A Study of Rating Curve and Flood Routing using Numerical Method

The stage discharge curve, depth-averaged velocity and boundary shear stress distributions are essentially determined for the flood extenuation scheme. The difficulties aroused in prediction of these parameters are usually due to the 3D nature of the fluid flow in open channel. The current study represents different analytical model for velocity distribution, boundary shear stress and stage-discharge curves and their application to the trapezoidal compound channel. The analytical solution to the depth-integrated Navier-Stokes equation is used for the same and their results are validated using experimental data. These parameters are not easy to predict because of the three-dimensional characteristics of the flow field. The model proposed by Shiono and Knight (1988, 1991) is compared with those by Ervine et al. (2000), Kordi et al. (2015) and K-ε model (ANSYS) through numerical modelling. This test shows that secondary flow parameter plays a vital role and its significance proliferates near side slope where momentum transfer from the main channel to flood plain is observed. The contrast in the results are shown with the help of lateral variation in percentage error. The flood routing is an important technique to determine the flood peak attenuation and the duration of the high water levels through channel routing. Beside stage-discharge curve, hydrographs also plays a vital role in flood prediction and forecasting. The present study shows the application of hydrological methods for channel routing, the constant coefficient Muskingum-Cunge (MC) methods on the River Brosna, Co. Offaly in Ireland. The results obtained are validated by two software packages MIKE 11 and HEC-RAS beside that the method ensuring the mass balance of the model is tested in terms of water storage. The results of all the tests are plotted and verified with respect to the mass conservation criteria. Data sets of the River Brosna, Co. Offaly in Ireland is taken from the Elbashir (2011) for the November 1994 flood event

Positivity preservers forbidden to operate on diagonal blocks

The question of which functions acting entrywise preserve positive semidefiniteness has a long history, beginning with the Schur product theorem [Crelle 1911], which implies that absolutely monotonic functions (i.e., power series with nonnegative coefficients) preserve positivity on matrices of all dimensions. A famous result of Schoenberg and of Rudin [Duke Math. J. 1942, 1959] shows the converse: there are no other such functions. Motivated by modern applications, Guillot and Rajaratnam [Trans. Amer. Math. Soc. 2015] classified the entrywise positivity preservers in all dimensions, which act only on the off-diagonal entries. These two results are at "opposite ends", and in both cases the preservers have to be absolutely monotonic. We complete the classification of positivity preservers that act entrywise except on specified "diagonal/principal blocks", in every case other than the two above. (In fact we achieve this in a more general framework.) This yields the first examples of dimension-free entrywise positivity preservers - with certain forbidden principal blocks - that are not absolutely monotonic.Comment: Minor edits in exposition, 19 pages. The paper now uses the style file of Trans. AMS (to appear

Intermediate uveitis as an initial presentation of HLA B27 associated spondyloarthropathy in an adolescent boy: A rare case report and review of literature

Juvenile ankylosing spondylitis is less prevalent in children, and usually, children are presented to the hospital with chronic inflammatory back pain, enthesitis, and often hip and shoulder joint involvement. A significant proportion of these children develop ocular complications such as anterior and intermediate uveitis. Most of these children have HLA B27 positivity. On the other hand, in cases with anterior and intermediate uveitis, a considerable proportion has positivity for HLA B27 antigen. Few of these patients, later on, develop other clinical features suggestive of ankylosing spondylitis. However, there are only a few anecdotal case reports of similar HLA B27 associated intermediate uveitis, who later on developed juvenile ankylosing spondylitis. The current case is a 12-year old boy, who initially had bilateral intermediate uveitis with HLA B27 positivity without any other systemic or musculoskeletal features. However, on follow-up he developed enthesis and sacroiliitis suggestive of ankylosing spondylitis. Both rheumatological and visual complains had an excellent clinical response to corticosteroids in this child. The current case report demonstrates the importance of evaluation for HLA B27 positivity in all children with isolated intermediate uveitis, even if systemic and musculoskeletal examinations are normal

Coarse-Grained Configurational Polymer Fingerprints for Property Prediction using Machine Learning

In this work, we present a method to generate a configurational level fingerprint for polymers using the Bead-Spring-Model. Unlike some of the previous fingerprinting approaches that employ monomer-level information where atomistic descriptors are computed using quantum chemistry calculations, this approach incorporates configurational information from a coarse-grained model of a long polymer chain. The proposed approach may be advantageous for the study of behavior resulting from large molecular weights. To create this fingerprint, we make use of two kinds of descriptors. First, we calculate certain geometric descriptors like Re2, Rg2 etc. and label them as Calculated Descriptors. Second, we generate a set of data-driven descriptors using an unsupervised autoencoder model and call them Learnt Descriptors. Using a combination of both of them, we are able to learn mappings from the structure to various properties of the polymer chain by training ML models. We test our fingerprint to predict the probability of occurrence of a configuration at equilibrium, which is approximated by a simple linear relationship between the instantaneous internal energy and equilibrium average internal energy

Pl\"ucker inequalities for weakly separated coordinates in totally nonnegative Grassmannian

We show that the partial sums of the long Pl\"ucker relations for pairs of weakly separated Pl\"ucker coordinates oscillate around $0$ on the totally nonnegative part of the Grassmannian. Our result subsumes the classical oscillating inequalities by Gantmacher--Krein (1941) and recent results on totally nonnegative matrix inequalities by Fallat--Vishwakarma (2023). In fact we obtain a characterization of weak separability, by showing that no other pair of Pl\"ucker coordinates satisfies this property.Comment: Updated the main theorem by reformulating the original claim and adding a converse result. Significant changes to the exposition. 19 pages, 20 figure

Effect of frequent hand washing for COVID-19 prevention

Background: Coronavirus disease 2019 (COVID-19) has become a global public health concern. While dealing with COVID-19 pandemic, hand washing and the use of hand-hygiene products has been advocated, as a preventive measure. However, frequent hand washing leads to an increased risk of skin changes ranging from dryness and peeling of skin to itching, redness and blister formation. This study aims to understand the hand-hygiene practices and compare side effects between group using hand sanitizers with the group using soap with water.Methods: A 12-item self-administered close ended questionnaire assessing the hand washing habits and effect of the same on skin was used. A total of 60 cases were enrolled. The correlation between use of hand hygiene measures and the clinical changes was studied.Results: In our study, 32 out of the 60 reported a frequency of hand washing between 5-10 times a day. The awareness about using hand moisturizer was noted in 75% individuals. Side effects were more commonly observed in group B using alcohol-based sanitizers as compared to group A using soap with water. Dryness was the most common symptom, observed in 23.3% individuals using alcohol-based sanitizers and 10% individuals using soap with water.Conclusions: Hand-hygiene measures remain the cornerstone of prevention of COVID-19 transmission. However, the use of hand-hygiene products is associated with side effects especially dryness. Regular use of hand moisturizer is essential in preventing the unnecessary effects of frequent hand washing