‎In this paper we take $mathcal A$ to be the category {bf Pos-S}‎ ‎of $S$-posets‎, ‎for a posemigroup $S$‎, ${mathcal M}_{pd}$ to‎ ‎be the class of partially ordered sequantially-dense‎ ‎monomorphisms and study the categorical properties‎, ‎such as‎ ‎limits and colimits‎, ‎of this class‎. ‎These properties are usually‎ ‎needed to study the homological notions‎, ‎such as injectivity‎, ‎of‎ ‎$S$-...

We construct multidimensional Schrödinger operators with a spectrum that has no gaps at high energies and is nowhere dense low energies. This gives the first example for which this widely expected topological structure of in class uniformly recurrent operators, namely coexistence half-line Cantor-type structure, can be confirmed. Our construction uses separable potentials decompose into one-dim...

0

The establishment and growth of an early Australian entrepreneurial firm supplying veterinary services and products is examined. John Pottie established a veterinary practice in Sydney in the 1860's and then proceeded to develop a large and successful family business that is still trading. By exploring the ingredients for its successful entry and growth, this study seeks to show through one lon...

Information Technology (IT) has significant impact on organisation’s success or failure. However, IT does not operate in a vacuum. It is influenced by non-technical factors, such as of human actions and structure, which are inseparable. Hence the relationship between the factors is critical as revealed in this chapter. Structuration was applied as a lens to examine the types of structures that ...

We prove that any topological group of a non-measurable cardinality is hereditarily paracompact and strongly σ-discrete as soon as it is submaximal. Consequently, such a group is zero-dimensional. Examples of uncountable maximal separable spaces are constructed in ZFC. 0. Introduction. This paper has been motivated by several unsolved problems in general topology and topological algebra. The co...

‎‎‎In this paper‎, ‎the‎ notion of injectivity with respect to order dense embeddings in ‎‎the category of $S$-posets‎, ‎posets with a monotone action of a‎ pomonoid $S$ on them‎, ‎is studied‎. ‎We give a criterion‎, ‎like the Baer condition for injectivity of modules‎, ‎or Skornjakov criterion for injectivity of $S$-sets‎, ‎for the order dense injectivity‎. ‎Also‎, ‎we consider such injectivit...

We study the effects of laser phase noise on a phase diversity coherent optical frequency domain (C-OFD) technique that has been recently proposed to measure passive devices used in dense wavelength division multiplexing (DWDM) systems. Theoretical expressions are provided to calculate the laser phase-noise to intensity-noise conversion in this technique under simplified circumstances. Obtained...

Let A be a C*-algebra with an identity. Consider the completed tensor product A®A of A with itself with respect to the minimal or the maximal C*-tensor product norm. Assume that A: A —>A®A is a non-zero •-homomorphism such that (A ® t)A = (i ® A)A where / is the identity map. Then A is called a comultiplication on A . The pair (A, A) can be thought of as a 'compact quantum semi-group'. A left i...