Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper. As an application of the main result, a formula for error estimate concerning Cauchy-Schwarz's inequality is provided. The results obtained here complement the recent work of the references

The group of units mod (prime p2) is known to be cyclic for k ≥ 1. For k=1 this corresponds to Fermat's Small Theorem: n= 1 mod p (n coprime to p). If p=2 and k 2 the 2 units (odd residues) require two generators, such as 3 and -1 mod 2, since 3 is semi-primitive root of 1 mod 2. So each...

Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper. As an application of the main result, a formula for error estimate concerning Cauchy-Schwarz's inequality is provided. The results obtained in the paper complement and improve the recent work...

We prove a generalization of Alex Heller's existence theorem for recursion categories; this generalization was suggested by work of Di Paola and Montagna on syntactic -recursion categories arising from consistent extensions of Peano Arithmetic, and by the examples of recursion categories of...

This paper developed time domain integral constraints on error response for SISO feedback control systems due to nominal plant's near cancellation of stable pole-zero near the -axis. This integral constraints are satisfied by any feedback control systems. These integral constraints gave new...

In this note, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal. As an application of the main results, many answers to the Hilbert space problem 160 are presented at the end of the paper