On Lebesgue measure of integral self-affine sets

Let $A$ be an expanding integer $n\times n$ matrix and $D$ be a finite subset of $Z^n$. The self-affine set $T=T(A,D)$ is the unique compact set satisfying the equality $A(T)=\cup_{d\in D} (T+d)$. We present an effective algorithm to compute the Lebesgue measure of the self-affine set $T$, the measure of intersection $T\cap (T+u)$ for $u\in Z^n$, and the measure of intersection of self-affine sets $T(A,D_1)\cap T(A,D_2)$ for different sets $D_1,D_2\subset Z^n$.Comment: 5 pages, 1 figur

VOLATILE LEAF OIL CONSTITUENTS OF OCIMUM AMERICANUM L. OCCURING IN WESTERN KENYA

Steam distilled volatile oils from the leaves of Ocimum americanum L. growing in Western Kenya were analysed by GC and GC-MS. A total of 36 compounds, representing a total of 88.51% of the total oil, were identified. The oil was classified as terpinen-4-ol-type according to the terpinen-4-ol content (43.21%). To the best of our knowledge this chemotype of O. americanum has not yet been reported from the East African region. This chemotype of O. americanum has only been reported from Togo. Other notable components include 1,8-cineole (16.13%), α-terpineol (4.01%), trans-caryophyllene (3.06%), α-bergamotene (2.68%) and cis-sabinene hydrate (2.59%). The oil contains mainly oxygenated monoterpenes which accounted for 71.24% of the total oil. The yield obtained was 4% w/w on a dry weight basis. KEY WORDS: Ocimum americanum, Lamiaceae, Chemotype, Terpinen-4-ol, 1,8-Cineole, µ-Terpineol, trans-Caryophyllene, Kenya Bull. Chem. Soc. Ethiop. 2006, 20(1), 177-180

Collective excitations of trapped Bose condensates in the energy and time domains

A time-dependent method for calculating the collective excitation frequencies and densities of a trapped, inhomogeneous Bose-Einstein condensate with circulation is presented. The results are compared with time-independent solutions of the Bogoliubov-deGennes equations. The method is based on time-dependent linear-response theory combined with spectral analysis of moments of the excitation modes of interest. The technique is straightforward to apply, is extremely efficient in our implementation with parallel FFT methods, and produces highly accurate results. The method is suitable for general trap geometries, condensate flows and condensates permeated with vortex structures.Comment: 6 pages, 3 figures small typos fixe

Mediation of oviposition site selection in the African malaria mosquito Anopheles gambiae (Diptera: Culicidae) by semiochemicals of microbial origin

Laboratory studies were carried out to investigate the role of larval habitat-derived microorganisms in the production of semiochemicals for oviposition site selection by Anopheles gambiae Giles sensu stricto mosquitoes. Dual-choice bioassays with gravid females were conducted in standard mosquito cages. Field-collected or laboratory-reared mosquitoes, individually or in groups, were offered a choice between unmodified (water or soil from a natural breeding site) or modified substrates (filtered water, autoclaved soil or sterile media to which bacterial suspensions had been added). Egg counts were used to assess oviposition preferences. Mosquitoes preferred to oviposit on unmodified substrates from natural larval habitats containing live microorganisms rather than on sterilized ones. Variable responses were observed when sterile substrates were inoculated with bacteria isolated from water and soil from natural habitats. We conclude that microbial populations in breeding sites produce volatiles that serve as semiochemicals for gravid An. gambiae. These signals, in conjunction with other (non-olfactory) chemical and physical cues, may be used by the female to assess the suitability of potential larval habitats in order to maximize the fitness of her offspring

Approximating a Behavioural Pseudometric without Discount for<br> Probabilistic Systems

Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of behavioural pseudometrics for probabilistic transition systems. These pseudometrics are a quantitative analogue of probabilistic bisimilarity. Distance zero captures probabilistic bisimilarity. Each pseudometric has a discount factor, a real number in the interval (0, 1]. The smaller the discount factor, the more the future is discounted. If the discount factor is one, then the future is not discounted at all. Desharnais et al. showed that the behavioural distances can be calculated up to any desired degree of accuracy if the discount factor is smaller than one. In this paper, we show that the distances can also be approximated if the future is not discounted. A key ingredient of our algorithm is Tarski's decision procedure for the first order theory over real closed fields. By exploiting the Kantorovich-Rubinstein duality theorem we can restrict to the existential fragment for which more efficient decision procedures exist

