Polynomial-time problems are a class of decision problems in computational complexity theory that can be solved by an algorithm in polynomial time, which means that the time taken to solve the problem is proportional to a polynomial function of the size of the input.

A decision problem is a type of problem in computer science and mathematics that can be posed as a question that requires a simple yes or no answer. In formal terms, a decision problem can be defined as a question phrased as a yes/no question about an input of some kind. Here are some key points to understand about decision problems: 1. **Binary Output**: The solution to a decision problem yields one of two possible outputs, typically denoted as "yes" or "no.

The Predecessor Problem is a computational problem often encountered in the context of data structures, particularly in search and retrieval operations within ordered sets, such as ordered lists, balanced binary search trees, and other similar structures. The problem can be stated as follows: given a value \( x \) in a sorted data structure (for example, a sorted list or a binary search tree), find the predecessor of \( x \).

As of my last knowledge update in October 2023, there is no widely recognized figure named Jonathan Keating in popular culture, politics, or academia. It is possible that Jonathan Keating refers to a private individual or a less public figure, or that new developments or recognitions have emerged since my last update.

Chinese numerals refer to the system of numbers used in the Chinese language, which has both characters for numerals and a counting system. There are two main styles of Chinese numerals: 1. **Arabic Numerals**: The Western numerical system (0, 1, 2, 3, etc.) is widely used in contemporary Chinese writing, especially in digital and casual contexts.

Rod calculus is a theoretical framework used for modeling and analyzing the behavior of specific types of mechanical systems, particularly those comprised of rods, beams, or similar structures. It provides a mathematical means to describe the interactions and motion of these elements under various forces and constraints. This approach is often applied in fields such as robotics, structural engineering, and biomechanics.

Mathematicians come from various nationalities around the world, reflecting the global nature of mathematics as a discipline. Here are some notable mathematicians categorized by their nationality: 1. **German**: - Karl Friedrich Gauss - David Hilbert - Bernhard Riemann 2. **French**: - Pierre-Simon Laplace - Henri Poincaré - Évariste Galois 3.