Pharmaceutical physical form characterisation with fast (>200 °C min<Superscript>−1</Superscript>) DSC heating rates

Differential scanning calorimetry (DSC) has many applications during preformulation screening of new drug candidates, but definitive assignment of peaks to specific events in the sample is difficult without supplementary data from other techniques. To some extent these problems can be overcome by running multiple experiments at different heating rates. Typically 2 and 20 °C min⁻¹ are indicated. However, modern instruments are capable of achieving much faster heating rates (up to 750 °C commercially); with this extended range comes a new capacity for investigating the physical form of materials. Here, the use of fast DSC heating rates for materials characterisation is explored, focussing on determination of melting temperatures, glass formation and polymorph screening.     

Computation of the Delta in Multidimensional Jump-Diffusion Setting with Applications to Stochastic Volatility Models

We study the robustness of options prices to model variation in a multidimensional jump-diffusion framework. In particular, we consider price dynamics in which small variations are modeled either by a Poisson random measure with infinite activity or by a Brownian motion. We consider both European and Exotic options and we study their deltas using two approaches: the Malliavin method and the Fourier method. We prove robustness of the deltas to model variation. We apply these results to the study of stochastic volatility models for the underlying and the corresponding options.     

Eigenvalues of the Laplacian and extrinsic geometry

We extend the results given by Colbois, Dryden and El Soufi on the relationships between the eigenvalues of the Laplacian and an extrinsic invariant called intersection index, in two directions. First, we replace this intersection index by invariants of the same nature which are stable under small perturbations. Second, we consider complex submanifolds of the complex projective space $\mathbb C P^N$ instead of submanifolds of $\mathbb R ^N$ and we obtain an eigenvalue upper bound depending only on the dimension of the submanifold which is sharp for the first non-zero eigenvalue.     

Application of tracer technique in remediation of Sr(II) from simulated low level radioactive waste

Journal of Radioanalytical and Nuclear Chemistry - Activity concentrations of natural (40K, 226Ra, 228Ra, 232Th, 238U) and artificial (134Cs, 137Cs) radionuclides were measured in powdered milk...     

Commuting Values of Generalized Derivations on Multilinear Polynomials

Let K be a commutative ring with unity, R a prime K-algebra of characteristic different from 2, U the right Utumi quotient ring of R, f(x ₁,…, x _n ) a noncentral multilinear polynomial over K, and G a nonzero generalized derivation of R. Denote f(R) the set of all evaluations of the polynomial f(x ₁,…, x _n ) in R. If [G(u)u, G(v)v] = 0, for any u, v ∈ f(R), we prove that there exists c ∈ U such that G(x) = cx, for all x ∈ R and one of the following holds: 1. f(x ₁,…, x _n )² is central valued on R;

2. R satisfies s ₄, the standard identity of degree 4.

     

Empirical Interpolation Decomposition

The Kantorovich metric provides a way of measuring the distance between two Borel probability measures on a metric space. This metric has a broad range of applications from bioinformatics to image processing, and is commonly linked to the optimal transport problem in computer science (Deng and Du in Electron. Notes Theor. Comput. Sci. 253: 73–82, 2009; Villani in Optimal Transport: Old and New, Grundlehren der mathematischen Wissenschaften, vol. 338, 2009). Noteworthy to this paper will be the role of the Kantorovich metric in the study of iterated function systems, which are families of contractive mappings on a complete metric space. When the underlying metric space is compact, it is well known that the space of Borel probability measures on this metric space, equipped with the Kantorovich metric, constitutes a compact, and thus complete metric space. In previous work, we generalized the Kantorovich metric to operator-valued measures for a compact underlying metric space, and applied this generalized metric to the setting of iterated function systems (Davison in Acta Appl. Math., 2014, https://doi.org/10.1007/s10440-014-9976-y; Generalizing the Kantorovich Metric to Projection-Valued Measures: With an Application to Iterated Function Systems, 2015; Acta Appl. Math., 2018, https://doi.org/10.1007/s10440-018-0161-6). We note that the work of P. Jorgensen, K. Shuman, and K. Kornelson provided the framework for our application to this setting (Jorgensen in Adv. Appl. Math. 34(3):561–590, 2005; Jorgenson et al. in J. Math. Phys. 48(8):083511, 2007; Jorgensen in Operator Theory, Operator Algebras, and Applications, Contemp. Math., vol. 414, pp. 13–26, 2006). The situation when the underlying metric space is complete, but not necessarily compact, has been studied by A. Kravchenko (Sib. Math. J. 47(1), 68–76, 2006). In this paper, we extend the results of Kravchenko to the generalized Kantorovich metric on operator-valued measures.

     

A Study on Oscillatory and Asymptotic Nature of Impulsive Neutral Differential Equations of Order Three

In this paper, we consider a class of third-order neutral impulsive differential equations. An equivalent class of neutral differential equations is obtained by using a suitable substitution. Some new oscillation results are proved. Moreover, we discuss the asymptotic behavior of the solution. The results presented here are illustrated via examples.     

A Kalman particle filter for online parameter estimation with applications to affine models

Statistical Inference for Stochastic Processes - In this paper we address the problem of estimating the posterior distribution of the static parameters of a continuous-time state space model with...     

Laser Induced Surface Morphology of Molybdenum Correlated with Breakdown Spectroscopy

Surface modifications of laser irradiated molybdenum have been correlated with plasma parameters. Nd:YAG laser (1064 nm, 10 ns) was employed at various laser irradiances ranging from 6 to 50 GW/cm² under argon environment. The ablation efficiency has been investigated by measuring the crater depth using surface profilometry analysis. Scanning electron microscope (SEM) analysis reveals the formation of coarse grains along with cracked boundaries, cavities and cones at the central ablated areas. Whereas, uplifted re-solidified material, cavities, ridges, droplets and cones were observed at boundary regions. Laser Induced Breakdown Spectroscopy (LIBS) analysis has been performed to evaluate electron temperature and number density of molybdenum plasma. Electron temperature and electron density varies from 6670 to 9305 K and 0.62 × 10¹⁸ to 0.72 × 10¹⁸ cm^?3 respectively. Both the parameters showed similar trend in variation with laser irradiance i.e. an initial increase from 13 to 19 GW/cm² followed by a decrease from 19 to 25 GW/cm² and then a saturation from 25 to 50 GW/cm². The initial increasing trend is attributed to the enhanced excited vapor content of the ablated material, confinement effects of the surrounding argon and absorption of laser energy into the molybdenum vapor plasma during the trailing part of laser pulse leading to ignition of laser supported combustion (LSW) waves. The decreasing trend is attributed to the shielding effect and saturation is explainable on the basis of the formation of a self-regulating regime. Surface modifications of laser irradiated molybdenum were correlated with the plasma parameters.