Continued fractions and Catalan problems

We find a generating function expressed as a continued fraction that enumerates ordered trees by the number of vertices at different levels. Several Catalan problems are mapped to an ordered-tree problem and their generating functions also expressed as a continued fraction. Among these problems is the enumeration of (132)-pattern avoiding permutations that have a given number of increasing patterns of length k. This extends and illuminates a result of Robertson, Wilf and Zeilberger for the case k=3.Comment: 9 pages, 1 figur

Violation of Porod law in a freely cooling granular gas in one dimension

We study a model of freely cooling inelastic granular gas in one dimension, with a restitution coefficient which approaches the elastic limit below a relative velocity scale v. While at early times (t << 1/v) the gas behaves as a completely inelastic sticky gas conforming to predictions of earlier studies, at late times (t >> 1/v) it exhibits a new fluctuation dominated phase ordering state. We find distinct scaling behavior for the (i) density distribution function, (ii) occupied and empty gap distribution functions, (iii) the density structure function and (iv) the velocity structure function, as compared to the completely inelastic sticky gas. The spatial structure functions (iii) and (iv) violate the Porod law. Within a mean-field approximation, the exponents describing the structure functions are related to those describing the spatial gap distribution functions.Comment: 4 pages, 5 figure

Composite multiple wavelength laser material and multiple wavelength laser for use therewith

A composite multiple wavelength laser material is provided and is typically constructed with a common axis of construction in the form of a rod of uniform cross-section. The rod comprises a plurality of segments of laser material bonded, e.g., diffusion bonded, to one another along the common axis. Each segment lases at a unique wavelength when excited to produce a laser emission. The segments can be made from a birefringent material doped with laser active ions. If the same birefringent host material is used for all segments, ground-state absorption losses can be reduced by terminating either end of the rod with end segments made from undoped pieces of the birefringent material

Obstetric and Gynecologic Departments, Faculty of Medicine Udayana University, Bali-Indonesia

The high risk of human papillomavirus (HPV) have already known widely and accepted as a causative agent for cervical cancer. Epidemiologically, predominant high-risk is HPV-16 and squamous cell carcinomas (SCC) is the most common histological type. HPV genotype probably correlates to histologic type. This study aims to determine how many fold is the risk of SCC on HPV-16 infection. This is a case control with SCC HPV-16 positive as the cases and SCC HPV-16 negative as the controls. Tissues diagnosed as SCC and non SCC was paraffin-embedded. SPF-10 and specific E7-primer types by LiPA were employed for genotyping of HPV-16. c2 was applied to analyze the correlation. A number of 65 SCC consisted of 33 cases and 32 controls were observed in this study. The risk of SCC on HPV-16 infection was 3.40-fold (95% CI = 1.44-8.03; p = 0.004) compare with HPV-16 negative. Controls in this study consist of 18 (27.69%) of HPV-18, 9 (13.85%) of HPV-52, and 5 (7.69%) of other HPV types. The mean-age of case group and control group infected by HPV were 52.28 ± 12.43 and 47.70 ± 8.02 year, respectively (p = 0.02). HPV-16 infection caused SCC is 3.5 more than other high risk group

Production and Quality Assessment of Pasture Crop in Red Lateritic Wasteland of Central Chhattisgarh

The livestock constitutes a very important component in rural economy, as in agriculture. Our country largely depends on livestock for manure and power. The availability of fodder is short from the requirement and an estimate of several agencies, there is more than 300 per cent gap between availability and requirement (Anon, 1980). Most of the livestock depend either partially or completely on natural and developed pastoral system, but the existing practices of utilization of range lands, grasslands and forest areas natural resources and increasing land degradation. In the improved pastoral system in wastelands, the carrying capacity of grass-legumes pastoral field is consistently noticed to deteriorated over a period by invasion of local species. Here improved pastoral system was studied for its production and structure behavior and nutritive value after 10 years of establishment

Coarse grained dynamics of the freely cooling granular gas in one dimension

We study the dynamics and structure of clusters in the inhomogeneous clustered regime of a freely cooling granular gas of point particles in one dimension. The coefficient of restitution is modeled as $r_0<1$ or 1 depending on whether the relative speed is greater or smaller than a velocity scale $\delta$. The effective fragmentation rate of a cluster is shown to rise sharply beyond a $\delta$ dependent time scale. This crossover is coincident with the velocity fluctuations within a cluster becoming order $\delta$. Beyond this crossover time, the cluster size distribution develops a nontrivial power law distribution, whose scaling properties are related to those of the velocity fluctuations. We argue that these underlying features are responsible behind the recently observed nontrivial coarsening behaviour in the one dimensional freely cooling granular gas.Comment: 7 Pages, 9 Figure