Quantum interference in optical fields and atomic radiation

We discuss the connection between quantum interference effects in optical beams and radiation fields emitted from atomic systems. We illustrate this connection by a study of the first- and second-order correlation functions of optical fields and atomic dipole moments. We explore the role of correlations between the emitting systems and present examples of practical methods to implement two systems with non-orthogonal dipole moments. We also derive general conditions for quantum interference in a two-atom system and for a control of spontaneous emission. The relation between population trapping and dark states is also discussed. Moreover, we present quantum dressed-atom models of cancellation of spontaneous emission, amplification on dark transitions, fluorescence quenching and coherent population trapping.

Molecular and functional characterization of an octopamine receptor from honeybee (Apis mellifera) brain

Biogenic amines and their receptors regulate and modulate many physiological and behavioural processes in animals. In vertebrates, octopamine is only found in trace amounts and its function as a true neurotransmitter is unclear. In protostomes, however, octopamine can act as neurotransmitter, neuromodulator and neurohormone. In the honeybee, octopamine acts as a neuromodulator and is involved in learning and memory formation. The identification of potential octopamine receptors is decisive for an understanding of the cellular pathways involved in mediating the effects of octopamine. Here we report the cloning and functional characterization of the first octopamine receptor from the honeybee, Apis mellifera . The gene was isolated from a brain-specific cDNA library. It encodes a protein most closely related to octopamine receptors from Drosophila melanogaster and Lymnea stagnalis . Signalling properties of the cloned receptor were studied in transiently transfected human embryonic kidney (HEK) 293 cells. Nanomolar to micromolar concentrations of octopamine induced oscillatory increases in the intracellular Ca2+ concentration. In contrast to octopamine, tyramine only elicited Ca2+ responses at micromolar concentrations. The gene is abundantly expressed in many somata of the honeybee brain, suggesting that this octopamine receptor is involved in the processing of sensory inputs, antennal motor outputs and higher-order brain functions.

Bilateral semidirect product decompositions of transformation monoids

In this paper we consider the monoid OR(n) of all full transformations on a chain with n elements that preserve or reverse the orientation, as well as its submonoids OD(n) of all order-preserving or order-reversing elements, OP(n) of all orientation-preserving elements and O(n) of all order-preserving elements. By making use of some well known presentations, we show that each of these four monoids is a quotient of a bilateral semidirectproduct of two of its remarkable submonoids.

Particle swarm optimization: dynamical analysis through fractional calculus

This chapter considers the particle swarm optimization algorithm as a system, whose dynamics is studied from the point of view of fractional calculus. In this study some initial swarm particles are randomly changed, for the system stimulation, and its response is compared with a non-perturbed reference response. The perturbation effect in the PSO evolution is observed in the perspective of the fitness time behaviour of the best particle. The dynamics is represented through the median of a sample of experiments, while adopting the Fourier analysis for describing the phenomena. The influence upon the global dynamics is also analyzed. Two main issues are reported: the PSO dynamics when the system is subjected to random perturbations, and its modelling with fractional order transfer functions.

On semigroups of endomorphisms of a chain with restricted range

Let X be a finite or infinite chain and let be the monoid of all endomorphisms of X. In this paper, we describe the largest regular subsemigroup of and Green's relations on. In fact, more generally, if Y is a nonempty subset of X and is the subsemigroup of of all elements with range contained in Y, we characterize the largest regular subsemigroup of and Green's relations on. Moreover for finite chains, we determine when two semigroups of the type are isomorphic and calculate their ranks.

On the ranks of certain monoids of transformations that preserve a uniform partition

The rank of a semigroup, an important and relevant concept in Semigroup Theory, is the cardinality of a least-size generating set. Semigroups of transformations that preserve or reverse the order or the orientation as well as semigroups of transformations preserving an equivalence relation have been widely studied over the past decades by many authors. The purpose of this article is to compute the ranks of the monoid

A numerical analysis of generalized Boussinesq-type equation using continuos/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time-dependent varying seabed are included. Thus, high-order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher-order models, an extra O(mu 2n+2) term (n ??? N) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth-order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor-corrector scheme with an initialization given by an explicit RungeKutta method is also used for the time-variable integration. Moreover, a CFL-type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved.

The cardinal of various monoids of transformations that preserve a uniform partition

In this paper we give formulas for the number of elements of the monoids ORm x n of all full transformations on it finite chain with tun elements that preserve it uniform m-partition and preserve or reverse the orientation and for its submonoids ODm x n of all order-preserving or order-reversing elements, OPm x n of all orientation-preserving elements, O-m x n of all order-preserving elements, O-m x n(+) of all extensive order-preserving elements and O-m x n(-) of all co-extensive order-preserving elements.

On divisors of pseudovarieties generated by some classes of full transformation semigroups

Algebra Colloquium, 15 (2008), p. 581–588

Presentations for monoids of finite partial isometries

In this paper we give presentations for the monoid DPn of all partial isometries on {1,..., n} and for its submonoid ODPn of all order-preserving partial isometries.

Presentations for some monoids of injective partial transformations on a finite chain.

Communications in Algebra, 33 (2005), p. 587-604

The cardinal and the idempotent number of various monoids of transformations on a finite chain

Bulletin of the Malaysian Mathematical Sciences Society, 2, 34 (1),(2011), p. 79–85

The cardinal of various monoids of transformations that preserve a uniform partition

Bulletin of the Malaysian Mathematical Sciences Society

Normally ordered semigroups

Glasgow Mathematical Journal, nº 50 (2008), p. 325-333

Chronofunctions of Heilu soil developed from Loess in Luochuan, on the chinese Loess plateau

Soil chronofunctions are an alternative for the quantification of soil-forming processes and underlie the modeling of soil genesis. To establish soil chronofunctions of a Heilu soil profile on Loess in Luochuan, selected soil properties and the 14C ages in the Holocene were studied. Linear, logarithmic, and third-order polynomial functions were selected to fit the relationships between soil properties and ages. The results indicated that third-order polynomial function fit best for the relationships between clay (< 0.002 mm), silt (0.002-0.02 mm), sand (0.02-2 mm) and soil ages, and a trend of an Ah horizon ocurrence in the profile. The logarithmic function indicated mainly variations of soil organic carbon and pH with time (soil age). The variation in CaCO3 content, Mn/Zr, Fe/Zr, K/Zr, Mg/Zr, Ca/Zr, P/Zr, and Na/Zr ratios with soil age were best described by three-order polynomial functions, in which the trend line showed migration of CaCO3 and some elements.