for functional dual affine quermassintegrals, building upon the estimates of Dann et al. To sharpen the...