A Qualified Electronic Signature (QES) is a type of electronic signature that is legally recognized and offers a high level of security and authenticity. It is defined under the European Union's eIDAS (Electronic Identification and Trust Services) Regulation, which came into effect on July 1, 2016.

German biophysicists are scientists from Germany who specialize in biophysics, a field that applies the principles and techniques of physics to understand biological systems. This interdisciplinary area of research explores a wide range of topics, including molecular biology, cell biology, and the physical properties of biomolecules, such as proteins, nucleic acids, and membranes.

In 1957, the field of computing was still in its early stages of development, with many foundational concepts and technologies being explored. Some key highlights related to computers and computing during that time include: 1. **Transistor Technology**: The late 1950s saw the increasing use of transistors in computer design, replacing vacuum tubes. Transistors were smaller, more reliable, and consumed less power, paving the way for the development of more compact and efficient computers.

In 1969, several significant events and developments in the field of computers took place, marking that year as an important time in the history of computing. Here are some notable highlights: 1. **ARPANET:** One of the most revolutionary achievements of 1969 was the creation of ARPANET, the precursor to the modern internet. The first message was sent over ARPANET on October 29, 1969, from UCLA to the Stanford Research Institute.

In 1985, the landscape of computing was significantly different from today, characterized by the emergence of personal computers, the development of software applications, and the expansion of networks. Here are some key aspects of the computer-related introductions and developments in that year: 1. **Personal Computers**: The mid-1980s saw the ongoing proliferation of personal computers. Companies like IBM, Apple, and Commodore were prominent in this market.

"Discoveries" by Plinio Antolini is a work that explores themes related to exploration, knowledge, and the pursuit of understanding in various contexts. Plinio Antolini is known for combining philosophical insights with a personal narrative, often reflecting on the implications of discoveries in both scientific and humanistic fields. In "Discoveries," Antolini's writing may delve into how new knowledge shapes our understanding of the world, influences culture, and impacts individual lives.

In 2020, computer-related introductions spanned various topics and innovations in technology, reflecting advancements in hardware, software, and the overall field of computing. Here are some significant trends and developments from that year: 1. **Remote Work Technologies**: The COVID-19 pandemic accelerated the adoption of remote work tools. Applications such as Zoom, Microsoft Teams, and Slack became essential for virtual communication and collaboration.

Geroch's splitting theorem is a result in general relativity that provides conditions under which a spacetime can be decomposed into a product of a lower-dimensional manifold and a time-like line. Specifically, it concerns the structure of spacetimes that admit a particular kind of symmetry, known as "time-like Killing vectors.

Gert Sabidussi is a mathematician known for his work in graph theory, particularly for the concepts related to the properties of graphs and the study of connectedness and connectivity. One of his notable contributions to the field is the development of the concept of "Sabidussi graph," a particular type of graph that arises in various contexts, especially in relation to algebraic structures and combinatorial designs. His research has influenced both theoretical aspects and practical applications in network analysis and related domains.

Bibliography:

The variables of the Lagrangian, e.g. the angles of a double pendulum. From that example it is clear that these variables don't need to be simple things like cartesian coordinates or polar coordinates (although these tend to be the overwhelming majority of simple case encountered): any way to describe the system is perfectly valid.

In quantum field theory, those variables are actually fields.

The period does depend on the initial height/angle, except for the very small angle approximation: