Directory

The Receiver Operating Characteristic (ROC) curve graphically represents the relationship between sensitivity and 1-specificity at various threshold values. It allows us to visualize the trade-off between correctly identifying true positives and true negatives, providing a comprehensive evaluation of a diagnostic test’s performance. The area under the ROC curve (AUC) quantifies the overall accuracy of the…

The equations for S curves, such as the logistic and Gompertz functions, describe growth processes using five variables: growth rate, carrying capacity, time, initial population, and inflection point. The logistic function models symmetrical growth, while the Gompertz function captures asymmetrical growth. The derivatives of these functions determine the shape and rate of change of the…

A cubic plane curve is a degree 3 polynomial in two variables that defines a geometric curve on a plane. It exhibits various singularities, including ordinary singular points, multiple points, and higher-order singularities. The curve’s geometry is analyzed using Plücker’s formulas and the Cayley-Bacharach theorem. The Weierstrass equation, Hesse matrix, and discriminant provide algebraic representations…

Spiral curves are a type of spiral characterized by a continuously changing curvature and torsion, resulting in a smooth, graceful shape. They are defined by parametric equations and exhibit unique mathematical properties such as a constant angle between the tangent and radial vectors. Spiral curves find practical applications in road design, architecture, and antennas, and…

S-Curve Formula The S-curve formula describes a pattern of growth that resembles the shape of an elongated “S.” It is mathematically represented by functions such as the logistic, sigmoid, Gompertz, and Richards equations. These functions model initial slow growth, followed by a period of rapid acceleration, and finally a leveling off or decline as the…

Generalized Voronoi diagrams (GVDs) are partitions of space that can be used to represent a set of weighted points. Given a set of weighted points in a metric space, the GVD for these points is a partition of the space into cells, where each cell is associated with one of the input points and contains…

Curves, common on roadways, present unique challenges for drivers. Roadway elements like narrow lanes, uneven shoulders, or slick surfaces can increase crash risk. Technologies such as lane departure warnings and adaptive cruise control assist drivers in staying within lanes and maintaining safe speeds. Vehicle factors like size and handling capabilities impact a vehicle’s stability around…

The historiography of the Vietnam War encompasses the various interpretations and perspectives that have shaped our understanding of this complex conflict. From the initial historical accounts written during and immediately after the war to the ongoing scholarly debates, the historiography of the Vietnam War has evolved over time, influenced by key entities such as historians,…

“War Hawks” and “Doves” emerged during the Vietnam War, representing opposing views on military intervention. “Hawks” supported aggressive warfare, advocating for increased military action and escalation. Conversely, “Doves” opposed the war, emphasizing peace negotiations, diplomacy, and anti-war protests. This division highlighted the polarization and controversy surrounding the conflict. The Vietnam War: A Kaleidoscope of Triumphs…

Vietnamese family life is characterized by strong familial bonds and a hierarchical structure. Family members play essential roles, with parents and grandparents holding positions of authority and respect. Confucian values emphasize collectivism, harmony, and ancestor worship, shaping family dynamics and relationships. Gender roles are traditional, with men often seen as the breadwinners and women responsible…

In Vietnam’s re-education camps, the Ministry of Public Security and Ministry of National Defense maintain security, with the People’s Police Force and People’s Army responsible for camp management. Five camps, such as Nam Ha and Yen Binh, hold political prisoners in harsh conditions. International organizations monitor but face challenges accessing camps. Government oversight and communist…

Non-governmental organizations (NGOs) in Vietnam play a crucial role in providing humanitarian assistance, supporting development projects, and promoting social well-being. NGOs with a closeness rating of 10 are highly influential and have close ties to the government, enabling them to effectively implement large-scale initiatives. Domestic NGOs, with a closeness rating of 8, are smaller in…