Related papers: Random integral currents
We define the notion of an invariant function on a cluster ensemble with respect to an action of the cluster modular group on its associated function fields. We realize many examples of previously studied functions as elements of this type…
Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.
We introduce the notion of porous invariants for multipath (or branching/nondeterministic) affine loops over the integers; these invariants are not necessarily convex, and can in fact contain infinitely many 'holes'. Nevertheless, we show…
It is proved that the random integral mappings (some type of functionals of L\'evy processes) are always isomorphisms between convolution semigroups of infinitely divisible measures. However, the inverse mappings are no longer of the random…
This study defines finite-type invariants for curves on surfaces and reveals the construction of these finite-type invariants for stable homeomorphism classes of curves on compact oriented surfaces without boundaries. These invariants are a…
The notion of Schnorr randomness refers to computable reals or computable functions. We propose a version of Schnorr randomness for subcomputable classes and characterize it in different ways: by Martin L\"of tests, martingales or measure…
We give the definition of an invariant random positive definite function on a discrete group, generalizing both the notion of an invariant random subgroup and a character. We use von Neumann algebras to show that all invariant random…
In calculus, an indefinite integral of a function $f$ is a differentiable function $F$ whose derivative is equal to $f$. In present paper, we generalize this notion of the indefinite integral from the ring of real functions to any ring. The…
For system of two ordinary differential equations of the second order representing autonomous non-conservative holonomic mechanical system, in case of dynamics such as one-frequency periodical oscillations, is found integrated invariant of…
It is well known that a k-dimensional smooth surface in a Euclidean space cannot be tangent to a non-involutive distribution of k-dimensional planes. In this paper we discuss the extension of this statement to weaker notions of surfaces,…
A sequence of monoidal transformations is defined, in terms of invariants, for a singular hypersurface embedded in a smooth scheme of positive characteristic. Some examples are added to illustrate the improvement of singularities by this…
Explicit generators are given for the ring of invariant polynomials under the coadjoint representation of certain inhomogeneous groups.
We define a new finite type invariant for stably homeomorphic class of curves on compact oriented surfaces without boundaries and extend to a regular homotopy invariant for spherical curves.
Several sets of quaternionic functions are described and studied. Residue current of the right inverse of a quaternionic function is introduced in particular cases.
We consider random fields that can be represented as integrals of deterministic functions with respect to infinitely divisible random measures and show that these random fields are infinitely divisible.
The description of invariants of surfaces with respect to the motion groups is reduced to the description of invariants of parameterized surfaces with respect to the motion groups. Existence of a commuting system of invariant partial…
We define a Gaussian invariant measure for the two-dimensional averaged-Euler equation and show the existence of its solution with initial conditions on the support of the measure. An invariant surface measure on the level sets of the…
For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…
A gauge invariant partition function is defined for gauge theories which leads to the standard quantization. It is shown that the descent equations and consequently the consistent anomalies and Schwinger terms can be extracted from this…
The random integral mappings (some type of functionals of L\'evy processes) are continuous homomorphisms between convolution subsemigroups of the semigroup of all infinitely divisible measures. Compositions of those random integrals…