Related papers: A Leibniz rule of distributional pairing and hyper…
We consider time-dependent dynamical systems arising as sequential compositions of self-maps of a probability space. We establish conditions under which the Birkhoff sums for multivariate observations, given a centering and a general…
The application of the Gershgorin circle theorem and some of its derivatives to estimate the eigenvalues of a matrix is considered. The obtained results are developed to obtain the localization region of the eigenvalues of a matrix with…
N=4 supersymmetric quantum mechanical model is formulated on the lattice. Two supercharges, among four, are exactly conserved with the help of the cyclic Leibniz rule without spoiling the locality. In use of the cohomological argument, any…
Supersymmetry is used to derive conditions on higher derivative terms in the effective action of type IIB supergravity. Using these conditions, we are able to prove earlier conjectures that certain modular invariant interactions of order…
This is part II of a two-part paper. Part I presented a universal Birkhoff theory for fast and accurate trajectory optimization. The theory rested on two main hypotheses. In this paper, it is shown that if the computational grid is selected…
A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory provides a law of large numbers: If the group satisfies…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
It is known that the balance laws of hyperelasticity (Green elasticity), i.e., conservation of mass and balance of linear and angular momenta, can be derived using the first law of thermodynamics by postulating its invariance under…
Let $u(x)$ be a subpolynomial function in a Hardy field. We establish necessary and sufficient conditions for the weighted uniform distribution of the sequences $(u(n))_{n\in\mathbb{N}}$ and $(u(p_n))_{n\in\mathbb{N}}$, where $p_n$ denotes…
Let $X$ be a ball Banach function space on $\mathbb{R}^n$. In this article, under some mild assumptions about both $X$ and the boundedness of the Hardy--Littlewood maximal operator on both $X$ and the associate space of its convexification,…
A fast and efficient numerical-analytical approach is proposed for modeling complex behaviour in the BBGKY hierarchy of kinetic equations. We construct the multiscale representation for hierarchy of reduced distribution functions in the…
This is the first of two papers in which we construct formal power series solutions in external parameters to the vacuum Einstein equations, implementing one bounce for the Belinskii-Khalatnikov-Lifshitz (BKL) proposal for spatially…
We show that the momentum sum rule is a necessary condition for factorization of double parton distributions into a product of two single parton distributions for small values of the parton momentum fractions x and large enough values of…
The standard formulation of thermostatistics, being based on the Boltzmann-Gibbs distribution and logarithmic Shannon entropy, describes idealized uncorrelated systems with extensive energies and short-range interactions. In this letter, we…
We consider the elliptic and parabolic superquadratic diffusive Hamilton-Jacobi equations with homogeneous Dirichlet conditions. For the elliptic problem in a half-space, we prove a Liouville-type classification, or symmetry result, which…
In this work, a subclass of the generalized Kerr-Schild class of spacetimes is specified, with respect to which the Ricci tensor (regardless of the position of indices) proves to be linear in the so-called profile function of the geometry.…
We study the breathing mode in systems of trapped interacting particles. Our approach, based on a dynamical ansatz in the first equation of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy allows us to tackle at once a wide range…
In the presence of feedback control by "Maxwell's demon," the second law of thermodynamics and the nonequilibrium equalities such as the Jarzynski equality need to be generalized. In this paper, we derive the generalized Jarzynski…
We revisit entropic formulations of the uncertainty principle for an arbitrary pair of positive operator-valued measures (POVM) $A$ and $B$, acting on finite dimensional Hilbert space. Salicr\'u generalized $(h,\phi)$-entropies, including…
The present article proposes a rigorous derivation of the Boltzmann equation in the half-space. We show an analog of the Lanford's theorem in this domain, with specular reflection boundary condition, stating the convergence in the low…