Among the best-known capillarity phenomena is a capillary rise, the understanding of which is essential in fluidics. Some capillary flows rise monotonically whereas others oscillate, but until now no criteria have been formulated for this scenario. In this paper, the Levine's capillary rise modelling is computed numerically, then the critical radius of the capillary tube is formulated by using the dimensional method and data fitting for identification of exponent index. The phase space diagram of capillary velocity versus height is obtained for the first time and shows that the phase transition from oscillating to monotonic rising happens when the phase trajectory decreases exponentially to somewhere other than the "attractor." Two general Maple codes of the problem are provided as an essential part of this paper.

The software design of autonomous vehicles (AVs) incorporates artificial intelligence (AI) characteristics to enhance their safety and overall driving performance. Central to vehicle’s operation is the ability to reason effectively in complex and uncertain environments. However, traditional logical systems, such as monotonic logic, often struggle to handle the inherent uncertainties and exceptions encountered in real-world scenarios. This paper proposes the utilization of non-monotonic logic in order to enhance the reasoning capabilities of autonomous vehicles. By incorporating non-monotonic reasoning, vehicles can navigate intricate traffic scenarios, make plausible inferences, and adapt their decisions when faced with conflicting information. This research aims to provide a comprehensive review of non-monotonic logic's application in autonomous vehicles, highlighting its advantages over traditional logical systems and its potential impact on safety and performance. Additionally, through this research, we seek to contribute to the advancement of autonomous driving technology by enhancing the reasoning capabilities of vehicles in various scenarios, such as car- following related to critical safety events. The personalized cognitive agent is proposed in driving behavior to consider particularly in their assumptions of homogeneous drivers. The personalized cognitive agent is incorporating heterogeneous driving behaviors, based on individual user preferences, characteristics, and needs. Driving behavior is a complex interplay of various factors, encompassing both human and external elements. Human factors, including age, experience, and gender, contribute significantly to how individuals navigate the roads. These factors influence decisions, reactions, and risk-taking tendencies on the part of drivers. Additionally, external factors such as weather conditions further compound this intricate dynamic, requiring drivers to adapt their behavior to the prevailing environment. The goal of a personalized cognitive agent is to provide tailored and customized experiences to cognitive vehicles, taking into account the unique requirements and individual preferences of occupants inside autonomous vehicles.

We analysed changes in magnitude and timing of the largest annual observed daily flow (Amax), in each water year, for 596 stations in high-value water resources catchments and flood risk locations across Australia. These stations are either included in the Bureau of Meteorology's Hydrologic Reference Stations, or used in its operational flood forecasting services. Monotonic trend (which are either consistently increasing or decreasing) analyses of the magnitude and timing of flood peaks (estimated using Amax) were performed using Theil-Sen and Mann-Kendell approach and circular statistics to identify strength of seasonality and timing. Regional significance at the drainage division scale was analysed using the Walker test. Monotonic decreasing trends in Amax flood magnitude were detected in the Murray-Darling River basin and in other drainage divisions in Victoria, south-west and mid-west of Western Australia and South Australia. No significant obvious pattern in Amax magnitude was detected in northern Queensland, coastal NSW, central Australia and Tasmania. Only the Tanami-Timor Sea Coast drainage division in northern Australia showed monotonic increasing trends. Monotonic trends in Amax magnitude were regionally significant at the drainage division scale. We found two distinct patterns in flood seasonality and timing. In the northern and southern parts of Australia, flood peaks generally occur during February to March and August to October, respectively. The strength of this seasonality varies across the country. Weaker seasonality was detected for locations in the Murray-Daring River basin, and stronger seasonality was evident in northern Australia, south-west of Western Australia, South Australia, Victoria and Tasmania. The trends of seasonality and timing reveal that in general, flood peaks are occurring later in the water year in recent years. In northern Australia, flood peaks are generally occurring earlier – at a rate of 12 days/decade. In Victoria, New South Wales and Tasmania, trends in timing are generally mixed. However, in the south-west of Western Australia, the largest change in timing was evident – with Amax peaks commencing later at a rate of 15 days/decade. Decadal variability in flood timing was found at the drainage division scale as well. Most stations show a decreasing trend in Amax magnitude, but how that trend is associated with the change in timing is not clear.

