Related papers: Characterization of distributivity in a solid
We compare the Egalitarian Equivalent and the Competitive Equilibrium with Equal Incomes rules to divide a bundle of goods (heirlooms) or a bundle of bads (chores). For goods the Competitive division fares better, as it is Resource…
We show that the de Rham theorem, interpreted as the isomorphism between distributional de Rham cohomology and simplicial homology in the dual dimension for a simplicial decomposition of a compact oriented manifold, is a straightforward…
Inheritances, divorces or liquidations of companies require common assets to be divided among the entitled parties. Legal methods usually consider the market value of goods, while fair division theory takes into account the parties'…
We present distributions of countable models and correspondent structural characteristics of complete theories with continuum many types: for prime models over finite sets relative to Rudin-Keisler preorders, for limit models over types and…
We discuss the property of the number density of a fluid of particles living in a curved surface without boundaries to be constant in the thermodynamic limit. In particular we find a sufficient condition for the density to be constant along…
The correction to Maxwell-Boltzmann's velocity distribution law is obtained in the framework of the modified special relativity theory. The detection of velocity and velocity rate distributions for thermal molecules or atoms or other…
The mollified uniform distribution is rediscovered, which constitutes a ``soft'' version of the continuous uniform distribution. Important stochastic properties are presented and used to demonstrate potential fields of applications. For…
In the paper, notions of relative separability for hypergraphs of models of a theory are defined. Properties of these notions and applications to ordered theories are studied: characterizations of relative separability both in a general…
The normal modes of a continuum solid endowed with a random distribution of line defects that behave like elastic strings are described. These strings interact with elastic waves in the bulk, generating wave dispersion and attenuation. As…
The continuous limit of large systems of particles of finite size on the line is described. The particles are assumed to move freely and stick under collision, to form compound particles whose mass and size is the sum of the masses and…
Using a probabilistic model, based on random walks on the additive group $\mathbb{Z}/m\mathbb{Z}$, we prove that the values of certain real character sums are uniformly distributed in residue classes modulo $m$.
Recently, Boehm and Stefan constructed duplicial (paracyclic) objects from distributive laws between (co)monads. Here we define the category of factorisations of a distributive law, show that it acts on this construction, and give some…
The notion of random self-decomposability is generalized further. The notion is then extended to non-negative integer-valued distributions.
The novel concept of spectral diffusivity is introduced to analyse the dissipative properties of continua. The dissipative components of a linear system of evolution equations are separated into noninteracting parts. This separation is…
In this paper, we define a new structure analogous to group, called partial group. This structure concerns the partial stability by the composition inner law. We generalize the three isomorphism theorems for groups to partial groups.
In nature or societies, the power-law is present ubiquitously, and then it is important to investigate the mathematical characteristics of power-laws in the recent era of big data. In this paper we prove the superposition of non-identical…
The paper discusses a test for the hypothesis that a random sample comes from the Cauchy distribution. The test statistics is derived from a characterization and is based on the characteristic function. Properties of the test are discussed…
The question of biological stability (permanence) of a replicator reaction-diffusion system is considered. Sufficient conditions of biological stability are found. It is proved that there are situations when biologically unstable…
We revisit the standard axioms of domain theory with emphasis on their relation to the concept of partiality, explain how this idea arises naturally in probability theory and quantum mechanics, and then search for a mathematical setting…
We introduce a new class of multiplications of distributions in one dimension merging together two different regularizations of distributions. Some of the features of these multiplications are discussed in a certain detail. We use our…