Andrzej Borowiec

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It has been recently shown that, in the first order (Palatini) formalism, there is universality of Einstein equations and Komar energy– momentum complex, in the sense that for a generic nonlinear Lagrangian depending only on the scalar curvature of a metric and a torsionless connection one always gets Einstein equations and Komar’s expression for the(More)
The current accelerated universe could be produced by modified gravitational dynamics as it can be seen in particular in its Palatini formulation. We analyze here a specific non-linear gravity-scalar system in the first order Palatini formalism which leads to a FRW cosmology different from the purely metric one. It is shown that the emerging FRW cosmology(More)
We demonstrate a polarization-managed 8-dimensional modulation format that is time domain coded to reduce inter-channel nonlinearity. Simulation results show a 2.3 dB improvement in maximum net system margin (NSM) relative to polarization multiplexed (PM)-BPSK, and a 1.0 dB improvement relative to time interleaved return-to-zero (RZ)-PM-BPSK, for five WDM(More)
The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative geometry and particle systems with generalized statistics are indicated. PACS. 02. 40. +m Differential geometry in(More)
A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed in [2]. In this paper we give an outline of the construction of a noncommutative analogy of the algebra of partial differential operators as well as its natural (Fock type) representation. We shall also define co-universal vector fields and(More)
A new family of Nyquist pulses for coherent optical single carrier systems is introduced and is shown to increase the nonlinearity tolerance of dual-polarization (DP)-QPSK and DP-16-QAM systems. Numerical investigations for a single-channel 28 Gbaud DP-16-QAM long-haul system without optical dispersion compensation indicate that the proposed pulse can(More)
A new notion of an optimal algebra for a first order free differential was introduced in [1]. Some relevant examples are indicated. Quadratic identities in the optimal algebras and calculi on quadratic algebras are studied. Canonical construction of a quantum de Rham complex for the coordinate differential is proposed. The relations between calculi and(More)