Related papers: On estimates of trigonometrical integrals

We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.

We give a new complexity bound for calculating the complex dimension of an algebraic set. Our algorithm is completely deterministic and approaches the best recent randomized complexity bounds. We also present some new, significantly sharper…

We obtain sharp estimates involving the mean curvatures of higher order of a complete bounded hypersurface immersed in a complete Riemannian manifold. Similar results are also given for complete spacelike hypersurfaces in Lorentzian ambient…

In this paper, new upper and lower bounds for the Trapezoid inequality of absolutely continuous functions are obtained. Applications to some special means are provided as well.

The article surveys published and not yet published results about moduli spaces of algebraic surfaces.

We augment the method of Wooley (2015) by some new ideas and in a series of results, improve his metric bounds on the Weyl sums and the discrepancy of fractional parts of real polynomials with partially prescribed coefficients. We also…

We give an attempt to build a classification of planar integral point sets. For two obtained classes, we provide general constructions of upper bounds for minimal diameter of integral point sets in higher dimensions of certain cardinality.…

This note gathers what is known about, and provides some new results concerning the operations of intersection, of ``generated $\sigma$-field'', and of ``complementation'' for (independent) complete $\sigma$-fields on probability spaces.

A posteriori residual and hierarchical upper bounds for the error estimates were proved when solving the hypersingular integral equation on the unit sphere by using the Galerkin method with spherical splines. Based on these a posteriori…

Given a birational parameterization of an algebraic surface S in the projective space, the purpose of this paper is to investigate the sets of points on S whose preimage consists in k or more points, counting multiplicities. They are…

: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…

This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…

In this paper we present a new approach for tightening upper bounds on the partition function. Our upper bounds are based on fractional covering bounds on the entropy function, and result in a concave program to compute these bounds and a…

We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.

We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with…

In this article we obtain lower and upper bounds for global dimensions of a class of artinian algebras in terms of global dimensions of a finite subset of their artinian subalgebras. Finding these bounds for the global dimension of an…

We review recent developments in the arithmetic of K3 surfaces. Our focus lies on aspects of modularity, Picard number and rational points. Throughout we emphasise connections to geometry.

In this paper we consider adjoint restriction estimates for space curves with respect to general measures and obtain optimal estimates when the curves satisfy a finite type condition. The argument here is new in that it doesn't rely on the…

We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new classes of bispectral operators.

There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…