Nonexistence of eventually positive solutions of a difference inequality with multiple and variable delays and coefficients

AbstractIn this paper, we consider the nonexistence of eventually positive solutions of the difference inequality ϰn+1 − ϰn + ∑i=1mpi(n)ϰn−ki(n) ≤ 0.Let m be a positive integer. Then for each positive integer i: 1 ≤ i ≤ m, {ki(n)}∞n=0 and {pi(n)}∞n=0 are a sequence of positive integers and a sequence of nonnegative real numbers, respectively. A sufficient condition guaranteeing the nonexistence of eventually positive solutions is obtained with the help of a new method. As an application of the main result, a conjecture is proved

Periodic solutions of a single species discrete population model with periodic harvest/stock

AbstractWe discuss a discrete population model describing single species growth with periodic harvest/stock. The theory of coincidence degree is applied to show that the model equation admits two periodic solutions. Under minor technical assumptions, we show that one of these two periodic solutions is positive and attracts almost all positive solutions

Poynting vector, energy density and energy velocity in anomalous dispersion medium

The Poynting vector, energy density and energy velocity of light pulses propagating in anomalous dispersion medium (used in WKD-like experiments) are calculated. Results show that a negative energy density in the medium propagates along opposite of incident direction with such a velocity similar to the negative group velocity while the direction of the Poynting vector is positive. In other words, one might say that a positive energy density in the medium would propagate along the positive direction with a speed having approximately the absolute valueof the group velocity. We further point out that neither energy velocity nor group velocity is a good concept to describe the propagation process of light pulse inside the medium in WKD experiment owing to the strong accumulation and dissipation effects.Comment: 6 page

Self-organising comprehensive handover strategy for multi-tier LTE-advanced heterogeneous networks

Long term evolution (LTE)-advanced was introduced as real fourth generation (4G) with its new features and additional functions, satisfying the growing demands of quality and network coverage for the network operators' subscribers. The term muti-tier has also been recently used with respect to the heterogeneity of the network by applying the various subnetwork cooperative systems and functionalities with self-organising capabilities. Using indoor short-range low-power cellular base stations, for example, femtocells, in cooperation with existing long-range macrocells are considered as the key technical challenge of this multi-tier configuration. Furthermore, shortage of network spectrum is a major concern for network operators which forces them to spend additional attentions to overcome the degradation in performance and quality of services in 4G HetNets. This study investigates handover between the different layers of a heterogeneous LTE-advanced system, as a critical attribute to plan the best way of interactive coordination within the network for the proposed HetNet. The proposed comprehensive handover algorithm takes multiple factors in both handover sensing and decision stages, based on signal power reception, resource availability and handover optimisation, as well as prioritisation among macro and femto stations, to obtain maximum signal quality while avoiding unnecessary handovers

The roles of sulfuric acid in new particle formation and growth in the mega-city of Beijing

Simultaneous measurements of gaseous sulfuric acid and particle number size distributions were performed to investigate aerosol nucleation and growth during CAREBeijing-2008. The analysis of the measured aerosols and sulfuric acid with an aerosol dynamic model shows the dominant role of sulfuric acid in new particle formation (NPF) process but also in the subsequent growth in Beijing. Based on the data of twelve NPF events, the average formation rates (2–13 cm−3 s−1) show a linear correlation with the sulfuric acid concentrations (R2=0.85). Coagulation seems to play a significant role in reducing the number concentration of nucleation mode particles with the ratio of the coagulation loss to formation rate being 0.41±0.16. The apparent growth rates vary from 3 to 11 nm h−1. Condensation of sulfuric acid and its subsequent neutralization by ammonia and coagulation contribute to the apparent particle growth on average 45±18% and 34±17%, respectively. The 30% higher concentration of sulfate than organic compounds in particles during the seven sulfur-rich NPF events but 20% lower concentration of sulfate during the five sulfur-poor type suggest that organic compounds are an important contributor to the growth of the freshly nucleated particles, especially during the sulfur-poor cases

Gravitational-wave Detection With Matter-wave Interferometers Based On Standing Light Waves

We study the possibility of detecting gravitational-waves with matter-wave interferometers, where atom beams are split, deflected and recombined totally by standing light waves. Our calculation shows that the phase shift is dominated by terms proportional to the time derivative of the gravitational wave amplitude. Taking into account future improvements on current technologies, it is promising to build a matter-wave interferometer detector with desired sensitivity.Comment: 7 pages, 3 figures. To be published in General Relativity and Gravitatio

Two-fermion bound state in a Bose-Einstein condensate

A nonlinear Schr\"odinger equation is derived for the dynamics of a beam of ultracold fermionic atoms traversing a Bose-Einstein condensate. The condensate phonon modes are shown to provide a nonlinear medium for the fermionic atoms. A two-fermion bound state is predicted to arise, and the signature of the bound state in a nonlinear atom optics experiment is discussed.Comment: 4 pages, 1 figure

Dispersive properties of quasi-phase-matched optical parametric amplifiers

The dispersive properties of non-degenerate optical parametric amplification in quasi-phase-matched (QPM) nonlinear quadratic crystals with an arbitrary grating profile are theoretically investigated in the no-pump-depletion limit. The spectral group delay curve of the amplifier is shown to be univocally determined by its spectral power gain curve through a Hilbert transform. Such a constraint has important implications on the propagation of spectrally-narrow optical pulses through the amplifier. In particular, it is shown that anomalous transit times, corresponding to superluminal or even negative group velocities, are possible near local minima of the spectral gain curve. A possible experimental observation of such effects using a QPM Lithium-Niobate crystal is suggested.Comment: submitted for publicatio

Direct Measurements of the Branching Fractions for D0→K−e+νeD^0 \to K^-e^+\nu_e and D0→π−e+νeD^0 \to \pi^-e^+\nu_e and Determinations of the Form Factors f+K(0)f_{+}^{K}(0) and f+π(0)f^{\pi}_{+}(0)

The absolute branching fractions for the decays $D^0 \to K^-e ^+\nu_e$ and $D^0 \to \pi^-e^+\nu_e$ are determined using $7584\pm 198 \pm 341$ singly tagged $\bar D^0$ sample from the data collected around 3.773 GeV with the BES-II detector at the BEPC. In the system recoiling against the singly tagged $\bar D^0$ meson, $104.0\pm 10.9$ events for $D^0 \to K^-e ^+\nu_e$ and $9.0 \pm 3.6$ events for $D^0 \to \pi^-e^+\nu_e$ decays are observed. Those yield the absolute branching fractions to be $BF(D^0 \to K^-e^+\nu_e)=(3.82 \pm 0.40\pm 0.27)$ and $BF(D^0 \to \pi^-e^+\nu_e)=(0.33 \pm 0.13\pm 0.03)$. The vector form factors are determined to be $|f^K_+(0)| = 0.78 \pm 0.04 \pm 0.03$ and $|f^{\pi}_+(0)| = 0.73 \pm 0.14 \pm 0.06$. The ratio of the two form factors is measured to be $|f^{\pi}_+(0)/f^K_+(0)|= 0.93 \pm 0.19 \pm 0.07$.Comment: 6 pages, 5 figure