The chromatic discrepancy of graphs

For a proper vertex coloring cc of a graph GG, let φc(G)φc(G) denote the maximum, over all induced subgraphs HH of GG, the difference between the chromatic number χ(H)χ(H) and the number of colors used by cc to color HH. We define the chromatic discrepancy of a graph GG, denoted by φ(G)φ(G), to be the minimum φc(G)φc(G), over all proper colorings cc of GG. If HH is restricted to only connected induced subgraphs, we denote the corresponding parameter by View the MathML sourceφˆ(G). These parameters are aimed at studying graph colorings that use as few colors as possible in a graph and all its induced subgraphs. We study the parameters φ(G)φ(G) and View the MathML sourceφˆ(G) and obtain bounds on them. We obtain general bounds, as well as bounds for certain special classes of graphs including random graphs. We provide structural characterizations of graphs with φ(G)=0φ(G)=0 and graphs with View the MathML sourceφˆ(G)=0. We also show that computing these parameters is NP-hard

Understanding and overcoming number difficulties

Across schools in the United Kingdom (UK), it is common for teachers to identify children as having significant difficulties with mathematics. The authors’ experiences in schools suggest that, despite interventions, these children continue to have significant mathematical difficulties. Currently there is little research and a lack of agreement across literature as to the aspects of mathematics that children find difficult and the characteristics of these children. In this paper, the authors provide a preliminary review of the literature in this field and propose a study in UK primary schools to address the gaps identified. The proposed study aims to investigate: (i) the characteristics of children who are identified as having significant mathematical difficulties; (ii) the mathematical profiles of these children; and (iii) different perspectives about the nature of a child’s number difficulties. With a clearer understanding of these children, we can suggest more appropriate ways to support their progress

Bacteriology of Acute Respiratory Infections in Children

Bacteriological investigations were carried out on 151 children (80 males and 71 females) suffering from acute respiratory infections (ARI) to And out bacteria associated with ARI. Fifty one children presenting with upper respiratory infections (URI) and 100 with lower respiratory infections (LRI) seen at the outpatient department of the Institute of Child Health and Hospital for Children, Madras, were included in this study. In all, 56% of the children yielded any one or a mixture of bacteria that could be potential or probable pathogens of ARI. Nonfermenting gram negative bacilli (NFGNB) were the predominant organisms isolated (27%) followed by non-typable ampicillin resistant Haemophilus influenzae (13%) and b. haemolytic streptococci groups C and G (11%). The other bacteria isolated in this study were Klebsiella pneumoniae (7%), Streptococcus pneumoniae (3%), Neisseria sps. pure (3%) and Staphylococcus aureus (1%). The isolation rate of NFGNB was maximum (47%) when the duration of illness exceeded 7 days. Mixed infections of potential or probable pathogens were observed in 11 patients which included NFGNB + K. pneumoniae (2); H. influenzae + NFGNB (2); b- haemolytic streptococci + H. influenzae (2); b- haemolytic streptococci + K. pneumoniae (1) ; S. aureus + K. pneumoniae (1) ; Neisseria sp. + K. pneumoniae (2) and NFGNB + b- haemolytic streptococci + H. influenzae (1)

Mussel farming initiatives in north Kerala, India: a case of successful adoption of technology, leading to rural livelihood transformation

The Malabar region, extending from Malappuram to Kasargode districts of Northern Kerala, is a well-known mussel fi shery zone of India. Over 7,000 t (80%) of the total green mussel (Perna viridis) catch is exploited annually from this zone. The Central Marine Fisheries Research Institute (CMFRI) developed techniques for mussel culture in 1971 and subsequently fi eld demonstrations in different areas with direct involvement of local rural folk were carried out1. Demonstrations to popularise this technology have led to adoption of this simple farming method particularly in the Malabar region2. The Malabar coast has extensive backwaters and estuaries, which are suitable for mussel farming during the post monsoon months (November to May) when higher saline conditions prevail. Farming activity during this period provides an opportunity for supplementary livelihood and additional income to the coastal rural population

Optical Properties of Mono-Dispersed AlGaN Nanowires in the Single-Prong Growth Mechanism

Growth of mono-dispersed AlGaN nanowires of ternary wurtzite phase is reported using chemical vapour deposition technique in the vapour-liquid-solid process. The role of distribution of Au catalyst nanoparticles on the size and the shape of AlGaN nanowires are discussed. These variations in the morphology of the nanowires are understood invoking Ostwald ripening of Au catalyst nanoparticles at high temperature followed by the effect of single and multi-prong growth mechanism. Energy-filtered transmission electron microscopy is used as an evidence for the presence of Al in the as-prepared samples. A significant blue shift of the band gap, in the absence of quantum confinement effect in the nanowires with diameter about 100 nm, is used as a supportive evidence for the AlGaN alloy formation. Polarized resonance Raman spectroscopy with strong electron-phonon coupling along with optical confinement due to the dielectric contrast of nanowire with respect to that of surrounding media are adopted to understand the crystalline orientation of a single nanowire in the sub-diffraction limit of about 100 nm using 325 nm wavelength, for the first time. The results are compared with the structural analysis using high resolution transmission microscopic study.Comment: 33 pages, 7 figures, journa

Fishery and resource of green mussel, Perna viridis along the west coast of India

The green mussel, Pema viridis, constitutes a sustenance fishery in India, particularly along the Malabar Coast. The paper deals with the distribution, extent of mussel beds, exploited resources, total stock and the man power employed in the fishery along the Kerala coast from Calicut to Cannanors and Karnataka coast from Bhatkal to Majali. In the Callcut-Cannanore area fishery Is from August to June and the catch is estimated at 3043 t, 3074 t and 2596 t during 1981-82, 1S82-83 and 1983'84, respectively. The mussels tanged in length from 20-129 mm. The total man power employed Is assessed as 685 in the Callcut-Cannanore area, of which 325 are traditional full time mussel divers and the rest are part time mussel divers, The seed resources varied from 4.57 to 6.52 kg/m- In December 1983 and the size of the seeds ranged from 10-40 mm. There is no regular commercial fishery in the Bhatkal-Majall area. The paper also deals with the constraints and prospects for development of the mussel fishery

Survey of green mussel seed resources of Kerala and Karnataka

Farming of marine mussels Is practiced extensively in the temperate and Southeast Asian countries. In India two species of mussels, Perna viridis and Perna indica commonly known as the green and brown mussels respectively have been reported