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A generalization of incidence relations in abstract polytope has been explored, and parameterized surfaces are used as primers. The abstract orientable incidence structure is defined as an algebraic model of incidence relations, in which…

We consider the problem of finding a condition for a univariate polynomial having a given multiplicity structure when the number of distinct roots is given. It is well known that such conditions can be written as conjunctions of several…

In our work we investigate quotient structures and quotient spaces of a space of orderings arising from subgroups of index two. We provide necessary and sufficient conditions for a quotient structure to be a quotient space that, among other…

Investigation of the approximation properties, convergence, and stability of the ADER-DG method for solving an ODE system is carried out. The ADER-DG method is $A$- and $AN$-stable, $L$-stable, $B$- and $BN$-stable, and algebraically…

We prove an equivalence between the existence of the first structure relation satisfied by a sequence of monic orthogonal polynomials $\{P_n\}_{n=0}^{\infty}$, the orthogonality of the second derivatives $\{\mathbb{D}_{x}^2P_n\}_{n=…

Let $\G$ denote a bipartite distance-regular graph with vertex set $X$ and diameter $D \ge 3$. Fix $x \in X$ and let $L$ (resp. $R$) denote the corresponding lowering (resp. raising) matrix. We show that each $Q$-polynomial structure for…

We construct manifold structures on various sets of solutions of the general relativistic initial data sets.

The Poisson structure arising in the Hamiltonian approach to the rational Gaudin model looks very similar to the so-called modified Reflection Equation Algebra. Motivated by this analogy, we realize a braiding of the mentioned Poisson…

We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…

We present a concept of uniform encodability of theories and develop tools related to this concept. As an application we obtain general undecidability results which are uniform for large families of structures. In the way, we define…

Let $k$ be a differential field of characteristic zero with an algebraically closed field of constants. In this article, we provide a classification of first order differential equations over $k$ and study the algebraic dependence of…

This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…

We provide a comprehensive survey of splitting and composition methods for the numerical integration of ordinary differential equations (ODEs). Splitting methods constitute an appropriate choice when the vector field associated with the ODE…

Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notions of solutions. Typical examples are satisfying…

Real-world phenomena can often be conveniently described by dynamical systems (that is, ODE systems in the state-space form). However, if one observes the state of the system only partially, the observed quantities (outputs) and the inputs…

Ordinary differential equations (ODE's) are a cornerstone of systems and control theory. Accordingly, they are standard material in undergraduate programs in engineering and there is abundant didactic literature about this topic. Yet, the…

This work reports and classifies the most general construction of rational quantum potentials in terms of the generalized Hermite polynomials. This is achieved by exploiting the intrinsic relation between third-order shape-invariant…

In order to construct solutions of the braid equation we consider bijective left non-degenerate set-theoretic type solutions, which correspond to regular q-cycle coalgebras. We obtain a partial classification of the different q-cycle…

Complex-linearization of a class of systems of second order ordinary differential equations (ODEs) has already been studied with complex symmetry analysis. Linearization of this class has been achieved earlier by complex method, however,…

We investigate the presence of defects in systems described by real scalar field in (D,1) spacetime dimensions. We show that when the potential assumes specific form, there are models which support stable global defects for D arbitrary. We…