Radiotherapy dose escalation in locally advanced NSCLC - The limits of conventional radiochemotherapy

The relative amounts of reactants and products represented in a balanced chemical equation are often referred to as stoichiometric amounts. However, in reality, the reactants are not always present in the stoichiometric amounts indicated by the balanced equation.

When analyzing a beam subjected to various loads, it is crucial to understand the internal forces and moments generated within the structure. These internal forces can be broadly classified into normal forces, shear forces, and bending moments. To determine these forces and moments, we use the method of sections and apply a specific sign convention based on their direction and the side of the section being analyzed.
The normal force acts perpendicular to the beam's cross-section and can...

The number e is a fundamental constant in calculus, playing a central role in describing continuous change, particularly exponential growth. It is most naturally defined through its relationship with the natural logarithm, which is the inverse of the exponential function with base e. This relationship allows e to be characterized using basic principles of differentiation rather than as an arbitrary numerical constant.A key property of the natural logarithm function, ln x, is that its derivative...

When a carbonyl compound is treated with a strong base, the α position gets deprotonated to give a resonance-stabilized intermediate called an enolate. Enolates are ambident nucleophiles because they possess two nucleophilic sites that can attack an electrophile owing to the delocalization of the negative charge between the α carbon and oxygen atoms. When the oxygen atom attacks an electrophile, it is called O-attack, whereas electrophilic attack via the α carbon is known as...

Limits are a key mathematical concept for understanding how functions behave as their input approaches specific values, particularly when the function is undefined. They help reveal trends and discontinuities by examining the values a function approaches rather than its actual value.One-sided limits focus on the direction from which a value is approached. When a function behaves differently depending on whether the input approaches from the left or the right, the two one-sided limits may not...

Limit laws provide essential tools for analyzing how functions behave as their input approaches a specific value. These laws are particularly useful when dealing with combinations of functions, provided the individual limits exist. The Sum and Difference Laws state that the limit of the sum or difference of two functions equals the sum or difference of their respective limits:The Product Law asserts that the limit of the product of two functions equals the product of their individual limits:A...