A stability test for time invariant linear systems can also be derived in the frequency domain. It is known as Nyquist stability criterion. It is based on the complex analysis result known as Cauchy's principle of argument. Note that the system transfer function is a complex function. By applying Cauchy's principle of argument to the open-loop system transfer function, we will get information a...

The Cannon Conjecture from the geometric group theory asserts that a word hyperbolic group that acts effectively on its boundary, and whose boundary is homeomorphic to the 2-sphere, is isomorphic to a Kleinian group. We prove the following Criterion for Cannon’s Conjecture: A hyperbolic group G (that acts effectively on its boundary) whose boundary is homeomorphic to the 2-sphere is isomorphic ...

Proofs that endomorphism (convolution) algebras are commutative most often depend upon identifying an anti-involution to interchange the order of factors, but which nevertheless acts as the identity on the algebra or suitable subalgebras. Silberger gave such an argument for the spherical Hecke algebras of p-adic reductive groups, for example. Apparently the first occurrence of the Gelfand-Kazhd...

This article describes and illustrates with two case studies a relatively novel form of the multiple-baseline design called the changing criterion design. It also presents the design's formal requirements, and suggests target behaviors and circumstances for which the design might be useful.

We introduce a separability criterion based on the positive map #:$ ̃(Tr $)!$ , where $ is a trace-class Hermitian operator. Any separable state is mapped by the tensor product of # and the identity into a nonnegative operator, which provides a simple necessary condition for separability. This condition is generally not sufficient because it is vulnerable to the dilution of entanglement. In the ...

he intelligibility of speech in communication systems is generally reduced by interfering noise. This interference, which can take the form of environmental noise, reverberation, competing speech, or electronic channel noise, reduces intelligibility by masking the signal of interest. The reduction in intelligibility is particularly troublesome for listeners with hearing impairments, who have gr...

A block cipher, such as the DES cipher, is used to encrypt binary plaintext in discrete blocks of length n using a key of length m, to form ciphertext blocks of length n. A block cipher is said to satisfy the strict key avalanche criterion if a one bit change in the key causes on the average one half of the ciphertext bit positions to change. In this paper the importance of the strict key avala...