We introduce the multigraded Hilbert scheme, which parametrizes all homogeneous ideals with fixed Hilbert function in a polynomial ring that is graded by any abelian group. Our construction is widely applicable, it provides explicit equations, and it allows us to prove a range of new results, including Bayer’s conjecture on equations defining Grothendieck’s classical Hilbert scheme and the cons...

In this paper, we will study some connections between Hilbert algebras and binary block-codes.With these codes, we can eassy obtain orders which determine suplimentary properties on these algebras. We will try to emphasize how, using binary block-codes, we can provide examples of classes of Hilbert algebras with some properties, in our case, classes of semisimple Hilbert algebras and classes of...

The p-norm of the Hilbert transform is the same as the p-norm of its truncation to any Lebesgue measurable set with strictly positive measure. This fact follows from two symmetry properties, the joint presence of which is essentially unique to the Hilbert transform. Our result applies, in particular, to the finite Hilbert transform taken over ( — 1,1), and to the one-sided Hilbert transform tak...

An iterative algorithm is described, based on the replication process of the Hilbert matrix, for encoding and decoding the Hilbert order. The time complexity of the proposed algorithm is smaller than those published previously, and the space complexity is bounded by a constant. Moreover, the new algorithm has a wider applicability when compared with existing algorithms for certain machine-word ...

We show that the Hilbert scheme, that parametrizes all ideals with the same Hilbert function over a Clements-Lindtröm ring W, is connected. More precisely, we prove that every graded ideal is connected by a sequence of deformations to the lex-plus-powers ideal with the same Hilbert function. Our result is an analogue of Hartshorne’s theorem that Grothendieck’s Hilbert scheme is connected; howev...

The main purpose of this paper is to introduce and study new classes of soft closed sets like soft regular generalized b-closed sets in soft topological spaces (briefly soft rgb-closed set) Moreover, soft rg-closed, soft gpr-closed, soft gb-closed, soft gsp-closed, soft g$alpha$-closed, soft g$alpha$b-closed, and soft sgb-closed sets in soft topological spaces are introduced in this paper and w...

• The history of the equations of gravitational field is of particular interest because they are related to two famous names: Albert Einstein and David Hilbert, and because the circumstances of their invention bear sometimes almost detective character. One of the early references is the book " Einstein, Hilbert and the Theory of Gravitation " by a renowned historian of science J. Mehra [1], whe...