We extend the results of Walters on the uniqueness of invariant measures with maximal entropy on compact groups to an arbitrary locally compact group. We show that the maximal entropy is attained at the left Haar measure and the measure of maximal entropy is unique.

let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . in this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . as an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via the linear operator .

The finite element method (FEM) can be applied to practically analyze the tall buildings in which the shear walls are used to resist the lateral loads. Accordingly, a variety of displacement and strain-based as well as frame macro elements have been proposed for analysis of the tall buildings. With respect to application of the lower order plane stress elements, analytical problems may arise wi...

We report on the investigation of symmetrical properties of lithium niobate (LiNbO3) domain walls utilizing the nonlinear Cherenkov radiation. Compared with LiNbO3 bulk crystals, new nonzero elements of the χ(2) tensor at domain walls are found by the Cherenkov second harmonic generation (CSHG) and Cherenkov sum frequency generation (CSFG) measurement. Experimen...

We have considered a two-particle Bell experiment to visualize the conflict between rotational invariance of physical laws and specific local realistic theory. The experiment is reproducible by a local realistic theory which is obtained in a twosetting Bell experiment. It turns out that the generalized Bell inequality [J. Phys. A: Math. Theor. 40, 13101 (2007)] which is derived under the assump...

Abstract We present different types of rotational symmetries for distances in homogeneous groups, showing that the area formula associated spherical measure takes a simple form.

Rotational cryptanalysis is a probabilistic attack applicable to word oriented designs that use (almost) rotation-invariant constants. It is believed that the success probability of rotational cryptanalysis against ciphers and functions based on modular additions, rotations and XORs, can be computed only by counting the number of additions. We show that this simple formula is incorrect due to t...