A Bayesian parameter inference problem is conducted to estimate the explosive yield of the first atomic explosion at Trinity in New Mexico. The first of its kind, the study advances understanding of fireball dynamics and provides an improved method for the determination of explosive yield. Using fireball radius-time data taken from archival film footage of the explosion and a physical model for the expansion characteristics of the resulting fireball, a yield estimate is made. Bayesian results from the Markov chain indicate that the estimated parameters are consistent with previous calculation except for the critical parameter that modifies the independent time variable. This unique result finds that this parameter deviates in a statistically significant way from previous predictions. Use of the Bayesian parameter estimates computed is found to greatly improve the ability of the fireball model to predict the observed data. In addition, parameter correlations are computed from the Markov chain and discussed. As a result, the method used increases basic understanding of fireball dynamics and provides an improved method for the determination of explosive yields.

It has been of concern for the most appropriate control mechanism associated with the growing complexity of dual HIV-HBV infectivity. Moreso, the scientific ineptitude towards an articulated mathematical model for co-infection dynamics and accompanying methodological application of desired chemotherapies inform this present investigation.  Therefore, the uniqueness of this present study is not only ascribed by the quantitative maximization of susceptible state components but opined to an insight into the epidemiological identifiability of dual HIV-HBV infection transmission routes and the methodological application of triple-dual control functions. Using ODEs, the model was formulated as a penultimate 7-Dimensional mathematical dynamic HIV-HBV model, which was then transformed to an optimal control problem, following the introduction of multi-therapies in the presence of dual adaptive immune system and time delay lags. Applying classical Pontryagin’s maximum principle, the system was analyzed, leading to the derivation of the model optimality system and uniqueness of the system. Specifically, following the dual role of the adaptive immune system, which culminated  into triple-dual application of multi-therapies, the investigation was characterized by dual delayed HIV-HBV virions decays from infected double-lymphocytes in a biphasic manner, accompanied by more complex decay profiles of infectious dual HIV-HBV virions. The result further led to significant triphasic maximization of susceptible double-lymphocytes and dual adaptive immune system (cytotoxic T-lymphocytes and humeral immune response) achieved under minimal systemic cost. Therefore, the model is comparatively a monumental and intellectual accomplishment, worthy of emulation for related and future dual infectivity.

A new linear programming-based algorithm has been demonstrated to find the best way for arc routing. In most arc routing problems, the main goal is to minimize the total cost on the lane. To find the minimum cost giving lane, the existing algorithms find the smallest possible sum of weights by ticking the shortest paths [7-12]. The proposed computer-based algorithm is based on focusing the minimized total cost with some constraint criteria of fixed values. The routes are marked with a series of variables that may differ according to the lane choice and more accurately estimates the exact total cost considering the remaining weight. Finally, a stochastic model for a private company vehicle transport has been discussed with some possible solution expectations.

Numerous scheduling algorithms have been developed and implemented in a bid to optimized CPU utilization. However, selecting a scheduling algorithm for real system is still very challenging as most of these algorithms have their peculiarities. In this paper, a comparative analysis of three CPU scheduling algorithms Shortest Job First Non-Preemptive, Dynamic Round-Robin even-odd number quantum Scheduling algorithm and Highest Response-Ratio-Next (HRRN) was carried out using dataset generated using Poisson Distribution. The performance of these algorithms was evaluated in the context of Average Waiting Time (AWT), Average Turnaround Time (ATT). Experimental results showed that Shortest Job First Non-Pre-emptive resulted in minimal AWT and ATT when compared with two other algorithms.

The slow invariant manifold is a unique trajectory of the dynamical system that describes the long-time dynamics of the system’s evolution efficiently. Determining such manifolds is of obvious importance. On one hand they provide a basic insight into the dynamics of the system, on the other hand they allow a reduction of dimension of the system occurs on the invariant manifold only. If the dimension of the invariant manifold is sufficiently low, this reduction may result in substantial savings in computational costs. In this paper, differential geometry based new developed approach called the flow curvature method is considered to analyse the Brusselator model. According to this method, the trajectory curve or flow of any dynamical system of dimension  considers as a curve in Euclidean space of dimension . Then the flow curvature or the curvature of the trajectory curve may be computed analytically. The set of points where the flow curvature is null or empty defines the flow curvature manifold. This manifold connected with the dynamical system of any dimension   directly describes the analytical equation of the slow invariant manifold incorporated with the same dynamical system. In this article, we apply the flow curvature method for the first time on the two-dimensional Brusselator model to compute the analytical equation of the slow invariant manifold where we use the Darboux theorem to prove the invariance property of the slow manifold.