Related papers: Generalized weighted Ostrowski and Ostrowski-Gr\"u…
Convergence properties of random ergodic averages have been extensively studied in the literature. In these notes, we exploit a uniform estimate by Cohen \& Cuny who showed convergence of a series along randomly perturbed times for…
This study is an example of a solid connection between fractional analysis and inequality theory, and includes new inequalities of the P\'{o}lya-Szeg% \"{o}-Chebyshev type obtained with the help of Generalized Proportional Fractional…
In the present work, we show how the generalized Cram\'er-Rao inequality for the estimation of a parameter, presented in a recent paper, can be extended to the mutidimensional case with general norms on $\mathbb{R}^{n}$, and to a wider…
We obtain several versions of the Hausdorff-Young and Hardy-Littlewood inequalities for the $(k,a)$-generalized Fourier transform recently investigated at length by Ben Sa\"i d, Kobayashi, and {\O} rsted. We also obtain a number of weighted…
We prove an inequality for the Kostka-Foulkes polynomials $K_{\lambda ,\mu}(q)$. As a corollary, we obtain a nontrivial lower bound for the Kostka numbers and a new proof of the Berenstein-Zelevinsky weight-multiplicity-one-criterium.
We present a simple technique to compute moments of derivatives of unitary characteristic polynomials. The first part of the technique relies on an idea of Bump and Gamburd: it uses orthonormality of Schur functions over unitary groups to…
The aim of this paper is to generalize the Hermite--Hadamard inequality for functions convex on the coordinates. Our composite result generalizes the result of Dragomir in \cite{Drag}. Many other interesting inequalities can be derived from…
This note addresses issues raised by Cox and Reid in their seminal paper in 1987 regarding parameter orthogonality in statistical inference. We extend the orthogonality condition to cases with multiple parameters of interest and demonstrate…
Jarnik's identity plays a major role in classical simultaneous approximation to two real numbers. O. German [2] has shown a generalization to the weighted setting in which the identity has to be replaced by two inequalities. His methods…
In this paper, we obtain new results related to Minkowski fractional integral inequality using generalized k-fractional integral operator which is in terms of the Gauss hypergeometric function.
This paper is concerned with orthonormal systems in real intervals, given with zero Dirichlet boundary conditions. More specifically, our interest is in systems with a skew-symmetric differentiation matrix (this excludes orthonormal…
We prove explicit upper bounds for weighted sums over prime numbers in arithmetic progressions with slowly varying weight functions. The results generalize the well-known Brun-Titchmarsh inequality.
Inference for statistics of a stationary time series often involve nuisance parameters and sampling distributions that are difficult to estimate. In this paper, we propose the method of orthogonal samples, which can be used to address some…
In this paper, we obtain generic bounds on the variances of estimation and prediction errors in time series analysis via an information-theoretic approach. It is seen in general that the error bounds are determined by the conditional…
This paper is devoted to improvements of Sobolev and Onofri inequalities. The additional terms involve the dual counterparts, i.e. Hardy-Littlewood-Sobolev type inequalities. The Onofri inequality is achieved as a limit case of Sobolev type…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
Companions of Ostrowski's integral ineqaulity for absolutely continuous functions and applications for composite quadrature rules and for p.d.f.'s are provided.
The setting is a stationary, ergodic time series. The challenge is to construct a sequence of functions, each based on only finite segments of the past, which together provide a strongly consistent estimator for the conditional probability…
We formulate axisymmetric general relativity in terms of real Ashtekar--Barbero variables. We study the constraints and equations of motion and show how the Kerr, Schwarzschild and Minkowski solutions arise. We also discuss boundary…
We provide algorithms for the absolute and alternating Ostrowski Expansions of the continuum and provide proofs for their uniqueness.