Speech balloon

Speech balloons (also speech bubbles, dialogue balloons or word balloons) are a graphic convention used most commonly in comic books, comics and cartoons to allow words (and much less often, pictures) to be understood as representing the speech or thoughts of a given character in the comic. There is often a formal distinction between the balloon that indicates thoughts and the one that indicates words spoken aloud: the balloon that conveys subjective thoughts is often referred to as a thought bubble.

History

One of the earliest antecedents to the modern speech bubble were the "speech scrolls," wispy lines that connected first person speech to the mouths of the speakers in Mesoamerican art between 600 and 900 AD.

In Western graphic art, labels that reveal what a pictured figure is saying have appeared since at least the 13th century. These were in common European use by the early 16th century. Word balloons (also known as "banderoles") began appearing in 18th-century printed broadsides, and political cartoons from the American Revolution (including some published by Benjamin Franklin) often used them. With the development of the comics industry in the 20th century, the appearance of speech balloons has become increasingly standardized, though the formal conventions that have evolved in different cultures (USA as opposed to Japan, for example), can be quite distinct.

Riemann zeta function

The Riemann zeta function or Euler–Riemann zeta function, ζ(s), is a function of a complex variable s that analytically continues the sum of the infinite series

which converges when the real part of s is greater than 1. More general representations of ζ(s) for all s are given below. The Riemann zeta function plays a pivotal role in analytic number theory and has applications in physics, probability theory, and applied statistics.

As a function of a real variable, Leonhard Euler first introduced and studied it in the first half of the eighteenth century without using complex analysis, which was not available at the time. Bernhard Riemann's 1859 article "On the Number of Primes Less Than a Given Magnitude" extended the Euler definition to a complex variable, proved its meromorphic continuation and functional equation, and established a relation between its zeros and the distribution of prime numbers.

The values of the Riemann zeta function at even positive integers were computed by Euler. The first of them, ζ(2), provides a solution to the Basel problem. In 1979 Apéry proved the irrationality of ζ(3). The values at negative integer points, also found by Euler, are rational numbers and play an important role in the theory of modular forms. Many generalizations of the Riemann zeta function, such as Dirichlet series, Dirichlet L-functions and L-functions, are known.

ZS

ZS, Zs, zS, or zs may refer to:

See also