A novel signaling scheme is presented, where a set of orthogonal signals is transmitted in parallel. The signals are selected according to the so-called residue number system (RNS). Hence the system is essentially a multiple code parallel communication scheme using high-modulation alphabets. It is demonstrated that the system performance can be substantially improved by exploiting a number of a...

In recent years, numerous functions which count the number of parts of various types of partitions have been studied. In this brief note, we consider the function pto(n) which counts the number of parts in all odd–part partitions of n (or what Chen and Ji recently called the number of rooted partitions of n into odd parts). In particular, we prove a number of results on the parity of pto(n), in...

A composition of an integer n is called Carlitz if adjacent parts are different. Several characteristics of random Carlitz compositions have been studied recently by Knopfmacher and Prodinger. We will complement their work by establishing asymptotics of the average number of distinct part sizes in a random Carlitz composition.

7 Rings Definition. A ring consists of a set R on which are defined operations of addition and multiplication satisfying the following axioms: • x+ y = y + x for all elements x and y of R (i.e., addition is commutative); • (x+ y) + z = x+ (y + z) for all elements x, y and z of R (i.e., addition is associative); • there exists an an element 0 of R (known as the zero element) with the property th...

The paper studies the history and recent developments in non-elementary model theory focusing in the framework of abstract elementary classes. We discuss the role of syntax and semantics and the motivation to generalize first order model theory to non-elementary frameworks and illuminate the study with concrete examples of classes of models. This second part continues to study the question of c...

In recent years, a new paradigm in theoretical physics has emerged known as the holographic principle. This principle states that the number of degrees of freedom in a d-dimensional region of a (d + 1)-dimensional spacetime is proportional to the area of a suitably defined surface associated with the region of spacetime. This principle was motivated by the fact that the entropy of a black hole ...

1238 NOTICES OF THE AMS VOLUME 47, NUMBER 10 H ow should 24-dimensional toy merchants most efficiently store their marbles? This is one rather fanciful statement of the “sphere packing problem” in R24. This problem is not just a plaything of high-dimensional Euclidean geometry: it relates to a surprising range of mathematical disciplines, pure as well as applied, including number theory, finite...

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A generalized stability theory (GST) analysis of baroclinic shear flow is performed using primitive equations (PEs), and typical synoptic-scale midlatitudinal values of vertical shear and stratification. GST is a comprehensive linear stability theory that subsumes modal stability theory and extends it to account for nonmodal interactions such as may occur among the approximately geostrophically...

The Validation Process To begin this process, we need a new set of observations, designed to challenge the model. The new observational data and their uncertainties will then be compared to the “predictions” of the model and its uncertainties for the physical scenarios in which the observations were made (the “validation scenarios”). Here, however, we encounter a problem: The validation observa...