We define Gauss-like sums over the Galois Ring GR(4, r) and bound them using the Cauchy-Schwarz inequality. These sums are then used to obtain an upper bound on the aperiodic correlation function of quadriphase m-sequences constructed from GR(4, r). Our first bound δ1 has a simple derivation and is better than the previous upper bound of Shanbag et. al. for small values of N. We then make use o...

Inseparability criteria for continuous and discrete bipartite quantum states based on moments of annihilation and creation operators are studied by developing the idea of Shchukin-Vogel criterion [Phys. Rev. Lett. 95, 230502 (2005)]. If a state is separable, then the corresponding matrix of moments is separable too. Generalized criteria, based on the separability properties of the matrix of mom...

We show that for any unitarily invariant norm k k on M n (the space of n-by-n complex matrices) where denotes the Hadamard (entrywise) product. These results are a consequence of an inequality for absolute norms on C n kx yk 2 kx xk ky yk for all x; y 2 C n : (2) We also characterize the norms on C n that satisfy (2), characterize the unitary similarity invariant norms on M n that satisfy (1), ...

play an important role in different branches of modernmathematics such as Hilbert space theory, classical real and complex analysis, numerical analysis, probability and statistics, qualitative theory of differential equations and their applications. To date, a large number of generalizations and refinements of the inequalities () and () have been investigated in the literature, e.g., [–]. R...

We establish a generalization of the inequality introduced by Mitrinović and Pečarić in 1988. We prove mean value theorems of Cauchy type for that new inequality by taking its difference. Furthermore, we prove the positive semidefiniteness of the matrices generated by the difference of the inequality which implies the exponential convexity and logarithmic convexity. Finally, we define new means...

As an application of the improved Cauchy-Schwartz inequality due to Walker (Statist. Probab. Lett. (2017) 122:86-90), we obtain an improved version of the Cramer-Rao inequality for randomly censored data derived by Abdushukurov and Kim (J. Soviet. Math. (1987) pp. 2171-2185). We derive a lower bound of Bhattacharya type for the mean square error of a parametric function based on randomly censor...

Some new reverses for the generalised triangle inequality in inner product spaces and applications are given. Applications in connection to the Schwarz inequality are provided as well.

We will consider some solution methods for the linear systems of algebraic equations which arise from second-order elliptic nite element problems. We rst consider iterative re nement methods. Historically these methods were called FAC and AFAC methods. Optimal bounds of the condition number for the AFAC iterative operator are established by proving a strengthened Cauchy-Schwarz inequality using...