相关论文: Okounkov bodies and transfinite diameter
An exact, number-conserving solution to the generalized, orbit-dependent pairing problem is derived by introducing an infinite-dimensional algebra. A method for obtaining eigenvalues and eigenvectors of the corresponding Hamiltonian is also…
We introduce f-divergence, a concept from information theory and statistics, for convex bodies in R^n. We prove that f-divergences are SL(n) invariant valuations and we establish an affine isoperimetric inequality for these quantities. We…
A formula for computation of the bivariate Poincar\'e series $\mathcal{P}_d(z,t)$ for the algebra of covariants of binary $d$-form is found.
The article is devoted to affine and wrap algebras over quaternions and octonions. Residues of functions of quaternion and octonion variables are studied. They are used for construction of such algebras. Their structure is investigated.
We prove that the existence of a finite Minkowski base for Okounkov bodies on a smooth projective variety with respect to an admissible flag implies rational polyhedrality of the global Okounkov body. As an application of this general…
A variant of the flatness problem from integer programming is studied, in which one considers convex bodies in $\mathbb{R}^d$ with at most $k$ interior lattice points. The maximum lattice width of such a body is denoted by Flt(d,k) and it…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
The discrete cosine transform is a valuable tool in analysis of data on undirected rectangular grids, like images. In this paper it is shown how one can define an analogue of the discrete cosine transform on triangles. This is done by…
We derive an explicit formula for the volume of a regular simplex in the hyperbolic space of any dimension.
In this paper we prove the isomorphism of the positive half of the quantum toroidal algebra and the positive half of the Maulik-Okounkov quantum affine algebra of affine type $A$ via the monodromy representation for the Dubrovin connection.…
We study perturbations of random dynamical systems whose associated transfer operators admit a uniform spectral gap. We provide a $k^{\text{th}}$-order approximation for the invariant density of the associated random dynamical system. We…
Krasnov (arXiv: hep-th/0005106) identified the renormalized volume of a Schottky 3-manifold with the action of the Liouville theory on the conformal infiinity. We try to compute the renormalized volume in terms of more transparent geometric…
This research article discusses a numerical solution of the radiative transfer equation based on the weak Galerkin finite element method. We discretize the angular variable by means of the discrete-ordinate method. Then the resulting…
An alternative treatment is proposed for the calculations carried out within the frame of Nikiforov-Uvarov method, which removes a drawback in the original theory and by pass some difficulties in solving the Schrodinger equation. The…
In this survey we review different instances in which the Drinfeld double of a finite group and its representations play a role, touching upon some of Tom Koornwinder's research interests: harmonic analysis, Lie algebras, quantum groups,…
A quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms is proved. We also give an application to eigenvalue spacing on flat 2-tori with Aharonov-Bohm flux.
We construct frieze patterns of type D_N with entries which are numbers of matchings between vertices and triangles of corresponding triangulations of a punctured disc. For triangulations corresponding to orientations of the Dynkin diagram…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…
We consider the question how well a floating body can be approximated by the polar of the illumination body of the polar. We establish precise convergence results in the case of centrally symmetric polytopes. This leads to a new affine…