Related papers: Decoupling inequalities and some mean-value theore…
We identify a new way to divide the $\delta$-neighborhood of surfaces $\mathcal{M}\subset\mathbb{R}^3$ into a finitely-overlapping collection of rectangular boxes $S$. We obtain a sharp $(l^2,L^p)$ decoupling estimate using this…
We investigate decoupling, one of the most important primitives in quantum Shannon theory, by replacing the uniformly distributed random unitaries commonly used to achieve the protocol, with repeated applications of random unitaries…
Baiocchi et al. generalized a few years ago a classical theorem of Ingham and Beurling by means of divided differences. The optimality of their assumption has been proven by the third author of this note. The purpose of this note to extend…
In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance…
In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…
Dedekind sums have applications in quite a number of fields of mathematics. Therefore, their distribution has found considerable interest. This article gives a survey of several aspects of the distribution of these sums. In particular, it…
A basic question of Diophantine approximation, which is the first issue we discuss, is to investigate the rational approximations to a single real number. Next, we consider the algebraic or polynomial approximations to a single complex…
We provide a set of sum rules relating CP-averaged branching ratios and CP-asymmetries of the $B \to \pi K$ modes. They prove to be useful as a mechanism to `test' experimental data given our expectations of the size of isospin breaking. A…
The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequalities which are more generalized than the inequalities of Dragomir and Cerone. The current article obtains bounds for the deviation of a function…
Decoupling multivariate polynomials is useful for obtaining an insight into the workings of a nonlinear mapping, performing parameter reduction, or approximating nonlinear functions. Several different tensor-based approaches have been…
The results of difference sequences theory are applied to analytic function theory and Diophantine equations. As a result we have the equation which connects the $n$-th derivative of a function with the difference sequence for the values of…
New estimates of the critical exponents have been obtained from the field-theoretical renormalization group using a new method for summing divergent series. The results almost coincide with the central values obtained by Le Guillou and…
We present a new variational principle for linking models of beams and deformable solids, providing also its mathematical analysis. Despite the apparent differences between the two types of governing equations, it will be shown that the…
We generalize Dirichlet's diophantine approximation theorem to approximating any real number $\alpha$ by a sum of two rational numbers $\frac{a_1}{q_1} + \frac{a_2}{q_2}$ with denominators $1 \leq q_1, q_2 \leq N$. This turns out to be…
The paper applies the theory developed in Part I to the discrete normal approximation in total variation of random vectors in ${\mathbb Z}^d$. We illustrate the use of the method for sums of independent integer valued random vectors, and…
The theory of summability of divergent series is a major branch of mathematical analysis that has found important applications in engineering and science. It addresses methods of assigning natural values to divergent sums, whose…
We prove a Diophantine approximation inequality for closed subschemes on surfaces which can be viewed as a joint generalization of recent inequalities of Ru-Vojta and Heier-Levin in this context. As applications, we study various…
A glimpse at $\sum{{\sin(kx)}\over{k}}$ gives a few lines exposition of Fourier series's quadratic mean convergence for square integrable functions and Dirichlet's convergence theorem of the Fourier serie of a piecewise differentiable…
In this paper we prove transference inequalities for regular and uniform Diophantine exponents in the weighted setting. Our results generalize the corresponding inequalities that exist in the `non-weighted' case.
Assuming some pointwise estimates on certain Weyl's sum, we prove the sharp estimates of the mean value associated to the following exponential sum $$ \sum_{n=1}^N e^{2\pi i tn^d +2\pi i xn}\,. $$