The groups of Poincaré and Galilei in arbitrary dimensional spaces

In arbitrary dimensional spaces the Lie algebra of the Poincaré group is seen to be a subalgebra of the complex Galilei algebra, while the Galilei algebra is a subalgebra of Poincar algebra. The usual contraction of the Poincar to the Galilei group is seen to be equivalent to a certain coordinate transformation.

Poincaré is a subgroup of Galilei in one space dimension more

Through an imaginary change of coordinates, the ordinary Poincar algebra is shown to be a subalgebra of the Galilei one in four space dimensions. Through a subsequent contraction the remaining Lie generators are eliminated in a natural way. An application of these results to connect Galilean and relativistic field equations is discussed.

Fractal dimension for Gaussian colored processes

The exact analytical expression for the Hausdorff dimension of free processes driven by Gaussian noise in n-dimensional space is obtained. The fractal dimension solely depends on the time behavior of the arbitrary correlation function of the noise, ranging from DX=1 for Orstein-Uhlenbeck input noise to any real number greater than 1 for fractional Brownian motions.

On the dimension of the core of the assignment game

The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position in the assignment matrix.

From local groups to early states: the development of complexity in protohistoric Catalonia

La recerca sobre la protohistoria de Catalunya s'ha fonamentat tradicionalment en la historia cultural, pero el treba11 deIs darrers vint-i-cinc anys ha comenat a donar 11um sobre aspectes crucials com el canvi social i la formació de l'Estat arcaico Aquest article és una visió general sobre aquests temes. S'hi analitza particularment el paper del creixement demogrMic com a element crucial del canvi social, pero també s'hi té en compte el paper que eventualment hi hagin pogut tenir els moviments de població i el comerç colonial.

Spatial behavior in groups: an agent-based approach

We present an agent-based model with the aim of studying how macro-level dynamics of spatial distances among interacting individuals in a closed space emerge from micro-level dyadic and local interactions. Our agents moved on a lattice (referred to as a room) using a model implemented in a computer program called P-Space in order to minimize their dissatisfaction, defined as a function of the discrepancy between the real distance and the ideal, or desired, distance between agents. Ideal distances evolved in accordance with the agent's personal and social space, which changed throughout the dynamics of the interactions among the agents. In the first set of simulations we studied the effects of the parameters of the function that generated ideal distances, and in a second set we explored how group macrolevel behavior depended on model parameters and other variables. We learned that certain parameter values yielded consistent patterns in the agents' personal and social spaces, which in turn led to avoidance and approaching behaviors in the agents. We also found that the spatial behavior of the group of agents as a whole was influenced by the values of the model parameters, as well as by other variables such as the number of agents. Our work demonstrates that the bottom-up approach is a useful way of explaining macro-level spatial behavior. The proposed model is also shown to be a powerful tool for simulating the spatial behavior of groups of interacting individuals.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Differences based on fine motor behaviour in Parkinson's patients compared to an age matched control group in proprioceptive and visuo-proprioceptive test conditions

Personality differences based on fine motor precision performance were studied in early stage Parkinson's patients and an age-matched control group under two different test conditions: proprioceptive + visual information and proprioceptive information alone. A comparative data analysis for deviations of three measured movement types (transversal, frontal and sagittal) was done for both hands (dominant and non-dominant) with relation to personality dimensions. There were found significant differences between the two groups in decision making dimension and emotionality. After splitting the data for gender subgroups, some significant differences were found for men but not for women. The differences in fine motor task performance varied, being better in some directions for the Parkinson"s patients and worse in others. The findings may suggest that medication has both positive and negative effects on motor performance and provoke personality changes, being more pronounced in men.

