Related papers: High dimensional Schwarzian derivatives and Painle…
We review recent results on superintegrable quantum systems in a two-dimensional Euclidean space with the following properties. They are integrable because they allow the separation of variables in Cartesian coordinates and hence allow a…
We consider higher-derivative perturbations of quantum gravity and quantum field theories in curved space and investigate tools to calculate counterterms and short-distance expansions of Feynman diagrams. In the case of single…
We study variational problems for integral invariants, which are defined as integrations of invariant functions of the second fundamental form, of a smooth map between pseudo-Riemannian manifolds. We derive the first variational formulae…
Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their derivatives with time are considered as…
The main purpose of this paper is to establish a Schwarz lemma for the solutions to the Dirichlet problems for the invariant Laplacians. The obtained result of this paper is a generalization of the corresponding known results [11, Theorem…
In this paper, we study the sharp Poincar\'e inequality and the Sobolev inequalities in the higher order Lorentz--Sobolev spaces in the hyperbolic spaces. These results generalize the ones obtained in \cite{Nguyen2020a} to the higher order…
Many-query problems, arising from uncertainty quantification, Bayesian inversion, Bayesian optimal experimental design, and optimization under uncertainty-require numerous evaluations of a parameter-to-output map. These evaluations become…
The Hurwitz form of a projective variety characterizes linear spaces of complementary dimension which meet the variety non-transversally. We extend this notion to varieties in a product of projective spaces. This parallels the multigraded…
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…
The field equations associated to Born-Infeld type brane theories are studied by using an auxiliary variables method. This approach hinges on the fact that the expressions defining the physical and geometrical quantities describing the…
For any $\varepsilon > 0$ we derive effective estimates for the size of a non-zero integral point $m \in \mathbb{Z}^d \setminus \{0\}$ solving the Diophantine inequality $\lvert Q[m] \rvert < \varepsilon$, where $Q[m] = q_1 m_1^2 + \ldots +…
High-frequency solutions of one or several Schr\"odinger-type equations are well known to differ very little from the plane wave solutions $\exp[\pm ik x]$. That is, the potential terms impact the envelope of a high-frequency plane wave by…
Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. In some special cases…
Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational…
We review non-autonomous Hamiltonian systems, polynomial in two dependent variables, with the property that all of their solutions are meromorphic functions in the complex plane. These are related to known Hamiltonian systems with the…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
We consider optimal design of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations that contain secondary reducible model uncertainties, in addition to the uncertainty in the inversion parameters.…
In this work, we propose to extend an approach to calculate at any order $(n)$, the functional derivative of the diffracted field with respect to the permittivity-contrast function. These derivatives obtained for different orders are used…
We develop a method for determining the density of squarefree values taken by certain multivariate integer polynomials that are invariants for the action of an algebraic group on a vector space. The method is shown to apply to the…
In recent years, significant progress has been made in the study of integrable systems from a gauge theoretic perspective. This development originated with the introduction of $4$d Chern-Simons theory with defects, which provided a…