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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 (G. Mack, Comm. Math. Phys. 55 (1977),1)., Comment: 20 pages, no figures

In the paper, the application of the machine learning methods in the food processing industry is presented to validate the quality of the production process and its parameters. These parameters e.g. raw products’ carbon footprint, energy resources and their carbon footprint usually may vary from day-to-day production because of meters’ instrumental errors or human random errors. One of the human factor is false accounting of the production in the system that sometimes happen. One of the instrumental errors can be the malfunction of the meters. In the authors’ project, the main goal is to optimize the production process so as to limit the carbon footprint. The problem that aroused is the trustworthiness of the data read from meters or provided by people operating the production line. That is why we applied the set of machine learning methods to validate the processes in order to choose the trustworthy ones. In the paper, we compare the results of processes classification k-Nearest Neighbors, Neural Network, C4.5, Random Forest and Support Vector Machines.

The quasiclassical theory of massless chiral fermions is considered. The effective action is derived using time-dependent variational principle which provides a clear interpretation of relevant canonical variables. As a result their transformation properties under the action of Lorentz group are derived from first principles., 11 pages, no figures; final version to appear in JHEP

The application of the chiral decomposition procedure to hybrid graphene h-BN systems revealed rules for the partition of the system into effective subsystems being bilayers plus monolayer in case the number of layers is odd. Three types of subsystems have been detected namely purely graphene bilayers and monolayers, mixed bilayers and pure h-BN monolayers depending on the hybrid composition. The effective parameters characterizing these chiral subsystems consist of the interlayer couplings and on-site potentials which shows the mechanism of compensation of the asymmetry introduced into the system by h-BN layers. For illustration, we provide a detailed overview about chiral tunneling in graphene subsystems present in hybrid with one h-BN layer. We have established the parameter ranges for which the characteristic features in the spectrum are observed, such as Fabry-Perot resonances in the case of graphene monolayer and “magic angles” in the case of effective graphene bilayer. We also consider different hybrid stacking in order to indicate effective systems with the desired properties required in the electronic and spintronic applications. We show that h-BN layers can promote specific graphene properties.

We discuss the chiral decomposition of non-symmetric stacking structures. It is shown that the low-energy electronic structure of a Bernal stacked graphene multilayer deposited on h-BN consists of chiral pseudospin doublets. N-layer graphene stacks on the h-BN layer have N/2 effective bilayer graphene systems and one effective h-BN layer if N is even or [Formula: see text] effective graphene bilayers plus one graphene monolayer modified by an h-BN layer if N is odd. We present the decomposition procedure and derive the recurrence relations for the effective parameters characterizing the chiral subsystems. In this case, the effective parameters consist of interlayer couplings and on-site potentials in contrast to pure graphene multilayer systems where only interlayer couplings are modified. We apply this procedure to discuss the Klein tunnelling phenomena and quantitatively compare the results with pure graphene multilayer systems.

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. We would like to thank the reviewers for their helpful suggestions.

Transition systems in which the state is described by a relational database found applications in artifact centric business process modeling, where the business artifacts are often modeled relationaly. We describe a framework implemented in term rewriting system Maude for specifying and model checking relational transition systems. The system was created to be a part of the future artifact centric business process modeling framework, but is of general interest on its own.

Allegories abstract and generalise (in the categorical framework) the algebra of binary relations. Arrows in an allegory enjoy a lot of properties and structure available for plain binary relations...

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., Comment: 26 opages; no figures; few references added

It is shown how a construction of so called θ - Poincare group - a global counterpart of twisted Poincare algebra (which can be considered as symmetry algebra of Noncommutative Field Theory (NCFT) with noncommutativity of coordinates being controlled by constant, antisymmetric matrix θ) can be extended to others groups containing translations as abelian subgroup.

It is shown that the symmetry algebra of quantum superintegrable system can be always chosen to be u(N),N being the number of degrees of freedom., Comment: 8 pages, no figures, a number of examples and references added

There are two basic approaches to business process modeling. One based on Petri nets, the other, newer, but with growing popularity, based on process algebras such as $$\pi $$-calculus. We have created a new variant of $$\pi $$-calculus which we call Object $$\pi $$-calculus. It has high level object oriented features such as method calls, mixins and additional process combinators. The calculus is of general interest, but it is particularly geared towards applications in business process modeling, especially document workflow modeling. Accordingly, we provide a proof-of-concept specification of a paper submission system in our dialect of $$\pi $$-calculus.

