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Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B which is embedded with a stronger structure S. By a proper subset one understands a set included in A,…
Nonlinear perturbation of Fuchsian systems are studied in a region including two singularities. It is proved that such systems are generally not analytically equivalent to their linear part (they are not linearizable) and the obstructions…
We find a representation of smooth solutions to the Cauchy problem for a scalar multidimensional conservation law as small diffusion limit of a stochastic perturbation along characteristics. It helps, in particular, to study the process of…
We consider systems of diffusion equations that have considerable interest in Soil Science and Mathematical Biology and focus upon the problem of finding those forms of this class that can be linearized. In particular we use the equivalence…
We show that a polynomial equation of degree less than 5 and with real parameters can be solved by regarding the variable in which the polynomial depends as a complex variable. For do it so, we only have to separate the real and imaginary…
In this paper we introduce an algebraic recursive multilevel incomplete factorization preconditioner, based on a distributed Schur complement formulation, for solving general linear systems. The novelty of the proposed method is to combine…
The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super-Yang-Mills. It is dual to another complex matrix…
We prove rigorously the convergence of the Cahn-Larch\'e system, which is a Cahn-Hilliard system coupled with the system of linearized elasticity, to a modified Hele-Shaw problem as long as a classical solution of the latter system exists.…
We establish a connection between finite fields and finite dynamical systems. We show how this connection can be used to shed light on some problems in finite dynamical systems and in particular, in linear systems.
Linear systems are the bedrock of virtually all numerical computation. Machine learning poses specific challenges for the solution of such systems due to their scale, characteristic structure, stochasticity and the central role of…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
We study a class of overdetermined algebraic systems of equations. We prove that the number of distinct solutions equals to the maximal possible if and only if certain matrices are commuting and semisimple. This gives a characterization of…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
A variety is rationally connected if two general points can be joined by a rational curve. A higher version of this notion is rational simple connectedness, which requires suitable spaces of rational curves through two points to be…
We deal with $m$-component vector-valued solutions to the Cauchy problem for linear both homogeneous and nonhomogeneous weakly coupled second order parabolic system in the layer ${\mathbb R}^{n+1}_T={\mathbb R}^n\times (0, T)$. We assume…
Causal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
In this chapter, I review the main methods and techniques of complex systems science. As a first step, I distinguish among the broad patterns which recur across complex systems, the topics complex systems science commonly studies, the tools…
The article attempts to find an algebraic formula describing the correlation coefficients between random variables and the principal components representing them. As a result of the analysis, starting from selected statistics relating to…