Related papers: Scalar second order evolution equations possessing…
The space of derivations of finite dimensional evolution algebras associated to graphs over a field with characteristic zero has been completely characterized in the literature. In this work we generalize that characterization by describing…
Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with…
We construct a scalar field based cosmological model, possessing a cosmological singularity characterized by a finite value of the cosmological radius and an infinite scalar curvature. Using the methods of the qualitative theory of…
This article deals with the second order linear differential equations with entire coefficients. We prove some results involving conditions on coefficients so that the order of growth of every non-trivial solution is infinite.
In this paper, we develop an algebraic approach to classifying contact symmetries of the second-order nonlinear evolution equations. Up to contact isomorphisms, all inequivalent PDEs admitting semi-simple algebras, solvable algebras of…
It is well-known that the space of derivations of $n$-dimensional evolution algebras with non-singular matrices is zero. On the other hand, the space of derivations of evolution algebras with matrices of rank $n-1$ has also been completely…
The main objective of this paper is to study the relationship between a solvable evolution algebra and its subalgebra lattice, emphasizing two of its main properties: distributivity and modularity. First, we will focus on the nilpotent…
In the paper we give a complete classification of $2$-dimensional evolution algebras over algebraically closed fields, describe their groups of automorphisms and derivation algebras.
In this work we investigate the derivations of $n-$dimensional complex evolution algebras, depending on the rank of the appropriate matrices. For evolution algebra with non-singular matrices we prove that the space of derivations is zero.…
The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…
All SL($n$) contravariant vector valuations on polytopes in $\mathbb R^n$ are completely classified without any additional assumptions. The facet vector is defined. It turns out to be the unique such valuation for $n\geq3$. In dimension…
We present numerical solutions of the hyperboloidal initial value problem for a self-gravitating scalar field in spherical symmetry, using a variety of standard hyperbolic slicing and shift conditions that we adapt to our hyperboloidal…
Conditions of the existence of solutions of linear and perturbed linear boundary value problems in the Hilbert spaces for the second order evolution equation are obtained.
We deal with the existence of solutions having L2 regularity for a class of non autonomous evolution equations. Associated with the equation, a general non local condition is studied. The technique we used combines a finite dimensional…
The method of parameter variation for linear differential equations is extended to classes of second order nonlinear differential equations. This allows to reduce the latter to first order differential equations. Known classical equations…
We give a classification of all third-order nonlinear evolution equations which admit solvable Lie symmetry algebras $\mathsf{A}$ and which are not linearized. We have found that there are 48 types of equations for $\dim\mathsf{A}=3$, 88…
We prove that every finite dimensional unitary representation of $\mathrm{SL}_{4}(\mathbf{Z})$ contains a non-zero $\mathrm{SL}_{2}(\mathbf{Z})$-invariant vector. As a consequence, there is no sequence of finite-dimensional representations…
We study evolution algebras of arbitrary dimension. We analyze in deep the notions of evolution subalgebras, ideals and non-degeneracy and describe the ideals generated by one element and characterize the simple evolution algebras. We also…
All finite-dimensional Leibniz algebra bimodules of a Lie algebra $\mathfrak{sl}_2$ over a field of characteristic zero are described.
We consider a class of linear ODEs of second order with variable coefficients and construct its Lie algebra of Lie group of equivalence transformations. Further we find invariants and differential invariants of this Lie algebra and by using…