Compactifications of discrete quantum groups

Given a discrete quantum group A we construct a certain Hopf *-algebra AP which is a unital *-subalgebra of the multiplier algebra of A. The structure maps for AP are inherited from M(A) and thus the construction yields a compactification of A which is analogous to the Bohr compactification of a locally compact group. This algebra has the expected universal property with respect to homomorphisms from multiplier Hopf algebras of compact type (and is therefore unique). This provides an easy proof of the fact that for a discrete quantum group with an infinite dimensional algebra the multiplier algebra is never a Hopf algebra

Population growth and status of the Nushagak Peninsula caribou herd in southwest Alaska following reintroduction, 1988 - 1993

Caribou were reintroduced to the Nushagak Peninsula, Alaska in February 1988, after an absence of over 100 years. The purpose was to reestablish caribou in the area and once again provide hunting to local residents. The Nushagak Peninsula caribou herd (NPCH) has grown rapidly from 146 reintroduced caribou to over 1000 in 6 years at an exponential rate of increase of r = 0.317 or about 38%. The dramatic growth of the herd was attributed to the initial high percentage of females in the herd, high calf production and survival, pristine range, few predators and no hunting. Abundant high quality forage on the Nushagak Peninsula is the probable reason for the enhanced body condition and high natality even among 2-year-olds, and it has most likely contributed to the high calf survival and recruitment. Lack of predators and hunting has allowed calf and adult mortality to remain low. Although the size of the NPCH has grown steadily over the past 6 years, no significant dispersal from the peninsula has occurred. The population density of the NPCH was estimated to be 1.0/km2 in 1993. We believe the herd will continue to grow, and could reach a density of 2.3/km2 by 1998, even with a 10% harvest beginning in 1995. While the current growth of the NPCH makes the réintroduction a success, the increasing density, lack of dispersal and potential for over-grazing, presents managers with hard decisions

Pairing and duality of algebraic quantum groupoids

Algebraic quantum groupoids have been developed by two of the authors (AVD and SHW) of this note in a series of papers. Regular multiplier Hopf algebroids are obtained also by two authors (TT and AVD). Integral theory and duality for those have been studied by one author here (TT). Finally, again two authors of us (TT and AVD) have investigated the relation between weak multiplier Hopf algebras and multiplier Hopf algebroids. In the paper 'Weak multiplier Hopf algebras III. Integrals and duality' (by AVD and SHW), one of the main results is that the dual of an algebraic quantum groupoid, admits a dual of the same type. In the paper 'On duality of algebraic quantum groupoids' (by TT), a result of the same nature is obtained for regular multiplier Hopf algebroids with a single faithful integral. The duality of regular weak multiplier Hopf algebras with a single integral can be obtained from the duality of regular multiplier Hopf algebroids. That is however not the obvious way to obtain this result. It is more difficult and less natural than the direct way. We will discuss this statement further in the paper. Nevertheless, it is interesting to investigate the relation between the two approaches to duality in greater detail. This is what we do in this paper. We build further on the intimate relation between weak multiplier Hopf algebras and multiplier Hopf algebroids. We now add the presence of integrals. That seems to be done best in a framework of dual pairs. It is in fact more general than the duality of these objects coming with integrals

Towards Low Cost Coupling Structures for Short-Distance Optical Interconnections

The performance of short distance optical interconnections in general relies very strongly on coupling structures, since they will determine the overall efficiency of the system to a large extent. Different configurations can be considered and a variety of manufacturing technologies can be used. We present two different discrete and two different integrated coupling components which can be used to deflect the light beam over 90 degrees and can play a crucial role when integrating optical interconnections in printed circuit boards. The fabrication process of the different coupling structures is discussed and experimental results are shown. The main characteristics of the coupling structures are given. The main advantages and disadvantages of the different components are discussed

Heisenberg double as braided commutative Yetter-Drinfel'd module algebra over Drinfel'd double in multiplier Hopf algebra case

Based on a pairing of two regular multiplier Hopf algebras $A$ and $B$, Heisenberg double $\mathscr{H}$ is the smash product $A \# B$ with respect to the left regular action of $B$ on $A$. Let $\mathscr{D}=A\bowtie B$ be the Drinfel'd double, then Heisenberg double $\mathscr{H}$ is a Yetter-Drinfel'd $\mathscr{D}$-module algebra, and it is also braided commutative by the braiding of Yetter-Drinfel'd module, which generalizes the results in [10] to some infinite dimensional cases.Comment: 18 pages. arXiv admin note: text overlap with arXiv:math/0404029 by other author

Comment on: a two-stage fourth-order “almost” P-stable method for oscillatory problems

AbstractIn Chawla and Al-Zanaidi (J. Comput. Appl. Math. 89 (1997) 115–118) a fourth-order “almost” P-stable method for y″=f(x,y) is proposed. We claim that it is possible to retrieve this combination of multistep methods by means of the theory of parameterized Runge-Kutta-Nyström (RKN) methods and moreover to generalize the method discussed by Chawla and Al-Zanaidi (J. Comput. Appl. Math. 89 (1997) 115–118)