Nucleophile-Catalyzed Additions to Activated Triple Bonds. Protection of Lactams, Imides, and Nucleosides with MocVinyl and Related Groups

Additions of lactams, imides, (S)-4-benzyl-1,3-oxazolidin-2-one, 2-pyridone, pyrimidine-2,4-diones (AZT derivatives), or inosines to the electron-deficient triple bonds of methyl propynoate, tert-butyl propynoate, 3-butyn-2-one, N-propynoylmorpholine, or N-methoxy-N-methylpropynamide in the presence of many potential catalysts were examined. DABCO and, second, DMAP appeared to be the best (highest reaction rates and E/Z ratios), while RuCl3, RuClCp*(PPh3)2, AuCl, AuCl(PPh3), CuI, and Cu2(OTf)2 were incapable of catalyzing such additions. The groups incorporated (for example, the 2-(methoxycarbonyl)ethenyl group that we name MocVinyl) serve as protecting groups for the above-mentioned heterocyclic CONH or CONHCO moieties. Deprotections were accomplished via exchange with good nucleophiles: the 1-dodecanethiolate anion turned out to be the most general and efficient reagent, but in some particular cases other nucleophiles also worked (e.g., MocVinyl-inosines can be cleaved with succinimide anion). Some structural and mechanistic details have been accounted for with the help of DFT and MP2 calculations.

Robust Detection of Incumbents in Cognitive Radio Networks Using Groups

Cognitive radio is a wireless technology aimed at improvingthe efficiency use of the radio-electric spectrum, thus facilitating a reductionin the load on the free frequency bands. Cognitive radio networkscan scan the spectrum and adapt their parameters to operate in the unoccupiedbands. To avoid interfering with licensed users operating on a givenchannel, the networks need to be highly sensitive, which is achieved byusing cooperative sensing methods. Current cooperative sensing methodsare not robust enough against occasional or continuous attacks. This articleoutlines a Group Fusion method that takes into account the behavior ofusers over the short and long term. On fusing the data, the method is basedon giving more weight to user groups that are more unanimous in their decisions.Simulations have been performed in a dynamic environment withinterferences. Results prove that when attackers are present (both reiterativeor sporadic), the proposed Group Fusion method has superior sensingcapability than other methods.

Comments on "On the relationship between fractal dimension and the performance of multi-resonant dipole antennas using Koch curves"

Comentaris referits a l'article següent: K. J. Vinoy, J. K. Abraham, and V. K. Varadan, “On the relationshipbetween fractal dimension and the performance of multi-resonant dipoleantennas using Koch curves,” IEEE Transactions on Antennas and Propagation, 2003, vol. 51, p. 2296–2303.

Nucleophile-Catalyzed Additions to Activated Triple Bonds. Protection of Lactams, Imides, and Nucleosides with MocVinyl and Related Groups

Additions of lactams, imides, (S)-4-benzyl-1,3-oxazolidin-2-one, 2-pyridone, pyrimidine-2,4-diones (AZT derivatives), or inosines to the electron-deficient triple bonds of methyl propynoate, tert-butyl propynoate, 3-butyn-2-one, N-propynoylmorpholine, or N-methoxy-N-methylpropynamide in the presence of many potential catalysts were examined. DABCO and, second, DMAP appeared to be the best (highest reaction rates and E/Z ratios), while RuCl3, RuClCp*(PPh3)2, AuCl, AuCl(PPh3), CuI, and Cu2(OTf)2 were incapable of catalyzing such additions. The groups incorporated (for example, the 2-(methoxycarbonyl)ethenyl group that we name MocVinyl) serve as protecting groups for the above-mentioned heterocyclic CONH or CONHCO moieties. Deprotections were accomplished via exchange with good nucleophiles: the 1-dodecanethiolate anion turned out to be the most general and efficient reagent, but in some particular cases other nucleophiles also worked (e.g., MocVinyl-inosines can be cleaved with succinimide anion). Some structural and mechanistic details have been accounted for with the help of DFT and MP2 calculations.

Orthogonal protecting groups in the synthesis of tryptophanyl-hexahydropyrroloindoles

The synthesis of various polycyclic systems containing a C3aNi bond between a hexahydropyrrolo[2,3-b]indole and an indole tryptophan is described here. A series of experiments were performed to determine the best combination of five orthogonal protecting groups and the best reaction conditions for formation of said bond, which is a common feature among many recently discovered marine natural products.