In this paper we survey some recent results due to the author concerning various inequalities and approximations for the finite Hilbert transform of a function belonging to several classes of functions, such as: Lipschitzian, monotonic, convex or with the derivative of bounded variation or absolutely continuous. More accurate estimates in the case that the higher order derivatives are absolutely continuous, are also provided. Some quadrature rules with error bounds are derived. They can be used in the numerical integration of the finite Hilbert transform and, due to the explicit form of the error bounds, enable the user to predict a priory the accuracy.

This paper aims to determine the effect of local corrosion at three different corrosion areas, the 1. entire area, 2. constant moment area, and 3. constant shear area, on the flexural performance of RC beams. To analyze this, an experimental study was carried out to prepare two series of RC beams (200×300×2800mm) created with three different degree of corrosion inducing local rebar corrosion. Furthermore, two-series of experimental tests were conducted under different loading types by monotonic and cyclic loading. It was observed that strength capacity reduction grows in the order of the corroded RC specimens induced: the 1. entire area > 2. constant moment area > 3. constant shear area, as the average corrosion rate increases. Our test results further show that the yield and ultimate strength was kept nearly equivalent to the uncorroded RC specimen by the average corrosion rate of 10% and 15%, respectively. Over these corrosion rates, the yield strength and ultimate strength dropped significantly. Compared to test results under a monotonic loading condition, the structural capacity under a cyclic loading condition decreased with a more pronounced tendency for each corrosion case as the corrosion rate increased. A longitudinal crack was developed throughout and adjacent to the corrosion areas, as the corrosion rate increased. Thus, we can infer that strength reduction may be strongly influenced by this longitudinal crack.

This paper gives a new unified formula for the Newtonian fluids valid for all pipe flow regimes from laminar to the fully rough turbulent. It includes laminar, unstable sharp jump from laminar to turbulent, and all types of the turbulent regimes: smooth turbulent regime, partial non-fully developed turbulent and fully developed rough turbulent regime. The formula follows the inflectional form of curves as suggested in Nikuradse’s experiment rather than monotonic shape proposed by Colebrook and White. The composition of the proposed unified formula consists of switching functions and of the interchangeable formulas for laminar, smooth turbulent and fully rough turbulent flow. The proposed switching functions provide a smooth and a computationally cheap transition among hydraulic regimes. Thus, the here presented formulation represents a coherent hydraulic model suitable for engineering use. The model is compared to existing literature models, and shows smooth and computationally cheap transitions among hydraulic regimes.

In the paper, by virtue of convolution theorem for the Laplace transforms, Bernstein's theorem for completely monotonic functions, and other techniques, the author finds necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic.

In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a Bernstein function and a completely monotonic function respectively, establishes a Lévy-Khintchine representation for the generating function of multivariate logarithmic polynomials, deduces an integral representation for multivariate logarithmic polynomials, presents an integral representation for the reciprocal of the generating function of multivariate logarithmic polynomials, computes real and imaginary parts for the generating function of multivariate logarithmic polynomials, derives two integral formulas, and denies the uniform convergence of a known integral representation for Bernstein functions.

In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem connected with the Stirling numbers of the first and second kinds, construct determinantal and product inequalities for these generalizations with aid of properties of the completely monotonic functions, and derive the logarithmic convexity for the sequence of these generalizations.

In the paper, the author introduces the notions "multi-order logarithmic numbers" and "multi-order logarithmic polynomials", establishes an explicit formula, an identity, and two recurrence relations by virtue of the Faa di Bruno formula and two identities of the Bell polynomials of the second kind in terms of the Stirling numbers of the first and second kinds, and constructs some determinantal inequalities, product inequalities, logarithmic convexity for multi-order logarithmic numbers and polynomials by virtue of some properties of completely monotonic functions.