Combed 3-Manifolds with Concave Boundary, Framed Links, and Pseudo-Legendrian Links

We provide combinatorial realizations, according to the usual objects/moves scheme, of the following three topological categories: (1) pairs (M,v) where M is a 3-manifold (up to diffeomorphism) and v is a (non-singular vector) field, up to homotopy; here possibly the boundary of M is non-empty and v may be tangent to the boundary, but only in a concave fashion, and homotopy should preserve tangency type; (2) framed links L in M, up to framed isotopy; (3) triples (M,v,L), with (M,v) as above and L transversal to v, up to pseudo-Legendrian isotopy (transversality-preserving simultaneous homotopy of v and isotopy of L). All realizations are based on the notion of branched standard spine, and build on results previously obtained. Links are encoded by means of diagrams on branched spines, where the diagram is smooth with respect to the branching. Several motivations for being interested in combinatorial realizations of the topological categories considered in this paper are given in the introduction. The encoding of links is suitable for the comparison of the framed and the pseudo-Legendrian categories, and some applications are given in connection with contact structures, torsion and finite-order invariants. An estension of Trace's notion of winding number of a knot diagram is introduced and discussed.Comment: 38 pages, 33 figure

Problem-formulation in a South African organization. Executive summary

Complex Problem Solving is an area of cognitive science that has received a good amount of attention, but theories in the field have not progressed accordingly. In general, research of problem solving has focussed on identifying preferable methods rather than on what happens when human beings confront problems in an organizational context Queseda, Kirtsch and Gomez (2005) Existing literature recognises that most organizational problems are ill-defined. Some problems can become well-defined whereas others are and remain ill-structured. For problems that can become well-defined, failure to pay attention to the area of problem definition has the potential to jeopardise the effectiveness of problem-formulation and thus the entire problem solving activity. Problem defining, a fundamental part of the problem-formulation process, is seen as the best defence against a Type III Error (trying to solve the wrong problem). Existing literature addresses possible processes for problem-formulation and recognises the importance of applying problem domain knowledge within them. However, inadequate attention is given to the possible circumstances that, within an organization, the participants do not know enough about the problem domain and do not recognise the importance of applying adequate problem domain knowledge or experience to the problem-formulation process. A case study is conducted into exactly these circumstances as they occurred and were successfully addressed within Eskom Holdings Ltd (Eskom), the national electricity utility in South Africa. The case study is a fundamental part of this research project, which explores the gap in the existing body of knowledge related to the circumstances described above and specifically to problems that can become well-defined, and provides the basis for the innovation developed herein that addresses that gap

The chemistry of comets An annotated bibliography

Annotated bibliography on chemistry of comets - free radicals, photochemistry, photolysis, and spectral analysi

Collective Rabi dynamics of electromagnetically-coupled quantum dot ensembles

Rabi oscillations typify the inherent nonlinearity of optical excitations in quantum dots. Using an integral kernel formulation to solve the 3D Maxwell-Bloch equations in ensembles of up to $10^4$ quantum dots, we observe features in Rabi oscillations due to the interplay of nonlinearity, non-equilibrium excitation, and electromagnetic coupling between the dots. This approach allows us to observe the dynamics of each dot in the ensemble without resorting to spatial averages. Our simulations predict synchronized multiplets of dots that exchange energy, dots that dynamically couple to screen the effect of incident external radiation, localization of the polarization due to randomness and interactions, as well as wavelength-scale regions of enhanced and suppressed polarization.Comment: 7 pages, 6 figures, 1 tabl

On the Spectral Efficiency and Fairness in Full-Duplex Cellular Networks

To increase the spectral efficiency of wireless networks without requiring full-duplex capability of user devices, a potential solution is the recently proposed three-node full-duplex mode. To realize this potential, networks employing three-node full-duplex transmissions must deal with self-interference and user-to-user interference, which can be managed by frequency channel and power allocation techniques. Whereas previous works investigated either spectral efficient or fair mechanisms, a scheme that balances these two metrics among users is investigated in this paper. This balancing scheme is based on a new solution method of the multi-objective optimization problem to maximize the weighted sum of the per-user spectral efficiency and the minimum spectral efficiency among users. The mixed integer non-linear nature of this problem is dealt by Lagrangian duality. Based on the proposed solution approach, a low-complexity centralized algorithm is developed, which relies on large scale fading measurements that can be advantageously implemented at the base station. Numerical results indicate that the proposed algorithm increases the spectral efficiency and fairness among users without the need of weighting the spectral efficiency. An important conclusion is that managing user-to-user interference by resource assignment and power control is crucial for ensuring spectral efficient and fair operation of full-duplex networks.Comment: 6 pages, 4 figures, accepted in IEEE ICC 2017. arXiv admin note: text overlap with arXiv:1603.0067