The deformed double covering of the E(2) group, denoted by Ẽκ(2), is obtained by contraction from the SUμ(2). The contraction procedure is then used for producing new examples of differential calculi: three-dimensional left covariant calculus on both Ẽκ(2) and the deformed Euclidean group Eκ(2) and two different four-dimensional (4D)-bicovariant calculi on Ẽκ(2) which correspond to the one 4D-bicovariant calculi on Eκ(2) described by Giller et al. [Acta Phys. Pol. B 28, 1121 (1997)].

We consider local field theory on κ-deformed Minkowski space which is an example of solvable Lie-algebraic noncommutative structure. Using integration formula over κ-Minkowski space and κ-deformed Fourier transform, we consider for deformed local fields the reality conditions as well as deformation of action functionals in standard Minkowski space. We present explicit formulas for two equivalent star products describing CBH quantization of field theory on κ-Minkowski space. We express also via star product technique the noncommutative translations in κ-Minkowski space by commutative translations in standard Minkowski space.

We describe free relativistic fields on noncommutative κ-deformed D=4 Minkowski space. Three possible types of κ-deformed Fourier transforms are discussed, related with three different κ-deformed mass-shell conditions.

The projective representations of k-Galilei group G k are found by contracting the relevant representations of κ–Poincare group. The projective multiplier is found. It is shown that it is not possible to replace the projective representations of G k by vector representations of some its extension.

Contemporary frameworks offer essentially two methods of accessing data in relational databases. The one using plain SQL requires writing a lot of boilerplate code and storing the SQL in a string, which is error prone and denies the benefits of static query analysis. The other one enforces the use of an additional (usually object oriented) abstraction layer which incurs additional runtime costs and hinders the use of advanced SQL capabilities. In this paper we present a working implementation of a radically different approach. Our tool uses the database engine to analyze the native SQL queries prepared by the user, and generates all the necessary classes representing query responses, single result rows and database connections. The use of native queries allows to utilize advanced and highly optimized SQL features. On the other hand, the use of the generated classes ensures that data access happens in a statically checked, type-safe way.

The representations of the oscillator algebra introduced by Brzezinski et al. [Phys. Lett. B 311 (1993) 202] are classified.

The general framework of bicrossproduct Hopf algebras given by Majid is extended to Z2‐graded bicrossproduct Hopf superalgebras. As examples of bicrossproduct Hopf superalgebras we provide the graded algebras of functions on undeformed as well as κ‐deformed D=4 Poincare supergroups.

Allegories are categories modeled upon the category of sets and binary relations where sets are objects and binary relations are morphisms composed using joins. In this paper we present a new conceptual data modeling formalism based on the language of allegories. We show that allegories provide more convenient framework for modeling data than more traditional categorical approaches in which arrows are interpreted as functional dependencies and in which many to many or partial relationships have to be represented as spans. Finally, we demonstrate that by using allegories different than the allegory of sets and binary relations, for example the allegory of sets and lattice valued relations, one can model replicated data or data stored in a valid time temporal database.

We describe here the general solution describing generators of κ-deformed Poincaré algebra as the functions of classical Poincaré algebra generators as well as the inverse formulas. Further we present analogous relations for the generators of N=1, D=4 κ-deformed Poincaré superalgebra expressed by the classical Poincaré superalgebra generators. In such a way we obtain the κ-deformed Poincaré (super)algebras with all the quantum deformation present only in the co-algebra sector. As an application we use the classical basis of κ-deformed Poincaré superalgebra for obtaining a new result: the κ-deformation of supersymmetric spin (Pauli-Lubanski) Casimir.

Nonrelativistic conformal groups, indexed by l=N/2, are analyzed. Under the assumption that the "mass" parametrizing the central extension is nonvanishing the coadjoint orbits are classified and described in terms of convenient variables. It is shown that the corresponding dynamical system describes, within Ostrogradski framework, the nonrelativistic particle obeying (N+1)-th order equation of motion. As a special case, the Schroedinger group and the standard Newton equations are obtained for N=1 (l=1/2)., Comment: 18 pages, no figures; few references added

The quantum group dual to the deformed eq(2) algebra obtained by Celeghini et al. [J. Math. Phys. 31, 2548 (1990)] is constructed.

The differential realization of the recently proposed deformed Poincaré algebra is considered. The notion of covariant wave functions is introduced and their explicit form in the "minimal" (in Weinberg's sense) case is given. The deformed Dirac equation is constructed.

A deformation map from the classical to the deformed Poincare algebra is given. The Hermitian representations of deformed algebra corresponding to all orbits in p space are explicitly constructed.

