Related papers: A generalization of Levin-Schnorr's theorem

The inverse problem of general rough sets, considered by the present author in some of her earlier papers, in one of its manifestations is essentially the question of when an agent's view about crisp and non crisp objects over a set of…

A derivation of the relative velocity used in the definition of the relativistic cross-section is given in terms of manifestly Lorentz invariant quantities. Along the way we find that there is a certain arbitrariness in the usual definition…

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

For a linear differential equation with a mild condition on its singularities, we discuss generalized continued fractions converging to expressions in its solutions and their derivatives. In the case of an order two linear differential…

It is known that Plotkin's reduction theorem is very important for his theory of universal algebraic geometry [arXiv:math. GM/0210187], [arXiv:math. GM/0210194]. It turns out that this theorem can be generalized to arbitrary categories…

By introducing a second complex variable, the integral relation between a complex density and the corresponding positive distribution is derived. Together with the positivity and normalizability conditions, this sum rule allows to construct…

Leibniz algebras are certain generalization of Lie algebras. It is natural to generalize concepts in Lie algebras to Leibniz algebras and investigate whether the corresponding results still hold. In this paper we introduce the notion of…

Recently, an infinite class of holographic generalized complexities was proposed. These gravitational observables display the behavior required to be duals of complexity, in particular, linear growth at late times and switchback effect. In…

The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…

We generalize Rado's extension theorem to complex spaces.

We carry out the complete group classification of the class of (1+1)-dimensional linear Schr\"odinger equations with complex-valued potentials. After introducing the notion of uniformly semi-normalized classes of differential equations, we…

We characterize the variation functions of computable Lipschitz functions. We show that a real z is computably random if and only if every computable Lipschitz function is differentiable at z. Beyond these principal results, we show that a…

We derive the spin-statistics theorem in both relativistic and non-relativistic first-quantized form, extending considerably the earlier proofs. Our derivation is based on the representation theories of the groups SU (2) and SL(2,C), latter…

Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…

The law of total probability may be deployed in binary classification exercises to estimate the unconditional class probabilities if the class proportions in the training set are not representative of the population class proportions. We…

We obtain a measure theoretical characterization of polynomials among rational functions on $\mathbb{P}^1$, which generalizes a theorem of Lopes. Our proof applies both classical and dynamically weighted potential theory.

The notion of random self-decomposability is generalized further. The notion is then extended to non-negative integer-valued distributions.

Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.

In this paper we give a factorization theorem for the ring of exponential polynomials in many variables over an algebraically closed field of characteristic 0 with an exponentiation. This is a generalization of the factorization theorem due…

We formulate generalizations of Pauli's theorem on the cases of real and complex Clifford algebras of even and odd dimensions. We give analogues of these theorems in matrix formalism. Using these theorems we present an algorithm for…