Let s ? 3 $s \geqslant 3$ be a natural number, let ? ( x ) $\psi (x)$ polynomial with real coefficients and degree d 2 $d 2$ , A $A$ some large, non-empty, finite subset of numbers. We use E $E_{s,2}(A)$ to denote the number solutions system equations ? i = 1 ? + 0 \begin{equation*}\hskip2.5pc \sum _{i=1}^{s} (\psi (x_i) - \psi (x_{i+s}) )= (x_i x_{i+s} 0, \end{equation*} where ? $x_i \in A$ fo...

Utilizing a weight matrix we study surfaces of prescribed weighted mean curvature which yield a natural generalisation to critical points of anisotropic surface energies. We first derive a differential equation for the normal of immersions with prescribed weighted mean curvature, generalising a result of Clarenz and von der Mosel. Next we study graphs of prescribed weighted mean curvature, for ...

The weighted mean has been used to estimate the common mean of several populations with unknown and different variances. However, the traditional estimator of the variance of the weighted mean estimator underestimates the variance. Two new variance estimators are proposed with smaller biases and correspondingly formed intervals that have much better coverage probabilities for the mean. Results ...

In this paper we have proved some theorems on weighted mean summability method by using analytical and summability techniques, which also extends the well known result of Hardy on the Cesàro summability.

p . It follows that inequality (1.2) holds for any a ∈ lp when U1/p ≥ ||C||p,p and fails to hold for some a ∈ lp when U1/p < ||C||p,p. Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cn,k = 1/n, k ≤ n and 0 otherwise, is bounded on l p and has norm ≤ p/(p−1). (The norm is in fact p/(p− 1).) We say a matrix A = (an,k) is a lower triangular matrix if an,k = 0 for n < k...

The paper presents a new method for all-pole model estimation based on minimization of the weighted mean square error in the sampled spectral domain. Due to discrete nature of the proposed distance measure, emphasis can be put on an arbitrary set of spectral samples what can greatly improve the model accuracy for periodic signals. Weighting can also be applied to improve the fitting in certain ...

In this paper, we investigate the multiple attribute decision making (MADM) problems with fuzzy linguistic information. Motivated by the ideal of generalized Bonferroni mean, we develop the generalized fuzzy linguistic Bonferroni Mean (GFLBM) operator for aggregating the fuzzy linguistic information. For the situations where the input arguments have different importance, we then define the gene...