Related papers: Simultaneous additive equations: Repeated and diff…
We give upper bounds for the number of integral solutions of bounded height to a system of equations $f_i(x_1,\ldots,x_n) = 0$, $1 \leq i \leq r$, where the $f_i$ are polynomials with integer coefficients. The estimates are obtained by…
Symmetries for wave equation with additional conditions are found. Some conditions yield infinite-dimensional symmetry algebra for the nonlinear equation. Ansatzes and solutions corresponding to the new symmetries were constructed.
We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…
For homogeneous difference equation of the second order we study the analogy of Hartman-Wintner problem on asymptotic integration of fundamental system of solutions as argument tends to infinity.
In this paper, we study the Hessian equation with infinite Dirichlet (blow-up) boundary value conditions. Using radial functions and techniques of ordinary differential inequality, we construct various barrier functions (super-solution and…
This paper deals with time stepping schemes for the Cahn--Hilliard equation with three different types of dynamic boundary conditions. The proposed schemes of first and second order are mass-conservative and energy-dissipative and -- as…
We study integrating (that is expanding to a Hasse-Schmidt derivation) derivations, and more generally truncated Hasse-Schmidt derivations, satisfying iterativity conditions given by formal group laws. Our results concern the cases of the…
In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under…
This paper develops necessary and sufficient conditions for the preservation of asymptotic convergence rates of deterministically and stochastically perturbed ordinary differential equations with regularly varying nonlinearity close to…
In this work we deal with a scalar spectral mixed boundary value problem in a spacial junction of thin rods and a plate. Constructing asymptotics of the eigenvalues, we employ two equipollent asymptotic models posed on the skeleton of the…
We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x>0, t>0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and…
We discuss several enumerative results for irreducible polynomials of a given degree and pairs of relatively prime polynomials of given degrees in several variables over finite fields. Two notions of degree, the {\em total degree} and the…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
We investigate the multiplicity of solutions for a Hamiltonian system coupling two systems associated with mixed boundary conditions. Corresponding to the first system, we impose periodic boundary conditions and assume the twist assumption…
We give an equivalent condition for the validity of the Hasse norm principle for finite separable extensions of prime squared degree of global fields. Our theorem recovers the result of Drakokhrust--Platonov, which claims that the Hasse…
Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as…
We establish new combinatorial transcendence criteria for continued fraction expansions. Let $\alpha = [0; a_1, a_2,...]$ be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
We extend the Gibbs conditioning principle to an abstract setting combining infinitely many linear equality constraints and non-linear inequality constraints, which need not be convex. A conditional large large deviation principle (LDP) is…
In the paper we give an upper bound for the Waldschmidt constants of the wide class of ideals. This generalizes the result obtained by Dumnicki, Harbourne, Szemberg and Tutaj-Gasinska, Adv. Math. 2014. Our bound is given by a root of a…