Let N be a positive integer and let A be a subset of {1, . . . , N} with the property that aa′ + 1 is a pure power whenever a and a′ are distinct elements of A. We prove that |A|, the cardinality of A, is not large. In particular, we show that |A| ≪ (logN)2/3(log logN)1/3.

In this survey we will define the Grigorchuk group and prove some of its properties. We will show that the Grigorchuk group is finitely generated but infinite. We will also show that the Grigorchuk group is a 2-group, meaning that every element has finite order a power of two. This, along with Burnside’s Theorem, gives that the Grigorchuk group is not linear.

The course of Technology and Material Testing prepare students with the ability to do a variety of material testing in the study of mechanical engineering. Students find it difficult to understand the materials to make them unable to carry out the material testing in accordance with the purpose of study. This happens because they knowledge is not adequately supported by the competence to find a...

A remarkable coincidence has led to the discovery of a family of packings of m2 + m − 2 m/2dimensional subspaces of m-dimensional space, whenever m is a power of 2. These packings meet the “orthoplex bound” and are therefore optimal.

We argue that two types of context are central to grounding the semantics for the mass/count distinction. We combine and develop the accounts of Rothstein (2010) and Landman (2011), which emphasize (non-)overlap at a context. We also adopt some parts of Chierchia’s (2010) account which uses precisifying contexts. We unite these strands in a two-dimensional semantics that covers a wide range of ...

The literature of home telehealth technology recommends that systems be designed to minimize their obtrusiveness to end users. However, this term is neither explicitly defined nor consistently used. This paper presents a definition of the concept of obtrusiveness. Within this definition, twenty-two categories of what may be perceived as obtrusive in home telehealth technology are proposed based...

A new methodology has been recently proposed for the efficient generation of multiple pseudo-random bit sequences that are statistically uncorrelated [1]. Random sequences that are uniformly distributed over a range ] , 0 [ K , where 1 + K is a power of 2, can be constructed by forming a vector of M independent bit sequences, where ) 1 ( log 2 + = K M . In this paper we demonstrate that this me...