Robust Linear Longitudinal Feedback Control of a Flapping Wing Micro Air Vehicle

This paper falls under the idea of introducing biomimetic miniature air vehicles in ambient assisted living and home health applications. The concepts of active disturbance rejection control and flatness based control are used in this paper for the trajectory tracking tasks in the flapping-wing miniature air vehicle (FWMAV) time-averaged model. The generalized proportional integral (GPI) observers are used to obtain accurate estimations of the flat output associated phase variables and of the time-varying disturbance signals. This information is used in the proposed feedback controller in (a) approximate, yet close, cancelations, as lumped unstructured time-varying terms, of the influence of the highly coupled nonlinearities and (b) the devising of proper linear output feedback control laws based on the approximate estimates of the string of phase variables associated with the flat outputs simultaneously provided by the disturbance observers. Numerical simulations are provided to illustrate the effectiveness of the proposed approach

Single Atom and Two Atom Ramsey Interferometry with Quantized Fields

Implications of field quantization on Ramsey interferometry are discussed and general conditions for the occurrence of interference are obtained. Interferences do not occur if the fields in two Ramsey zones have precise number of photons. However in this case we show how two atom (like two photon) interferometry can be used to discern a variety of interference effects as the two independent Ramsey zones get entangled by the passage of first atom. Generation of various entangled states like |0,2>+|2,0> are discussed and in far off resonance case generation of entangled state of two coherent states is discussed.Comment: 20 pages, 5 figures, revised version. submitted to Phys. Rev.

The finite-temperature chiral transition in QCD with adjoint fermions

We study the nature of the finite-temperature chiral transition in QCD with N_f light quarks in the adjoint representation (aQCD). Renormalization-group arguments show that the transition can be continuous if a stable fixed point exists in the renormalization-group flow of the corresponding three-dimensional Phi^4 theory with a complex 2N_f x 2N_f symmetric matrix field and symmetry-breaking pattern SU(2N_f)->SO(2N_f). This issue is investigated by exploiting two three-dimensional perturbative approaches, the massless minimal-subtraction scheme without epsilon expansion and a massive scheme in which correlation functions are renormalized at zero momentum. We compute the renormalization-group functions in the two schemes to five and six loops respectively, and determine their large-order behavior. The analyses of the series show the presence of a stable three-dimensional fixed point characterized by the symmetry-breaking pattern SU(4)->SO(4). This fixed point does not appear in an epsilon-expansion analysis and therefore does not exist close to four dimensions. The finite-temperature chiral transition in two-flavor aQCD can therefore be continuous; in this case its critical behavior is determined by this new SU(4)/SO(4) universality class. One-flavor aQCD may show a more complex phase diagram with two phase transitions. One of them, if continuous, should belong to the O(3) vector universality class.Comment: 36 page

Search for Invisible Decays of η\eta and η′\eta^\prime in J/ψ→ϕηJ/\psi \to \phi\eta and ϕη′\phi \eta^\prime

Using a data sample of $58\times 10^6$ $J/\psi$ decays collected with the BES II detector at the BEPC, searches for invisible decays of $\eta$ and $\eta^\prime$ in $J/\psi$ to $\phi\eta$ and $\phi\eta^\prime$ are performed. The $\phi$ signals, which are reconstructed in $K^+K^-$ final states, are used to tag the $\eta$ and $\eta^\prime$ decays. No signals are found for the invisible decays of either $\eta$ or $\eta^\prime$, and upper limits at the 90% confidence level are determined to be $1.65 \times 10^{-3}$ for the ratio $\frac{B(\eta\to \text{invisible})}{B(\eta\to\gamma\gamma)}$ and $6.69\times 10^{-2}$ for $\frac{B(\eta^\prime\to \text{invisible})}{B(\eta^\prime\to\gamma\gamma)}$. These are the first searches for $\eta$ and $\eta^\prime$ decays into invisible final states.Comment: 5 pages, 4 figures; Added references, Corrected typo

Observation of Two New N* Peaks in J/psi -> ppi−nˉp pi^- \bar n and pˉπ+n\bar p\pi^+n Decays

The $\pi N$ system in decays of $J/\psi\to\bar NN\pi$ is limited to be isospin 1/2 by isospin conservation. This provides a big advantage in studying $N^*\to \pi N$ compared with $\pi N$ and $\gamma N$ experiments which mix isospin 1/2 and 3/2 for the $\pi N$ system. Using 58 million $J/\psi$ decays collected with the Beijing Electron Positron Collider, more than 100 thousand $J/\psi \to p \pi^- \bar n + c.c.$ events are obtained. Besides two well known $N^*$ peaks at 1500 MeV and 1670 MeV, there are two new, clear $N^*$ peaks in the $p\pi$ invariant mass spectrum around 1360 MeV and 2030 MeV. They are the first direct observation of the $N^*(1440)$ peak and a long-sought "missing" $N^*$ peak above 2 GeV in the $\pi N$ invariant mass spectrum. A simple Breit-Wigner fit gives the mass and width for the $N^*(1440)$ peak as $1358\pm 6 \pm 16$ MeV and $179\pm 26\pm 50$ MeV, and for the new $N^*$ peak above 2 GeV as $2068\pm 3^{+15}_{-40}$ MeV and $165\pm 14\pm 40$ MeV, respectively