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The nongeneric six- and eightdimensional orbits of SO(4,2) are described in explicitly covariant way. The relevant Hamiltonian dynamical systems are constructed and canonically quantized. It is shown that the resulting unitary representations of conformal group fit into the classification described by Mack (1977) [31].

In the paper, the research on the process of optimizing the carbon footprint to obtain the low-carbon products is presented. The optimization process and limits were analyzed based on the CFOOD project co-financed by the Polish Research and Development Agency. In the article, the carbon footprint (CF) testing methods with particular emphasis on product life cycle assessment (LCA) are discussed. The main problem is that the energy received from the energy-meters per the production stage is not directly represented in the raw data set obtained from the factory because many production line machines are connected to a single measurement point. In the paper, we show that in some energy-demanding production stages connected with cooling processes the energy used for the same stage and similar production can differ even 25-40%. That is why the energy optimization in the production can be very demanding.

The extensive analysis of the dynamics of relativistic spinning particles is presented. Using the coadjoint orbits method the Hamiltonian dynamics is explicitly described. The main technical tool is the factorization of general Lorentz transformation into pure boost and rotation. The equivalent constrained dynamics on Poincare group (viewed as configuration space) is derived and complete classification of constraints is performed. It is shown that the first class constraints generate local symmetry corresponding to the stability subgroup of some point on coadjoint orbit. The Dirac brackets for second class constraints are computed. Finally, canonical quantization is performed leading to infinitesimal form of irreducible representations of Poincare group.

The explicit form of conformal generators is found which provides the extension of Poincare symmetry for massless particles of arbitrary helicity. The helicity 12 particles are considered as the particular example. The realization of conformal symmetry in the semiclassical regime of Weyl equation is obtained.

The relativistic (Poincaré and conformal) symmetries of classical elementary systems are briefly discussed and reviewed. The main framework is provided by the Hamiltonian formalism for dynamical systems exhibiting symmetry described by a given Lie group. The construction of phase space and canonical variables is given using the tools from the coadjoint orbits method. It is indicated how the “exotic” Lorentz transformation properties for particle coordinates can be derived; they are shown to be the natural consequence of the formalism.

The coadjoint orbit method is applied to the construction of Hamiltonian dynamics of massless particles of arbitrary helicity. The unusual transformation properties of canonical variables are interpreted in terms of nonlinear realizations of Poincare group. The action principle is formulated in terms of new space–time variables with standard transformation properties.

Allegories are enriched categories generalizing a category of sets and binary relations. Accordingly, relational products in an allegory can be viewed as a generalization of Cartesian products. There are several definitions of relational products currently in the literature. Interestingly, definitions for binary products do not generalize easily to n-ary ones. In this paper, we provide a new definition of an n-ary relational product, and we examine its properties.

Allegories are enriched categories generalizing a category of sets and binary relations. In this paper, we extend a new, recently-introduced conceptual data model based on allegories by adding support for modal operators and developing a modal interpretation of the model in any allegory satisfying certain additional (but natural) axioms. The possibility of using different allegories allows us to transparently use alternative logical frameworks, such as fuzzy relations. Mathematically, our work demonstrates how to enrich with modal operators and to give a many world semantics to an abstract algebraic logic framework. We also give some examples of applications of the modal extension.

An important aspect of realizations of the Internet of Things containing sophisticated sensors and actuators is their integration with the Cloud, by the use of a middleware. This integration results in handling streams of data produced by sensors as well as streams sent back to actuators. In cases for which both large streams and a short reaction time are required, a special real-time oriented approach is necessary to design and build an interconnecting middleware. This paper proposes a hybrid low-cost, low-power middleware architecture for handling and processing of sensor related data streams. It is based on two microprocessor boards interconnected by high speed USB link. Variants including three embedded hardware implementations of the proposed architecture, two software realizations (single and multithread ones), and two process scheduling algorithms have been examined to evaluate their real-time performances. Series of experiments have been performed in order to measure closed loop control times and sensor data streams achievable in practice. An outcome is presented and discussed in detail. Obtained results confirm that the proposed architecture can be applied as middleware to integrate such elements of Internet of Things as robots and similarly time-constrained systems with the Cloud. The results can serve as reference point in research and development of real-time middleware solutions.