Nonrough norms in spaces with small diameter

In this work, we study the non rough norms in Banach spaces with small diameter properties, namely the Ball Dentable Property (BDP), the Ball Huskable Property (BHP) and the Ball Small Combination of Slice Property (BSCSP). We introduce two more notions of non rough norms, namely the weakly average non rough norms and average non rough norms in Banach spaces. We prove the duality between these three versions of non rough norms and the small diameter properties in Banach spaces. We also prove that each of the three non rough norms is a three space property under certain assumptions

Two aspects of small diameter properties

In this short note, we study two different geometrical aspects of Banach spaces with small diameter properties, namely the Ball Dentable Property (BDP), Ball Huskable Property (BHP) and Ball Small Combination of slice Property (BSCSP). We show that BDP, BHP and BSCSP are separably determined properties. We also explore the stability of these properties over Kothe Bochner spaces

Nonrough norms in Lipschitz free spaces

In this paper we characterise nonrough norms of Lipschitz free spaces F(M) in terms of a new geometric property of the underlying metric space M

A characterization of dentability via ball separation properties in Banach spaces

In this work, we study ball separation property of Banach spaces. We characterize geometric properties Ball Dentable Property (BDP), Ball Huskable Property (BHP) and their w* versions in terms of ball separation in Banach spaces. We also obtain a necessary condition for a space with Ball Small Comination of Slice Property (BSCSP) in terms of ball separation. We also obtain a necessary and sufficient condition for a Banach space X having property (II), that characterizes every element in S_X* . Motivating from definitions of A -denting point and A -poin of continuity in [4], we introduce the notion of A -small combination of slice point, and obtain a necessary ball separation condition for the existence of A -small combination of slice point that provide us an improvement of the result [1, Proposition 2.5]. We prove that if the linear span of A -small combination of slice points of B_X* is {\tau} A -dense in X* , then every closed bounded convex subset in A is ball generated. We end up this note by introducing w* semi pc in B_X* and we prove that a Banach space X has property (II) if and only if every point in S_X* is w* semi pc of B_X*

Socio-Demographic and Clinical Profile of Drug Resistant Tuberculosis Patients in a Tertiary Care Centre of Kolkata

Background: Drug resistant tuberculosis is a major public health threat that hinders progress in tuberculosis control worldwide. In 2019, India contributed highest cases of TB (27%) Worldwide. In 2019, 3.3% of new TB cases and 18% of previously treated cases had MDR/RRTB worldwide and India (27%) had the largest share of the global burden. This study was done to find out the sociodemographic and clinical profile of drug resistant TB patients. Methodology: It is an observational descriptive study with cross-sectional design, conducted at the drug resistant tuberculosis centre of R. G. Kar Medical College of Kolkata, West Bengal. Study Population consisted of the patients who were registered for the DR-TB regimen. Study duration was July 2016 –March 2017. Pre-tested, semi-structured schedule was designed to capture their sociodemographic profile, treatment history, clinical findings and available medical records. Data were compiled in MS Excel and analyzed in IBM SPSS 23.0. Results: Out of 159 cases, 27% patients were between 21-30 years. Males were predominant (68.6%). Most patients (56.6%) were underweight (BMI<18.5kg/m2). HIV seropositivity was found in 4 (2.5%) cases. Among all cases, 81.1% had history of taking ATD and 34.4% was cured in previous episode of treatment. The commonest associated comorbidity was DM (15.7%). Rifampicin resistance (93.1%) was most common followed by Isoniazid (8.2%). Pallor was found among 94.3% patients. Most patients had bilateral (62.3%) and moderately extensive (57.2%) lesions in chest x-ray. Conclusion: DR-TB control should focus adequately on younger age group as numbers of resistance is increasing among them. Relapse in previously cured cases was found to be major contributor of DR-TB suspect cases. Though, Rifampicin resistance was so common but prevalence of resistance to 2nd line drugs is still low. Focus should be given on early detection of drug resistance in all TB cases and improvement of nutritional status of the TB patient

Remnant vegetation in farmland - its significance in ethnobotany and local ecosystem

This paper evaluated the structure of remnant vegetation (RV) in and around the farmlands of Kancheepuram District, Tamil Nadu of Southern India, to understand its significance in the local ecosystem. Stratified quadrats along nine randomly selected transects were used for sampling vegetation. The study recorded 2495 specimens of 96 plant species under 43 families in 1848 quadrats (88 of 10 m × 10 m, 352 of 5 m × 5 m and 1408 of 1 m × 1 m dimensions) while there was a possibility of recording more species with better sampling efforts. To know the ethnobotanical uses of plants, interviews were conducted with local villagers and people belonging to the Irula tribe, and later the data were collated with published information. Sixty -six plant species were recorded with traditional uses in food, fodder, fuel, condiment and medicine. Prosopis juliflora, an alien invasive species, was a serious threat to the native flora since higher P. juliflora abundance was associated with declining diversity of other plants. The study found that the absence of monitoring and management protocols leading to uncontrolled propagation of invasive species could cause potential damage to the region’s dry evergreen forests, which were often located near the farmlands