Using the notion of Galilean conformal algebra (GCA) in arbitrary space dimension d, we introduce for d=3 quantized nonrelativistic counterpart of twistors as the spinorial representation of O(2,1){\oplus}SO(3) which is the maximal semisimple subalgebra of three-dimensional GCA. The GC-covariant quantization of such nonrelativistic spinors, which shall be called also Galilean twistors, is presented. We consider for d=3 the general spinorial matrix realizations of GCA, which are further promoted to quantum-mechanical operator representations, expressed as bilinears in quantized Galilean twistors components. For arbitrary Hermitian quantum-mechanical Galilean twistor realizations we obtain the result that the representations of GCA with positive-definite Hamiltonian do not exist. For non-positive H we construct for N{\geq}2 the Hermitian Galilean N-twistor realizations of GCA; for N=2 such realization is provided explicitly., v3: 1+12 pages, with typos corrected in PLB proofs included

The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables yields proper equations of motion; no additional Lagrange multipliers are necessary (ii) the Legendre transformation can be performed in a straightforward way provided the Lagrangian is nonsingular in Ostrogradski sense. The generalization to singular Lagrangians as well as field theory are presented., 22 pages; no figures; some comments added; accepted for publication in Phys. Rev. D

The q-covariant wave equation describing a spin-1 massive particle in three-dimensional space-time is constructed. It exhibits a gauge symmetry which is a generalisation of QED3 gauge symmetry.

We consider the Euclidean path integral approach to higher-derivative theories proposed by Hawking and Hertog (Phys. Rev. D65 (2002), 103515). The Pais-Uhlenbeck oscillator is studied in some detail. The operator algebra is reconstructed and the structure of the space of states revealed. It is shown that the quantum theory results from quantizing the classical complex dynamics in which the original dynamics is consistently immersed. The field-theoretical counterpart of Pais-Uhlenbeck oscillator is also considered., 14 pages; no figures;the paper considerably extended; field-theoretical part added

It is argued that the twisted gauge theory is consistent provided it exhibits also the standard noncommutative gauge symmetry., Comment: 7 pages, no figures;two references added

The global counterpart of infinitesimal symmetries of noncommutative space-time is discussed., Comment: 7 pages, no figures; minor changes in the bibliography; final version accepted for publication in Phys. Rev.D

We consider the deformed Poincare group describing the space-time symmetry of noncommutative field theory. It is shown how the deformed symmetry is related to the explicit symmetry breaking., 7 pages, no figures, final version, accepted for publication in Phys. Lett. B

We discuss the definition of particle velocity in doubly special relativity theories. The general formula relating the velocity and four-momentum of the particle is given.

We consider a particle of half-integer spin which is nonrelativistic in the rest frame. Assuming the particle is completely polarized along third axis we calculate the Bloch vector as seen by a moving observer. The result for its length is expressed in terms of dispersion of some vector operator linear in momentum. The relation with the localization properties is discussed., Comment: 5 pages

A simple theorem concerning the sensitivity of Berry's phases/matrices to the additional degeneracies of the Hamiltonian is proven.

The family of Hamiltonians obtained by the action of a group of canonical transformations is considered. The formula for Hannay's angles is derived which allows us to express them in terms of the geometry of a group. The Berry formula relating Hannay's angles and Berry's phase is rederived.

We describe the extension of the Wigner`s infinite-dimensional unitary representations of Poincar\'{e} group to the case of $\kappa$-deformed Poincar\'{e} group. We show that the corresponding coordinate wave functions on noncommutative space-time are described by free field equations on $\kappa$-deformed Minkowski space. The cases of Klein--Gordon, Dirac, Proca and Maxwell fields are considered. Finally some aspects of second quantization are also discussed., Comment: LaTeX2e, 14 pages. Talk given by J.L. at the D.V. Volkov Memorial Conference "Supersymmetry and Quantum Field Theory", Kharkov, 25-29 July 2000, to be published in Nuclear Physics B Conference Supplements

We review shortly present status of quantum deformations of Poincare and conformal super symmetries. After recalling the κ-deformation of D=4 Poincare supersymmetries we describe the corresponding star product multiplication for chiral superfields. In order to describe the deformation of chiral vertices in momentum space the integration formula over κ-deformed chiral superspace is proposed.

The star product technique translates the framework of local fields on noncommutative space-time into nonlocal fields on standard space-time. We consider the example of fields on $\kappa$- deformed Minkowski space, transforming under $\kappa$-deformed Poincar\'{e} group with noncommutative parameters. By extending the star product to the tensor product of functions on $\kappa$-deformed Minkowski space and $\kappa$-deformed Poincar\'{e} group we represent the algebra of noncommutative parameters of deformed relativistic symmetries by functions on classical Poincar\'{e} group., Comment: LaTeX2e, 10 pages. To appear in the Proceedings of XXIII International Colloquium on Group-Theoretical Methods in Physics, July 31- August 5, Dubna, Russia". The names of the authors corrected