Related papers: Discrete Nodal Domain Theorems

Eq.(19) is added and related issues are further clarified. Also some typos and signs a re corrected.

We present a multivariable generalization of the digital binomial theorem from which a q-analog is derived as a special case.

In this paper, we prove Gromov's flat corner domination conjecture in all dimensions. As a consequence, we answer positively the Stoker conjecture for convex Euclidean polyhedra in all dimensions. By applying the same techniques, we also…

We propose the existence theorem for bounded solutions to the system of 2-nd order ODE. Dynamical applications have been considered.

In this paper we give two theorems from the Propositional Calculus of the Boolean Logic with their consequences and applications and we prove them axiomatically.

Here we define a Caputo like discrete fractional difference and we compare it to the earlier defined Riemann-Liouville fractional discrete analog. Then we produce discrete fractional Taylor formulae for the first time, and we estimate their…

We give a q-analogue of Gauss' divisibility theorem

An technically interesting proof of a known theorem.

We derive a symplectic analogue of A-directed immersion theorem.

By using some elementary techniques from operator theory, we prove constructively prove the existence of solutions to Dirichl\'et problems for planar Jordan domains with at least two boundary curves. An iterative method is thus obtained,…

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

We say that a knot $k_1$ in the $3$-sphere {\it $1$-dominates} another $k_2$ if there is a proper degree 1 map $E(k_1) \to E(k_2)$ between their exteriors, and write $k_1 \ge k_2$. When $k_1 \ge k_2$ but $k_1 \ne k_2$ we write $k_1 > k_2$.…

We prove that the real parts of equivariant (but non-invariant) eigenfunctions of generic bundle metrics on nontrivial principal $S^1$ bundles over manifolds of any dimension have connected nodal sets and exactly 2 nodal domains. This…

We introduce and systematically develop two classes of discrete integrable operators: those with $2\times 2$ matrix kernels and those possessing general differential kernels, thereby generalizing the discrete analogue previously studied. A…

This is the second combinatorial proof of the compactness theorem for singular from 1977. In fact it gives a somewhat stronger theorem.

The weakly relational domain of Octagons offers a decent compromise between precision and efficiency for numerical properties. Here, we are concerned with the construction of non-numerical relational domains. We provide a general…

A new generalization of the classical separate algebraicity theorem is suggested and proved.

The purpose of this note is to provide an alternative proof of two quadratic transformation formulas contiguous to that of Gauss using a differential equation approach.

We prove an analogue of Pleijel's nodal domain theorem for piecewise analytic planar domains with Neumann boundary conditions. This confirms a conjecture made by Pleijel in 1956. The proof is a combination of Pleijel's original approach and…