The study of a pair (V 1 , V 2 ) of commuting isometries is a classical theme. We shine new light on it by using the defect operator. In the cases when the defect operator is zero or positive or negative, or the difference of two mutually orthogonal projections adding up to ker(V 1 V 2 ) * , we write down structure theorems forThe structure theorems allow us to compute the joint spectra in each of the cases above. Moreover, in each case, we also point out at which stage of the Koszul complex the exactness breaks. With (V 1 , V 2 ), a pair of operator valued functions φ 1 , φ 2 can be canonically associated. In certain cases, ∪ z∈D σ(φ 1 (z), φ 2 (z)) is the same as σ(V 1 , V 2 ) and in certain cases, it is smaller. All such cases are described.A major contribution of this note is to figure out the fundamental pair of commuting isometries with negative defect. We construct this pair of commuting isometries on the Hardy space of the bidisc (It has been known that the fundamental pair of commuting isometries with positive defect is the pair of multiplication operators by the coordinate functions on the Hardy space of the bidisc).

BACKGROUND:Little information is available about the prevalence of skin conditions among children in the general population in India. Low socioeconomic status, malnutrition, overcrowding and poor standards of hygiene are important factors accounting for the distribution of skin diseases in developing countries such as India. AIM OF THE STUDY: To study prevalence of skin diseases among children presenting to paediatric OPD. METERIALS AND METHODS: A predesigned and pretested questionnaire was used to gather information about socio-demographic profile, personal history, social history and all the children were thoroughly examined by detailed clinical examination depending on signs and symptoms. Suspected cases were subjected to bacterial cultures, KoH examination was done. RESULTS: In the present study, pyoderma was the most common frequent skin disorder accounting to 11.2% followed by Scabies 10.6%, Papular urtricaria 8.8%, Impetigo 6.8% and the least prevalent were Measles 0.8%, Acanthosis nigricans 0.4% and Psoriasis 0.2%. CONCLUSION: In the present study pyoderma, utericaria and scabies were highly prevalent among children's. Personal hygine, health education and periodic deworming measures will prevent majority of skin diseases.