Characterization of Probability Distributions via Functional Equations of Power-Mixture Type

We study power-mixture type functional equations in terms of Laplace–Stieltjes transforms of probability distributions on the right half-line [0,∞). These equations arise when studying distributional equations of the type Z=dX+TZ, where the random variable T≥0 has known distribution, while the distribution of the random variable Z≥0 is a transformation of that of X≥0, and we want to find the distribution of X. We provide necessary and sufficient conditions for such functional equations to have unique solutions. The uniqueness is equivalent to a characterization property of a probability distribution. We present results that are either new or extend and improve previous results about functional equations of compound-exponential and compound-Poisson types. In particular, we give another affirmative answer to a question posed by J. Pitman and M. Yor in 2003. We provide explicit illustrative examples and deal with related topics.

A Dynamic Failure Time Degradation-Based Model

A novel methodology for modelling time to failure of systems under a degradation process is proposed. Considering the method degradation may have influenced the failure of the system under the setup of the model several implied lifetime distributions are outlined. Hazard rate and mean residual lifetime of the model are obtained and a numerical situation is delineated to calculate their amounts. The problem of modelling the amount of degradation at the failure time is also considered. Two monotonic aging properties of the model is secured and a characterization property of the symmetric degradation models is established.

Green Synthesis of Zinc based Nanoparticles for Thermal Industry based Applications

Spinel ZnAl2O4 nanoparticles were prepared effectively by simplistic, economical microwave heating method using Hibiscus rosa-sinensis extract as reducing agent. The samples were successfully characterized by XRD pattern, EDX spectra, FT-IR analysis, HR-SEM analysis, and VSM instrumentation techniques. XRD, EDX and FT-IR results demonstrated that the products contain a pure single-phase spinel structure lacking of other secondary phase impurities. SEM results confirmed the spherical shaped nanoparticle morphology of the sample. Magnetic characterization property was confirmed by VSM analysis. VSM hysteresis loop established the superparamegnetism of the sample and the magnetization (Ms) value of ZnAl2O4 is 0.023 emu/g.

Traversing the profile of biomimetically nanoengineered iron substituted hydroxyapatite: synthesis, characterization, property evaluation, and drug release modeling

Heuristic picture connoting the green synthesis of iron substituted hydroxyapatite nanoparticles having versatile properties.

A Study of Cho-Kwon-Srivastava Operator with Applications to Generalized Hypergeometric Functions

We introduce a new class of meromorphically analytic functions, which is defined by means of a Hadamard product (or convolution) involving some suitably normalized meromorphically functions related to Cho-Kwon-Srivastava operator. A characterization property giving the coefficient bounds is obtained for this class of functions. The other related properties, which are investigated in this paper, include distortion and the radii of starlikeness and convexity. We also consider several applications of our main results to generalized hypergeometric functions.