Related papers: A new Euclidean tight 6-design
We show how recent progress in computing elliptic genera of strings in six dimensions can be used to obtain expressions for elliptic genera of strings in five-dimensional field theories which have a six-dimensional parent. We further…
We provide some new sharp embeddings for p-Carleson and related measures in the unit disk of the complex plane
We consider a new matrix model based on the simply connected compact exceptional Lie group E6. A matrix Chern-Simons theory is directly derived from the invariant on E6. It is stated that the similar argument as Smolin which derives an…
We study the 6-vertex model with fixed boundary conditions. In the thermodynamical limit there is a formation of the limit shape. We collect most of the known results about the analytical properties of the free energy of the model as the…
A method to construct trihamiltonian extensions of a separable system is presented. The procedure is tested for systems, with a natural Hamiltonian, separable in classical sense in one of the four orthogonal separable coordinate systems of…
An $s$-extremal optimal unimodular lattice in dimension $52$ is constructed for the first time. This lattice is constructed from a certain self-dual $\mathbb{F}_5$-code by Construction A. In addition, as neighbors of the lattice, two more…
We introduce and study symmetric polynomials, which as very special cases include polynomials related to the supersymmetric eight-vertex model, and other elliptic lattice models with $\Delta=\pm 1/2$. There is also a close relation to…
A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that…
We give an optimal bound on normal curvatures of immersed n-torus in a Euclidean ball of large dimension.
An ellipsoid, the simplest non-spherical shape, has been extensively used as models for elongated building blocks for a wide spectrum of molecular, colloidal and granular systems. Yet the densest packing of congruent hard ellipsoids, which…
In this paper, we characterize round spheres in the Euclidean space under some suitable conditions on the r-mean curvature.
A classical 6j-symbol is a real number which can be associated to a labelling of the six edges of a tetrahedron by irreducible representations of SU(2). This abstract association is traditionally used simply to express the symmetry of the…
In this paper, we continue the study of almost squares and extend the result of the author's fourth paper of the series to almost squares with closer factors.
We describe and analyze a new construction that produces new Eulerian lattices from old ones. It specializes to a construction that produces new strongly regular cellular spheres (whose face lattices are Eulerian). The construction does not…
The main results of the paper are Proposition 3 and 4 which provide an effective way to construct minimal hypersurfaces in a Euclidean space. We demonstrate our technique by several new examples. This note is English translation of an…
A simple construction is given of a class of Euclidean invariant, reflection positive measures on a compactification of the space of distributions. An unusual feature is that the regularizations used are not reflection positive.
We apply an improvement of the Delsarte LP-bound to give a new proof of the non-existence of finite projective planes of order 6, and uniqueness of finite projective planes of order 7. The proof is computer aided, and it is also feasible to…
I give an elementary proof that a quasi-symmetric design without repeated blocks on $v$ points has at most $v\choose2$ blocks, with equality if and only if it is a tight $4$-design.
Using Fourier analysis, we derive Wirtinger-type inequalities of arbitrary high order. As applications, we prove various sharp geometric inequalities for closed curves on the Euclidean plane. In particular, we obtain both sharp lower and…
Strong difference families are an interesting class of discrete structures which can be used to derive relative difference families. Relative difference families are closely related to $2$-designs, and have applications in constructions for…