The recently developed theory of geometrically uniform trellis codes is applied to the case of multidimensional PSK constellations. The symmetry group of an L X MPSK constellation is completely characterized. Conditions for rotational invariance of geometrically uniform partitions of a signal constellation are given. Through suitable algorithms, geometrically uniform partitions of L X MPSK ( M ...

We extend the construction of Born’s Reciprocal Relativity theory in ordinary phase spaces to an extended phase space based on Quaternions. The invariance symmetry group is the (pseudo) unitary quaternionic group U(N+, N−,H) which is isomorphic to the unitary symplectic group USp(2N+, 2N−,C). It is explicitly shown that the quaternionic group U(N+, N−,H) leaves invariant both the quadratic norm...

A macroscopic symmetry group describing the superconducting state of an orthorhombically twinned crystal of YBCO is introduced. This macroscopic symmetry group is different for different symmetries of twin boundaries. Josephson tunneling experiments performed on twinned crystals of YBCO determine this macroscopic symmetry group and hence determine the twin boundary symmetry (but do not experime...

We review the extrapolation of the single-particle string spectrum on AdS5 ×S5 to the Higher Spin enhancement point and the successful comparison of the resulting spectrum with the one of single-trace gaugeinvariant operators in N = 4 supersymmetric Yang-Mills theory. We also describe how to decompose the common spectrum in terms of massless and massive representations of the relevant Higher Sp...

Felgenhauer and Jarvis famously showed in [2], although it was first mentioned earlier, in [7], that there are 6,670,903,752,021,072,936,960 possible completed Sudoku boards. In a later paper, Jarvis and Russell [8] used a Sudoku symmetry group of size 3, 359, 232 · 9! = 1, 218, 998, 108, 160 and Burnside’s Lemma to show that there are 5,472,730,538 essentially different Sudoku boards. Both of ...

This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to obtain explicit expressions of the reduced system by exploiting the geometry. In particular, we show how to obtain a principal connection to be used in the red...

This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the basis of the attractors which can be identified and the mere sight of models. It is known that the knowledge of the symmetry group allows you to specify the fo...

We prove that given a fixed radius r, the set of isometry-invariant probability measures supported on “periodic” radius-r sphere packings in hyperbolic space Hn is dense in the space of all isometry-invariant probability measures on the space of radius-r sphere packings when n = 2, 3. By a periodic packing, we mean one with cofinite symmetry group. As a corollary, we prove the maximum density a...

A symmetry classification of possible interactions in a diatomic molecular chain is provided. For nonlinear interactions the group of Lie point transformations, leaving the lattice invariant and taking solutions into solutions, is at most five-dimensional. An example is considered in which subgroups of the symmetry group are used to reduce the dynamical differential-difference equations to pure...