Impacts of TV and radio advertisements on the dynamics of an infectious disease: A modeling study

TV and radio advertisements are widely acknowledged as important interventions in raising issues of public health care and play promising role to control the infection through propagating awareness among the individuals. In this paper, a nonlinear susceptible‐infected‐susceptible (SIS) model is proposed and analyzed to see the impacts of TV and radio advertisements on the spread of influenza epidemic. In the model formulation, it is assumed that the susceptible individuals contract infection through the direct contact with infected individuals. The information regarding the protection against the disease is propagated via TV and radio advertisements, and their growth rates are assumed to be proportional to the fraction of infected individuals. However, the growth rate of TV advertisements decreases with the increase in number of aware individuals. The information broadcasted through TV and radio advertisements induces behavioral changes among the susceptible individuals, and they form an isolated aware class. The epidemiological feasible equilibria, their stability properties, and direction of bifurcation are discussed. The expression for modified basic reproduction number is obtained. The model analysis shows that the dissemination rate of awareness among susceptible individuals due to TV and radio advertisements and baseline number of TV and radio advertisements have potential to reduce the epidemic peak and, thus, control the spread of infection. Further, the analytical findings are well supported through numerical simulation.     

On unbounded subnormal operators

A minimal normal extension of unbounded subnormal operators is established and characterized and spectral inclusion theorem is proved. An inverse Cayley transform is constructed to obtain a closed unbounded subnormal operator from a bounded one. Two classes of unbounded subnormals viz analytic Toeplitz operators and Bergman operators are exhibited.     

Secure optical system that uses fully phase-based encryption and lithium niobate crystal as phase contrast filter for decryption

In this paper, the implementation of a secure optical system using fully phase encryption is described. A two-dimensional phase image obtained from an amplitude image is encrypted and decrypted by using a spatial light modulator working in phase mode. The fully phase encryption is achieved using double random phase encoding. The encrypted image is holographically recorded in a photorefractive crystal and is then decrypted by generating, through phase conjugation, the conjugate of the encrypted image. A lithium niobate crystal has been used as a phase contrast filter to change the decrypted phase image into an amplitude image, thus alleviating the need for alignment of the phase contrast set-up in the Fourier plane. Simulation results are provided to verify the proposed study. The mean square error between the primary image and decrypted image has been calculated to study the sensitivity of the system.     

Mixed Ligand Complexes of Chromium (III) Ethylenediamine Tartrate: A Polarographic Study

Polarographic techniques have been used to investigate the complexing behaviour of chromium (III)-ethylenediamine-tartrate in aqueous solution. These complexes are reduced irreversibly at the dropping mercury electrode. The stability constants have been calculated by the method of Sundaresan and Sundaram. The values of the kinetic parameters; standard rate constant (K_s), transfer coefficient (α) and activation energy (Q) have also been calculated in each case.     

Polarization switching properties of spray deposited CsNO3: PVA composite films

The ferroelectric and switching properties of spray deposited cesium nitrate: poly (vinyl alcohol) composite films at different substrate temperatures (T _s ) have been studied. The optimum value of remanent polarization was obtained in the film deposited at T _s =200°C, which may be due to larger structural distortion (c/a ratio) and less porosity as revealed by x-ray diffraction and field emission scanning electron microscope (FESEM) analysis. The switching current transients have been analyzed by nucleation limited switching model (NLS) with the Lorentzian distribution function. This model gives excellent agreement with the experimental polarization current throughout the whole time range. The switching parameters were determined in the composite films deposited at different T _s and found to be optimum at T _s =200°C. The effect of pulse amplitude on the domain switching properties has also been studied and analyzed. The peak value of polarization current exhibits an exponential dependence on the external applied field.     

XANES of the AuLIII edge in gold metal and in two compounds AuCN and AuCl3

The X-ray Absorption Near Edge Structure (XANES) of the AuL_III edge in gold metal and in its two compounds AuCN and AuCl₃ have been recorded. The observed chemical shifts of the edge and the fine structure peaks in the compounds are discussed. It is observed that the energy shifts ΔE of the AuL_III due to chemical effects in aurous cyanide (AuCN) and auric chloride (AuCl₃) with respect to the pure Au edge is 2.9 eV in AuCN and 0.7eV in AuCl₃. The edge widths in AuCN and AuCl₃ are found to be almost the same for both the compounds, presumably because electronegativities of CN and Cl are not very different. The observed fine structure peaks of the discontinuities of AuCN and AuCl₃ are displaced progressively away from the main edge.     

Efficient Krylov subspace methods for uncertainty quantification in large Bayesian linear inverse problems

Uncertainty quantification for linear inverse problems remains a challenging task, especially for problems with a very large number of unknown parameters (e.g., dynamic inverse problems) and for problems where computation of the square root and inverse of the prior covariance matrix are not feasible. This work exploits Krylov subspace methods to develop and analyze new techniques for large‐scale uncertainty quantification in inverse problems. In this work, we assume that generalized Golub‐Kahan‐based methods have been used to compute an estimate of the solution, and we describe efficient methods to explore the posterior distribution. In particular, we use the generalized Golub‐Kahan bidiagonalization to derive an approximation of the posterior covariance matrix, and we provide theoretical results that quantify the accuracy of the approximate posterior covariance matrix and of the resulting posterior distribution. Then, we describe efficient methods that use the approximation to compute measures of uncertainty, including the Kullback‐Liebler divergence. We present two methods that use the preconditioned Lanczos algorithm to efficiently generate samples from the posterior distribution. Numerical examples from dynamic photoacoustic tomography demonstrate the effectiveness of the described approaches.