Related papers: On a second-order rational difference equation and…

A new formulation of boundary value problems in gradient elasticity is presented in this work. The main outcome is the construction of partial differential systems of second order, which are typically equivalent with the well known fourth…

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…

By folding an autonomous system of rational equations in the plane to a scalar difference equation, we show that the rational system has coexisting periodic orbits of all possible periods as well as stable aperiodic orbits for certain…

This paper studies the second moment boundedness of solutions of linear stochastic delay differential equations. First, we give a framework, for general $\mathrm{N}$-dimensional linear stochastic differential equations with a single…

The main purpose of this paper is the study of second-order optimality conditions for the bilinear control of a strongly degenerate parabolic equation. The equation is degenerate at the boundary of the spatial domain. The well-posedness of…

We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…

We give explicit necessary and sufficient conditions for the boundedness of the general second order differential operator L with real- or complex-valued distributional coefficients acting from the Sobolev space W^{1,2}(R^n) to its dual…

Two main approaches for evaluating the quality of machine-generated rationales are: 1) using human rationales as a gold standard; and 2) automated metrics based on how rationales affect model behavior. An open question, however, is how…

This continues the investigation of a combinatorial model for the variation of dynamics in the family of rational maps of degree two, by concentrating on those varieties in which one critical point is periodic. We prove some general results…

The asymptotic behavior (such as convergence to an equilibrium, convergence to a 2-cycle, and divergence to infinity) of solutions of the following multi-parameter, rational, second order difference equation x_{n+1} =(ax_{n}^3+…

A general principle of `causal duality' for physical systems, lying at the base of representation theorems for both compound and evolving systems, is proved; formally it is encoded in a quantaloidal setting. Other particular examples of…

The systems of complex analytic second order ordinary differential equations whose solutions close up to become rational curves (after analytic continuation) are characterized by the vanishing of an explicit differential invariant, and turn…

Recently, various systems of nonlinear difference equations, of different forms, were studied. In this existing work, two earlier published papers, due respectively to Bayram and Das. [Appl. Math. Sci. (Ruse), 4(7) (2010) pp. 817-821] and…

For a certain class of genuinely nonlinear two-by-two planar hyperbolic systems we show that any classical solution on a smoothly bounded domain has nontangential boundary limits except on a set whose Hausdorff dimension is bounded by some…

We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under relation…

We consider periodic second-order equations having an ordered pair of lower and upper solutions and show the existence of asymptotic trajectories heading towards the maximal and minimal periodic solutions which lie between them.

This paper is concerned with the existence of positive solutions of second-order impulsive differential equations with integral boundary conditions on an infinite interval. As an application, an example is given to demonstrate our main…

We study the semiclassical behaviour of a two--dimensional nonintegrable system. In particular we analyze the question of quantum corrections to the semiclassical quantization obtaining up to the second order of perturbation theory an…

This paper explores the hard problem of consciousness from a different perspective. Instead of drawing distinctions between the physical and the mental, an exploration of a more foundational relationship is examined: the relationship…

We first highlight the main differences between second order and higher order linear parabolic equations. Then we survey existing results for the latter, in particular by analyzing the behavior of the convolution kernels. We illustrate the…