Related papers: Totally real Thue inequalities over imaginary quad…
In this note we prove optimal inequalities for bounded functions in terms of their deviation from their mean. These results extend and generalize some known inequalities due to Thong (2011) and Perfetti (2011)
We obtain complete classification of in-equivalent realizations of the Virasoro algebra by Lie vector fields over the three-dimensional field of real numbers. As an application we construct new classes of nonlinear second-order partial…
We present some partial results regarding subadditivity of maximal shifts in finite graded free resolutions.
We use the solution space of a pair of ODEs of at least second order to construct a smooth surface in Euclidean space. We describe when this surface is a proper embedding which is geodesically complete with finite total Gauss curvature. If…
In this paper we obtain some new Schwarz related inequalities in inner product spaces over the real or complex number field. Applications for the generalized triangle inequality are also given.
Affine quantization is a relatively new procedure, and it can solve many new problems. This essay reviews this new, and novel, procedure for particle problems, as well as those of fields and gravity. New quantization tools, which are…
Some aspects of analysis involving fields with absolute value functions are discussed, which includes the real or complex numbers with their standard absolute values, as well as ultrametric situations like the p-adic numbers.
We revisit the third fundamental theorem of Lie (Lie III) for finite dimensional Lie algebras in the context of infinite dimensional matrices.
In this paper we present some results showing the good behavior of the $\tau$-invariant of a Rees algebra with integral closure and elimination (of variables).
In this work, we improve upon the guarantees for sparse random embeddings, as they were recently provided and analyzed by Freksen at al. (NIPS'18) and Jagadeesan (NIPS'19). Specifically, we show that (a) our bounds are explicit as opposed…
In this current work, we revisit the recent improvement of the discrete Hardy's inequality in one dimension and establish an extended improved discrete Hardy's inequality with its optimality. We also study one-dimensional discrete Copson's…
For absolutely convergent series we state explicitly a one-sided summation estimate that can be viewed as the discrete analogue of the change of variable formula on the half line. This estimate is implicit in Pascal Lef\`evre's recent…
We investigate a variant of Wirsing's problem on approximation to a real number by real algebraic numbers of degree exactly $n$. This has been studied by Bugeaud and Teulie. We improve their bounds for degrees up to $n=7$. Moreover, we…
New Hardy type inequalities in sectorial area and as a limit in an exterior of a ball are proved. Sharpness of the inequalities is shown as well.
Some reverses for the generalised triangle inequality in complex inner product spaces that improve the classical Diaz-Metcalf results and applications are given.
In this paper, we sharpen and simplify our earlier results based on Thue's Fundamentaltheorem and use it to obtain effective irrationality measures for certain roots of polynomials of the form $(x-\sqrt{t})^{n}+(x+\sqrt{t})^{n}$, where $n…
We improve constants in the Rademacher-Menchov inequality.
We provide a complete classification of well-rounded ideal lattices arising from real quadratic fields. We show that the ideals that give rise to such lattices are precisely the ones that correspond to divisors $a$ of the discriminant $d$…
Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid…
We prove an explicit upper bound on the number of real quadratic fields that admit a universal quadratic form of a given rank, thus establishing a density zero statement. More generally, we obtain such a result for totally positive definite…