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We use microlocal and paradifferential techniques to obtain $L^8$ norm bounds for spectral clusters associated to elliptic second order operators on two-dimensional manifolds with boundary. The result leads to optimal $L^q$ bounds, in the…
Binary duadic codes are an interesting subclass of cyclic codes since they have large dimensions and their minimum distances may have a square-root bound. In this paper, we present several families of binary duadic codes of length $2^m-1$…
In this paper, we obtain two new lower bounds for the smallest singular value of nonsingular matrices which is better than the bound presented by zou \cite{zou2012lower}, Lin, Minghua and Xie, Mengyan \cite{lin2021some} under certain…
This note shows how to apply the James-Stein estimator to the case of entropic uncertainty relations of more than two observables. A better result is found compared to applying the ordinary estimator and we find a more optimal model…
Best possible bounds are established for families without s pairwise disjoint members and the more general problem for several families. The results are shown to apply several classical results.
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
The approximate computation of twin-width has attracted significant attention already since the moment the parameter was introduced. A recently proposed approach (STACS 2024) towards obtaining a better understanding of this question is to…
Measuring inter-dataset similarity is an important task in machine learning and data mining with various use cases and applications. Existing methods for measuring inter-dataset similarity are computationally expensive, limited, or…
In this work we present two particular cases of the general duality result for linear optimisation problems over signed measures with infinitely many constraints in the form of integrals of functions with respect to the decision variables…
We consider the question of learning the natural parameters of a $k$ parameter minimal exponential family from i.i.d. samples in a computationally and statistically efficient manner. We focus on the setting where the support as well as the…
In this paper we have suggested two classes of estimators for population median M_Y of the study character Y using information on two auxiliary characters X and Z in double sampling. It has been shown that the suggested classes of…
By introducing a parameter, we give a unified generalization of some quadrature rules, which not only unify the recent results about error bounds for generalized mid-point, trapezoid and Simpson's rules, but also give some new error bounds…
It is known that the family of power means tends to maximum pointwise if we pass argument to infinity. We will give some necessary and sufficient condition for the family of quasi-arithmetic means generated by a functions satisfying certain…
We establish a regularity result for optimal sets of the isoperimetric problem with double density under mild ($\alpha$-)H\"older regularity assumptions on the density functions. Our main Theorem improves some previous results and allows to…
We propose a family of boundary terms for the action of a causal set with a spacelike boundary. We show that in the continuum limit one recovers the Gibbons-Hawking-York boundary term in the mean. We also calculate the continuum limit of…
Let $I\subseteq\mathbb{R}$ be a nonempty open subinterval. We say that a two-variable mean $M:I\times I\to\mathbb{R}$ enjoys the \emph{balancing property} if, for all $x,y\in I$, the equality \begin{equation}\tag{1}…
For a,b>0 with a\not=b, let T(a,b) denote the second Seiffert mean defined by T(a,b)=((a-b)/(2arctan((a-b)/(a+b)))) and A_{r}(a,b) denote the r-order power mean. We present the sharp bounds for the second Seiffert mean in terms of power…
This paper introduces two new robust methods for estimation of parameters in a given parametric family. The first method is that of `minimum weighted L2', effectively minimising an estimate of the integrated (and possibly weighted) squared…
Seeking the available precision limit of unknown parameters is a significant task in quantum parameter estimation. One often resorts to the widely utilized quantum Cramer-Rao bound (QCRB) based on unbiased estimators to finish this task.…
We provide a lower bound for the ratio between the ordinary and uniform exponent of both simultaneous Diophantine approximation and Diophantine approximation by linear forms in any dimension. This lower bound was conjectured by Schmidt and…