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Jensen's inequality, with its broad applications across various fields, presents an important subject for investigation and research. In this article, we introduce novel enhancements to Jensen's inequality by utilizing the convexity properties of a thrice differentiable function in the absolute sense. We conducted numerical experiments to compare our primary results with previously established findings. Additionally, we provided several applications of our major results to classical inequalities, means, and divergences.

The Jensen inequality is of fundamental importance because of its influential and interesting consequences. In recent years, the Jensen inequality has been supposed to be the most engaging source for research. We present interesting improvements to the continuous version of Jensen's inequality through the application of the concept of 6-convexity. For real visualization and comparison to other results, some numerical experiments were provided. With the aid of the acquired results, improvements for the Hermite-Hadamard and Hölder inequalities were presented. Some relationships between the means were granted as applications of established improvements. In addition, some estimations of the Csiszár divergence and its associated cases were received as further applications of the obtained results. The major techniques employed in formulating the proposed improvements included the Jensen inequality and the concept of convexity.

Thermal decomposition experiment of 5-(4-Pyridyl)tetrazolate (H4-PTZ) was carried out. The heat flow curve and reaction rate data under different heating rates were obtained. The characteristic parameters were obtained. The apparent activation energy for each individual reaction was calculated by applying different methods. On this basis, the Malek method was used to predict the most probable mechanism function of thermal decomposition reaction of H4-PTZ. The thermal safety parameters, including self-accelerating decomposition temperature, hot spot fire temperature and thermal explosion critical temperature were also predicted. The activation enthalpy, activation entropy, and activation Gibbs free energy of H4-PTZ are calculated. Gaussian16 program was used to optimize the molecular structure, search the transition state and calculate the intrinsic reaction coordinates of H4-PTZ. The most probable decomposition path of H4-PTZ was found, and the activation energy calculated by experiment was compared with that calculated by the theory.

Fractional calculus has been a concept used to acquire new variants of some well-known integral inequalities. In this study, our primary goal is to develop majorized fractional Simpson’s type estimates by employing a differentiable function. Practicing majorization theory, we formulate a new auxiliary identity by utilizing fractional integral operators. In order to obtain new bounds, we employ the idea of convex functions on the Niezgoda–Jensen–Mercer inequality for majorized tuples, along with some fundamental inequalities including the Hölder, power mean, and Young inequalities. Some applications to the quadrature rule and examples for special functions are provided as well. Interestingly, the main findings are the generalizations of many known results in the existing literature.

Abstract Current efforts of modelling COVID-19 are often based on the standard compartmental models such as SEIR and their variations. As pre-symptomatic and asymptomatic cases can spread the disease between populations through travel, it is important to incorporate mobility between populations into the epidemiological modelling. In this work, we propose to modify the commonly-used SEIR model to account for the dynamic flight network, by estimating the imported cases based on the air traffic volume and the test positive rate. We conduct a case study based on data found in Canada to demonstrate how this modification, called Flight-SEIR, can potentially enable (1) early detection of outbreaks due to imported pre-symptomatic and asymptomatic cases, (2) more accurate estimation of the reproduction number and (3) evaluation of the impact of travel restrictions and the implications of lifting these measures. The proposed Flight-SEIR is essential in navigating through this pandemic and the next ones, given how interconnected our world has become.

In traditional 3D NAND design, peripheral circuit accounts for 20-30% of the chip real-estate, which reduces the memory density of flash memory. As 3D NAND technology stacks to 128 layers or higher, peripheral circuits may account for more than 50% of the overall chip area. On the contrast, the XtackingTM technology arranges array and logic parts on two different wafers, and connects the memory arrays to the logic circuit by metal VIAs (Vertical Interconnect Accesses) to achieve unprecedented high storage density as well as DRAM level I/O speed. As a consequence, it becomes increasingly significant to monitor metal VIAs depth before wafer bonding process as to ensure reliability of array-logic connections. Currently, AFM (Atom Force Microscopy) is the main stream method of VIA depth monitoring. Apparently, AFM wins the battle of precision, however the low throughput limited its usage in mass production. In order to accomplish the requirement of VLSI production, a WLI (White Light Interference) metrology is revisited and a novel WLI method was developed to monitor VIAs depth. Basically there are two major limitations that keep WLI tools from wider use, transparent film impact and diffraction limitation. In this work, the engineering solutions are illustrated and inline dishing measurement is achieved with high accuracy and precision.

The Jensen inequality is of fundamental importance because of its influential and interesting consequences. In recent years, the Jensen inequality has been supposed to be the most engaging source for research. We present interesting improvements to the continuous version of Jensen's inequality through the application of the concept of 6-convexity. For real visualization and comparison to other results, some numerical experiments were provided. With the aid of the acquired results, improvements for the Hermite-Hadamard and Hölder inequalities were presented. Some relationships between the means were granted as applications of established improvements. In addition, some estimations of the Csiszár divergence and its associated cases were received as further applications of the obtained results. The major techniques employed in formulating the proposed improvements included the Jensen inequality and the concept of convexity. [ABSTRACT FROM AUTHOR]

Thermal decomposition experiment of 5-(4-Pyridyl)tetrazolate (H4-PTZ) was carried out. The heat flow curve and reaction rate data under different heating rates were obtained. The characteristic parameters were obtained. The apparent activation energy for each individual reaction was calculated by applying different methods. On this basis, the Malek method was used to predict the most probable mechanism function of thermal decomposition reaction of H4-PTZ. The thermal safety parameters, including self-accelerating decomposition temperature, hot spot fire temperature and thermal explosion critical temperature were also predicted. The activation enthalpy, activation entropy, and activation Gibbs free energy of H4-PTZ are calculated. Gaussian16 program was used to optimize the molecular structure, search the transition state and calculate the intrinsic reaction coordinates of H4-PTZ. The most probable decomposition path of H4-PTZ was found, and the activation energy calculated by experiment was compared with that calculated by the theory. [ABSTRACT FROM AUTHOR]