Related papers: Characterization of distributivity in a solid
An inequality for the variance of an additive function defined on random decomposable structures, called assemblies, is established. The result generalizes estimates obtained earlier in the cases of permutations and mappings of a finite set…
A wide range of materials can exist in microscopically disordered solid forms, referred to as amorphous solids or glasses. Such materials -- oxide glasses and metallic glasses, to polymer glasses, and soft solids such as colloidal glasses,…
There may be a link between the quantum properties of the vacuum and the parameters describing the properties of light propagation, culminating in a sum over all types of elementary particles existing in Nature weighted only by their…
In this paper, we analyze the set of all possible aggregate distributions of the sum of standard uniform random variables, a simply stated yet challenging problem in the literature of distributions with given margins. Our main results are…
A geometrical interpretation of the $G$-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of…
This note formally defines the concept of coinductive validity of judgements, and contrasts it with inductive validity. For both notions it shows how a judgement is valid iff it has a formal proof. Finally, it defines and illustrates the…
By working with coefficients in $\mathbb{Z}$ or $\mathbb{R}$, one can define two different notions of stability for a sandpile on a graph. We call a sandpile immutable when these notions agree. Our main results give linear-algebraic…
The generalized allocation scheme is studied. Its extension for coloured balls is defined. Some analogues of the Law of the Iterated Logarithm and the Strong Law of Large Numbers are obtained for the number of boxes containing fixed numbers…
We give necessary and sufficient criteria for a distribution to be smooth or uniformly H\"{o}lder continuous in terms of approximation sequences by smooth functions; in particular, in terms of those arising as regularizations…
The one-dimensional Dickman distribution arises in various stochastic models across number theory, combinatorics, physics, and biology. Recently, a definition of the multidimensional Dickman distribution has appeared in the literature,…
Symmetry properties of conservation laws of partial differential equations are developed by using the general method of conservation law multipliers. As main results, simple conditions are given for characterizing when a conservation law…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
We study a two-dimensional granular system where external driving force is applied to each particle in the system in such a way that the system is driven into a steady state by balancing the energy input and the dissipation due to inelastic…
We discuss the statistical properties of a single vortex line in a perfect fluid. The partition function is calculated up to the end in the thin vortex approximation. It turns out that corresponding theory is renormalizable, and the…
We provides some new equivalent forms of collection principle over some very weak set theories after reviewing the existing ones.
On contrary to the customary thought, the well-known ``lemma'' that the distribution function of a collisionless Boltzmann gas keeps invariant along a molecule's path represents not the strength but the weakness of the standard theory. One…
Highly acurate numerical simulations are employed to highlight the subtle but important differences in the mechanical stability of perfect crystalline solids versus amorphous solids. We stress the difference between strain values at which…
We consider a finite, closed and selfbound many--body system in which a collective degree of freedom is excited. The redistribution of energy and momentum into a finite number of the non-collective degrees of freedom is referred to as…
We develop a theory of sets with distributive products (called shelves and multi-shelves) and of their homology. We relate the shelf homology to the rack and quandle homology.
It is known that few characterization results of the logistic distribution were available before, although it is similar in shape to the normal one whose characteristic properties have been well investigated. Fortunately, in the last…