Bubbling and bistability in two parameter discrete systems

We present a graphical analysis of the mechanisms underlying the occurrences of bubbling sequences and bistability regions in the bifurcation scenario of a special class of one dimensional two parameter maps. The main result of the analysis is that whether it is bubbling or bistability is decided by the sign of the third derivative at the inflection point of the map function.Comment: LaTeX v2.09, 14 pages with 4 PNG figure

GALEX Observations of Diffuse UV Radiation at High Spatial Resolution from the Sandage Nebulosity

Using the GALEX ultraviolet imagers we have observed a region of nebulosity first identified as starlight scattered by interstellar dust by Sandage (1976). Apart from airglow and zodiacal emission, we have found a diffuse UV background of between 500 and 800 \phunit in both the \galex FUV (1350 -- 1750 \AA) and NUV (1750 -- 2850 \AA). Of this emission, up to 250 \phunit is due to \htwo fluorescent emission in the FUV band; the remainder is consistent with scattering from interstellar dust. We have estimated the optical constants to be $a = 0.3; g = 0.7$ in the FUV and $a = 0.5; g = 0.7$ in the NUV, implying highly forward scattering grains, plus an extragalactic contribution of as much as 150 \phunit. These are the highest spatial resolution observations of the diffuse UV background to date and show an intrinsic scatter beyond that expected from instrumental noise alone. Further modeling is required to understand the nature of this scatter and its implications for the ISM.Comment: Total 20 pages, Figures 9, Accepted for publication in Astrophysical Journa

Measurement of Dust Optical Properties in Coalsack

We have used FUSE and Voyager observations of dust scattered starlight in the neighborhood of the Coalsack Nebula to derive the optical constants of the dust grains. The albedo is consistent with a value of $0.28 \pm 0.04$ and the phase function asymmetry factor with a value of $0.61 \pm 0.07$ throughout the spectral range from 900 -- 1200 \AA, in agreement with previous determinations as well as theoretical predictions. We have now observed two regions (Ophiuchus and Coalsack) with intense diffuse background radiation and in both cases have found that the emission is due to light from nearby hot stars scattered by a relatively thin foreground cloud, with negligible contribution from the background molecular cloud.Comment: Total 19 pages, Figures 9, Accepted for publication in Astrophysical Journa

Navigating The Digital Marketing Landscape: A Comprehensive Study On Effectiveness, Influencing Factors, And Strategic Recommendations For Businesses

This study explores the dynamics of digital marketing effectiveness and its implications for businesses. The research investigates the correlation between income levels and the duration of digital marketing utilization, revealing nuanced insights for tailoring strategies based on income brackets. Emphasizing the significance of website promotion in driving organic search revenue, the study advocates for prioritizing comprehensive online marketing campaigns. Insights from a literature review highlight the dynamic nature of digital marketing trends, challenges in measuring ROI, and the importance of understanding consumer behavior in the digital realm. Practical recommendations include staying abreast of technological advancements, investing in robust analytics, and focusing on personalized marketing strategies. Overcoming challenges in digital marketing implementation, especially data security concerns, is crucial. Small and medium-sized enterprises (SMEs) are encouraged to leverage cost-effective strategies, while fostering long-term relationships with digital marketing companies is recommended. The study concludes by providing actionable insights to guide businesses in optimizing their digital marketing efforts and adapting to the ever-evolving online landscape

Observations of Diffuse Ultraviolet Emission from Draco

We have studied small scale (2 arcmin) spatial variation of the diffuse UV radiation using a set of 11 GALEX deep observations in the constellation of Draco. We find a good correlation between the observed UV background and the IR 100 micron flux, indicating that the dominant contributor of the diffuse background in the field is the scattered starlight from the interstellar dust grains. We also find strong evidence of additional emission in the FUV band which is absent in the NUV band. This is most likely due to Lyman band emission from molecular hydrogen in a ridge of dust running through the field and to line emissions from species such as C IV (1550 A) and Si II (1533 A) in the rest of the field. A strong correlation exists between the FUV/NUV ratio and the FUV intensity in the excess emission regions in the FUV band irrespective of the optical depth of the region. The optical depth increases more rapidly in the UV than the IR and we find that the UV/IR ratio drops off exponentially with increasing IR due to saturation effects in the UV. Using the positional details of Spitzer extragalactic objects, we find that the contribution of extragalactic light in the diffuse NUV background is 49 +/- 13 photon units and is 30 +/- 10 photon units in the FUV band.Comment: 30 pages, 13 figures, Accepted for publication in The Astrophysical Journal (ApJ), November 2010, v723 issu