Solutions for certain classes of Riccati differential equation

We derive some analytic closed-form solutions for a class of Riccati equation y'(x)-\lambda_0(x)y(x)\pm y^2(x)=\pm s_0(x), where \lambda_0(x), s_0(x) are C^{\infty}-functions. We show that if \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1} and s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1}, n=1,2,..., then The Riccati equation has a solution given by y(x)=\mp s_{n-1}(x)/\lambda_{n-1}(x). Extension to the generalized Riccati equation y'(x)+P(x)y(x)+Q(x)y^2(x)=R(x) is also investigated.Comment: 10 page

Column adsorption studies for the removal of U by phosphonated cross-linked polyethylenimine: modelling and optimization.

A continuous fixed-bed adsorption study was carried out by using phosphonated cross-linked polyethylenimine as an adsorbent for the removal of uranium (U) from aqueous solutions. The effect of inlet metal ion concentration (40, 70, and 100 mg L-1), feed flow rate (1, 2, and 3 mL min(-1)), and polymer bed height (2.5, 3.2 and 4.5 cm) on the breakthrough characteristics of the fixed-bed adsorption system at pH 2 were studied. The results showed that the breakthrough time appeared to increase with increase of bed height but decreased with increase of both influent U concentration and flow rate. Modelling of the dynamics of the fixed-bed adsorption process was studied and the application of different models to describe the breakthrough curves showed that the Thomas and Yoon-Nelson model gave better results for the operating conditions.SP201

Solvable Systems of Linear Differential Equations

The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear differential equations. The termination criteria of AIM will be re-examined and the whole theory is re-worked in order to fit this new application. As a result of our investigation, an interesting connection between the solution of linear systems and the solution of Riccati equations is established. Further, new classes of exactly solvable systems of linear differential equations with variable coefficients are obtained. The method discussed allow to construct many solvable classes through a simple procedure.Comment: 13 page

Effects of restoring portal flow with anticoagulation and partial splenorenal shunt embolization

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/110757/1/hep27241.pd

Green's function for a Schroedinger operator and some related summation formulas

Summation formulas are obtained for products of associated Lagurre polynomials by means of the Green's function K for the Hamiltonian H = -{d^2\over dx^2} + x^2 + Ax^{-2}, A > 0. K is constructed by an application of a Mercer type theorem that arises in connection with integral equations. The new approach introduced in this paper may be useful for the construction of wider classes of generating function.Comment: 14 page

Spectral characteristics for a spherically confined -1/r + br^2 potential

We consider the analytical properties of the eigenspectrum generated by a class of central potentials given by V(r) = -a/r + br^2, b>0. In particular, scaling, monotonicity, and energy bounds are discussed. The potential $V(r)$ is considered both in all space, and under the condition of spherical confinement inside an impenetrable spherical boundary of radius R. With the aid of the asymptotic iteration method, several exact analytic results are obtained which exhibit the parametric dependence of energy on a, b, and R, under certain constraints. More general spectral characteristics are identified by use of a combination of analytical properties and accurate numerical calculations of the energies, obtained by both the generalized pseudo-spectral method, and the asymptotic iteration method. The experimental significance of the results for both the free and confined potential V(r) cases are discussed.Comment: 16 pages, 4 figure

Transfer Learning with Deep Convolutional Neural Network (CNN) for Pneumonia Detection using Chest X-ray

Pneumonia is a life-threatening disease, which occurs in the lungs caused by either bacterial or viral infection. It can be life-endangering if not acted upon in the right time and thus an early diagnosis of pneumonia is vital. The aim of this paper is to automatically detect bacterial and viral pneumonia using digital x-ray images. It provides a detailed report on advances made in making accurate detection of pneumonia and then presents the methodology adopted by the authors. Four different pre-trained deep Convolutional Neural Network (CNN)- AlexNet, ResNet18, DenseNet201, and SqueezeNet were used for transfer learning. 5247 Bacterial, viral and normal chest x-rays images underwent preprocessing techniques and the modified images were trained for the transfer learning based classification task. In this work, the authors have reported three schemes of classifications: normal vs pneumonia, bacterial vs viral pneumonia and normal, bacterial and viral pneumonia. The classification accuracy of normal and pneumonia images, bacterial and viral pneumonia images, and normal, bacterial and viral pneumonia were 98%, 95%, and 93.3% respectively. This is the highest accuracy in any scheme than the accuracies reported in the literature. Therefore, the proposed study can be useful in faster-diagnosing pneumonia by the radiologist and can help in the fast airport screening of pneumonia patients.Comment: 13 Figures, 5 tables. arXiv admin note: text overlap with arXiv:2003.1314