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Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
Based on the generalized non-Markovian equations obtained earlier for a nonequilibrium one-particle distribution function and potential part of the averaged enthalpy density [Markiv B.B., Omelyan I.P, Tokarchuk M.V., Condens. Matter Phys.,…
In this paper, we consider sums of values of degenerate falling factorials and give a probabilistic proof of a recurrence relation for them. This may be viewed as a degenerate version of the recent probabilistic proofs on sums of powers of…
In this paper, we prove new convergence results improving the ones by Chassagneux, Elie and Kharroubi [Ann. Appl. Probab. 22 (2012) 971--1007] for the discrete-time approximation of multidimensional obliquely reflected BSDEs. These BSDEs,…
This paper presents calculations of the Castaing (Physica D, 46, 177, 1990) cascade kernels for five well-known models of the turbulent cascade and demonstrates that these kernels provide conceptually simple and direct descriptions of…
The motivation of this work is the study of the error term e_t^{\epsilon}(x,\omega) in the averaging method for differential equations perturbed by a dynamical system. Results of convergence in distribution for…
The cascade kinetic fragmentation process of solids is investigated when the condition probability density of splinter formation do not depends on time and has the property $P(\rho, r, t) = P(\rho/r)$. It is obtained the evolution equation…
We provide a detailed derivation of the Karhunen-Lo\`eve expansion of a stochastic process. We also discuss briefly Gaussian processes, and provide a simple numerical study for the purpose of illustration.
In [3], we have introduced a probability measure to study the power and exponential sums for a certain coding system. The distribution function of the probability measure gives explicit formulas for the power and exponential sums.…
This paper studies the distribution of chain and maximal chain lengths in a causal set. We first provide a new derivation for these distributions for a causal set uniformly embedded in Minkowski space, for various dimensionalities, which…
Starting from well-known expressions for the $T$-matrix and its derivative in standard nonrelativistic potential scattering I rederive recent path-integral formulations due to Efimov and Barbashov et al. Some new relations follow…
This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtaining scale covariance, which holds…
The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply and urban pollution. Motivated by this, we develop a large-deviation theory that…
Expression for probability distribution is got taking into account a presence and removal of degeneracy on the microstates. Its application allows to describe the process of melting of solids, as saltatory phase transition of the first kind…
We write explicit contour integral formulas for probability distributions of the multi-species q-TAZRP and the multi-species ASEP starting with q-exchangeable initial conditions. The formulas are equal to the corresponding explicit contour…
It is shown that in the complex trajectory representation of quantum mechanics, the Born's Psi^{\star}\Psi probability density can be obtained from the imaginary part of the velocity field of particles on the real axis. Extending this…
Dedekind sums have applications in quite a number of fields of mathematics. Therefore, their distribution has found considerable interest. This article gives a survey of several aspects of the distribution of these sums. In particular, it…
Comment on Proximity breakdown of hydrides in superconducting niobium cavities [arXiv:1212.3384].
We present a new one parameter family of second derivative discontinuous solutions to the simplest scale invariant linear ordinary differential equation. We also point out how the construction could be extended to generate families of…
The probability distributions of the masses of the clusters spanning from top to bottom of a percolating lattice at the percolation threshold are obtained in all dimensions from two to five. The first two cumulants and the exponents for the…