Extremal graph theory is a branch of combinatorial mathematics that studies the extremal properties of graphs. Specifically, it focuses on questions related to the maximal or minimal number of edges in a graph that satisfies certain properties or conditions. The primary goal is often to determine the extremal (that is, maximum or minimum) values for specific parameters of graphs (like the number of edges, number of vertices, etc.) that meet certain constraints, such as containing a particular subgraph or avoiding certain configurations.

Graph databases are a type of database specifically designed to represent and store data in the form of graphs, which consist of nodes (entities) and edges (relationships). This model excels in scenarios where relationships and connections between data points are crucial and often complex. ### Key Characteristics of Graph Databases: 1. **Nodes and Edges**: - **Nodes**: Represent entities or objects, such as people, places, products, etc.

The history of the Internet is a complex tale of innovation, collaboration, and technological evolution that spans several decades. Here are the key milestones in its development: ### 1960s: The Foundations - **ARPANET**: The Advanced Research Projects Agency Network (ARPANET) was developed by the U.S. Department of Defense's ARPA (Advanced Research Projects Agency) in the late 1960s. It is often considered the precursor to the modern Internet.

The history of computer networks is a fascinating evolution that reflects the advancements in technology, communication theories, and computing power. Here's an overview of the significant milestones in the development of computer networks: ### 1960s: The Beginning - **Early Concepts**: The idea of networking devices for communication emerged alongside the development of computers. Theories about packet switching were proposed by researchers like Paul Baran and Donald Davies.

"Computing by year" typically refers to a historical overview or timeline of significant events, developments, and milestones in the field of computing and technology throughout the years. This can include the invention of key technologies, the creation of programming languages, advancements in hardware and software, and the rise of the internet, among other important developments.

A **powerful \( p \)-group** is a special type of \( p \)-group (a group where the order of every element is a power of a prime \( p \)) that satisfies certain conditions regarding its commutator structure.

The history of computer companies is a fascinating journey through technological innovation, commercialization, and the evolution of the computer industry over decades. Below is a brief overview highlighting key milestones and notable companies: ### 1940s - 1950s: The Birth of Computing - **ENIAC (1945)**: Often considered the first general-purpose electronic digital computer, designed by John W. Mauchly and J. Presper Eckert.

CP/M, which stands for Control Program for Microcomputers, is an early operating system designed for microcomputers. It was developed in the mid-1970s by Gary Kildall of Digital Research, Inc. CP/M became one of the first widely used operating systems for personal computers, particularly those based on Intel 8080 and Zilog Z80 microprocessors.

Classical logic is a formal system of reasoning that was developed in the late 19th and early 20th centuries. It is characterized by several key features: 1. **Propositional and Predicate Logic**: Classical logic includes systems like propositional logic, which deals with propositions as whole units, and predicate logic, which incorporates the use of quantifiers and predicates to express more complex statements about objects.

Andrew V. Haeff does not appear to be a widely recognized figure in public discourse, literature, or other fields up to my last knowledge update in October 2021. It's possible that he could be a private individual, a professional in a specific field, or someone who has gained prominence after that time.

As of my last update in October 2021, Arthi Jayaraman is a researcher and professor known for her work in the field of materials science and engineering, particularly focusing on polymeric materials and their applications. She has contributed to the understanding of various material properties and behaviors, often exploring topics related to nanotechnology, molecular dynamics, and the synthesis and characterization of materials.

Daniel Schwartz is a name that could refer to several individuals depending on the context. One prominent figure is Daniel Schwartz, who is known in the business world as the former CEO of Restaurant Brands International, the parent company of brands like Burger King, Tim Hortons, and Popeyes Louisiana Kitchen. He has been noted for his leadership in the fast-food industry.