Related papers: Random integral currents
Musical chords, harmonies or melodies in Just Intonation have note frequencies which are described by a base frequency multiplied by rational numbers. For any local section, these notes can be converted to some base frequency multiplied by…
We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…
We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…
We study two actions of a stochastic flow $\varphi_t$ on the space of $0-$currents $T$ of a differentiable manifold $M$. In particular, we give conditions on a current $T$ to be invariant under these actions. Also, we apply our results to…
The definition of conservative-irreversible functions is extended to smooth manifolds. The local representation of these functions is studied and reveals that not each conservative-irreversible function is given by the weighted product of…
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…
A result is given to find points where a real valued function on the plane is not smooth. Provided this function is induced by a smooth mapping from three dimensions to the plane, from a function on surfaces in three dimensions. This has…
In this paper, the Authors establish a new identity for differentiable functions. By the well-known H\"older and power mean inequality, they obtain some integral inequalities related to the convex functions and apply these inequalities to…
We provide new bounds on a flux integral over the portion of the boundary of one regular domain contained inside a second regular domain, based on properties of the second domain rather than the first one. This bound is amenable to…
Two-dimensional potential flows of an ideal fluid with a free surface are considered in situations when shape of the bottom depends on time due to external reasons. Exact nonlinear equations describing surface waves in terms of the so…
This is a survey of the inverse spectral problem on (mainly compact) Riemannian manifolds, with or without boundary. The emphasis is on wave invariants: on how wave invariants have been calculated and how they have been applied to concrete…
We consider the behavior of the photon number integral under inversion, concentrating on euclidean space. The discussion may be framed in terms of an additive differential $I$ which arises under inversions. The quantity $\int \int I$ is an…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
We give criteria for which a principal curvature becomes a bounded $C^\infty$-function at non-degenerate singular points of wave fronts by using geometric invariants. As applications, we study singularities of parallel surfaces and extended…
We discuss some conjectural inequalities that are related to singular integrals, martingales, quasiconformal mappings, and the calculus of variations. Specifically, we present evidence for a conjecture of Iwaniec concerning the best…
The number of functionally independent scalar invariants of arbitrary order of a generic pseudo--Riemannian metric on an $n$--dimensional manifold is determined.
Invariant functions and metrics are studied on various classes of domains in $\Bbb C^n.$
We use the G-signature theorem to define an invariant of strongly invertible knots analogous to the knot signature.
This paper shows a simple construction of the continuous involutions of real intervals in terms of the continuous even functions. We also study the smooth involutions defined by symmetric equations. Finally, we review some applications, in…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…