相关论文: Classification of quad-equations on a cuboctahedro…
In this work we will discuss the facial structure of the cone of nonnegative ternary quartics with real coefficients. We will establish an equivalence relation on the set of all faces, which preserves certain properties like dimension or…
In this paper, we introduce notions of partitionability and characteristic sets of homogeneous polynomials and give a complete classification of groups faithfully acting on smooth cubic fivefolds. Specifically, we prove that there exist 20…
This paper details an algorithm for unfolding a class of convex polyhedra, where each polyhedron in the class consists of a convex cap over a rectangular base, with several restrictions: the cap's faces are quadrilaterals, with vertices…
The M\"obius polynomial is an invariant of ranked posets, closely related to the M\"obius function. In this paper, we study the M\"obius polynomial of face posets of convex polytopes. We present formulas for computing the M\"obius…
This paper investigates the rigidity of bordered polyhedral surfaces. Using the variational principle, we show that bordered polyhedral surfaces are determined by boundary value and discrete curvatures on the interior edges. As a corollary,…
Some upper bounds for the number of monogenizations of quartic orders are established by considering certain classical Diophantine equations, namely index form equations in quartic number fields, and cubic and quartic Thue equations.
The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in H-J equation is clarified.
The action of ring automorphisms of the polynomial ring in two variables over the real numbers on real plane curves is considered. The orbits containing degree-three polynomials are computed, with one representative per orbit being…
The definition of principal nest is supplemented with a system of frames that make possible the classification of combinatorial types for every level of the nest. As a consequence, we give necessary and sufficient conditions for the…
We study relations between the eigenvectors of rational matrix functions on the Riemann sphere. Our main result is that for a subclass of functions that are products of two elementary blocks it is possible to represent these relations in a…
We prove that certain polynomials previously introduced by the author can be identified with tau functions of Painlev\'e VI, obtained from one of Picard's algebraic solutions by acting with a four-dimensional lattice of B\"acklund…
Let $Y$ be a cubic threefold with a non-Eckardt type involution $\tau$. Our first main result is that the $\tau$-equivariant category of the Kuznetsov component $\mathcal{K}u_{\mathbb{Z}_2}(Y)$ determines the isomorphism class of $Y$ for…
A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…
This paper addresses the classical and discrete Euler-Lagrange equations for systems of $n$ particles interacting quadratically in $\mathbb{R}^d$. By highlighting the role played by the center of mass of the particles, we solve the previous…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
The paper represents the method for construction of the families of particular solutions to some new classes of $(n+1)$ dimensional nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic…
We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical…
We derive a system of difference equations satisfied by the three-term recurrence coefficients of some families of discrete orthogonal polynomials.
We investigate the average number of solutions of certain quadratic congruences. As an application, we establish Manin's conjecture for a cubic surface whose singularity type is A_5+A_1.
We prove some positivity results on the coefficients in the complexified Hilbert polynomial of a semi-stable object. After applying these results on the classical slope stability conditions, we get sequences of quadratic inequalities for…