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Whenever an It\^o-Wentsel type of formula holds for composition of flows of a certain differential dynamics, there exists locally a decomposition of the corresponding flow according to complementary distributions (or foliations, in the case…
We compute the Donaldson-Thomas invariants of a local elliptic surface with section. We introduce a new computational technique which is a mixture of motivic and toric methods. This allows us to write the partition function for the…
Perturbations due to round-off errors in computer modeling are discontinuous and therefore one cannot use results like KAM theory about smooth perturbations of twist maps. We elaborate a special approximation scheme to construct two smooth…
We study some harmonic properties of slice regular functions in one and several Clifford variables and give explicit formulas of the iterated Laplacian applied to slice regular functions and to their spherical derivative, which are new also…
We construct fractional Sobolev spaces on arbitrary time scales, both in one dimension and on product time scales. In 1D, we define $W^{\alpha(\cdot),p}_{\mathrm{rd}}(\mathcal I)$ through a variable-order Gagliardo-type seminorm and prove…
We derive Berry-Esseen approximation bounds for general functionals of independent random variables, based on chaos expansions methods. Our results apply to $U$-statistics satisfying the weak assumption of decomposability in the Hoeffding…
An important open problem in geometric complex analysis is to find algorithms for explicit determination of basic functionals intrinsically connected with conformal and quasiconformal maps, such as their Teichmuller and Grunsky norms,…
Decomposition theorems in classical Fourier analysis enable us to express a bounded function in terms of few linear phases with large Fourier coefficients plus a part that is pseudorandom with respect to linear phases. The Goldreich-Levin…
The variation procedure on a teleparallel manifold is studied. The main problem is the non-commutativity of the variation with the Hodge dual map. We establish certain useful formulas for variations and restate the master formula due to…
We consider additive functionals of stationary Markov processes and show that under Kipnis-Varadhan type conditions they converge in rough path topology to a Stratonovich Brownian motion, with a correction to the Levy area that can be…
Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…
We consider a stochastic process $Y$ defined by an integral in quadratic mean of a deterministic function $f$ with respect to a Gaussian process $X$, which need not have stationary increments. For a class of Gaussian processes $X$, it is…
We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional…
In this paper we investigate certain fusion relations associated to an integrable vertex model on the square lattice which is invariant under $Sp(4)$ symmetry. We establish a set of functional relations which include a transfer matrix…
Following the classical results of Stong, we introduce a cohomological analogue of a core of a finite sheaved topological space and propose an algorithm for simplification in this category. In particular we generalize the notion of beat…
A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…
This paper presents necessary, sufficient, and equivalent conditions for the spherical convexity of non-homogeneous quadratic functions. In addition to motivating this study and identifying useful criteria for determining whether such…
We present a new path integral method to analyze stochastically perturbed ordinary differential equations with multiple time scales. The objective of this method is to derive from the original system a new stochastic differential equation…
The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…
Quantum field theory in curved spacetime may be defined either through a manifestly unitary canonical approach or via the manifestly covariant path integral formalism. For gauge theories, these two approaches have produced conflicting…