A variable geometry turbomachine refers to a type of turbomachine, typically a turbine or compressor, designed with adjustable components that allow for changes in flow path or geometry during operation. This capability enables the machine to optimize performance across a range of operating conditions, improving efficiency, responsiveness, and overall performance.

Betül Tanbay is a prominent Turkish mathematician known for her contributions to both mathematics and education. She has worked in areas such as mathematical analysis and mathematical education, and is also recognized for her efforts in promoting mathematics among young people and improving mathematics teaching practices. Tanbay has been involved in various initiatives to enhance mathematics curricula and has held positions in academic and educational organizations.

Mehmet Burak Erdoğan is a Turkish businessman and the son of Recep Tayyip Erdoğan, the President of Turkey. He has been involved in various business ventures and is known for his connections in both the business and political spheres in Turkey. He has been associated with several family-owned enterprises and is often mentioned in the context of the Erdoğan family's influence in Turkish politics and economics.

The 20th century saw significant contributions from Ukrainian mathematicians, many of whom made important advances in various fields of mathematics. Here are some notable figures and their contributions: 1. **Mykola Bogolyubov** (1909–1993) - A prominent mathematician and theoretical physicist, Bogolyubov made significant contributions to various areas, including functional analysis and statistical mechanics. He is well-known for his work in quantum field theory and the theory of integrable systems.

An English auction is a type of auction that is characterized by the open and ascending nature of bidding. In this auction format, potential buyers place progressively higher bids until no one is willing to bid further. Here are some key features of an English auction: 1. **Open Bidding**: Bids are announced openly, allowing all participants to hear the current highest bid.

Sefaattin Tongay may refer to an individual, but as of my last update in October 2021, there is no widely known public figure or relevant topic by that name. It’s possible that Sefaattin Tongay is a private individual, an emerging figure in a specific field, or a name that has gained recognition after that date.

A multi-attribute auction is a type of auction in which bidders compete to win an item or a set of items that can be evaluated based on multiple attributes or criteria rather than a single price. Unlike traditional auctions where the highest bid typically wins, multi-attribute auctions consider various factors that contribute to the overall value or utility of the items being auctioned.

A Vickrey auction, also known as a second-price sealed-bid auction, is a type of auction where bidders submit written bids without knowing the other bidders' offers. The highest bidder wins the auction, but the price paid is determined by the second-highest bid. Key characteristics of a Vickrey auction include: 1. **Sealed Bids**: Bidders submit their bids privately and do not know the bids of other participants.

A first-price sealed-bid auction is a type of auction where bidders submit their bids without knowing the bids of the other participants. The key features of this auction format include: 1. **Sealed Bids**: Bidders submit their bids in a sealed manner. This means that once bids are submitted, they cannot be changed, and participants cannot see how much other bidders have offered.

A French auction, also known as a descending price auction, is a type of auction in which the auctioneer starts with a high asking price and gradually lowers it until a bidder accepts the current price. Once a bidder agrees to the price, they win the item, and the auction ends at that point. Here's how it typically works: 1. **Starting Price**: The auctioneer announces a high initial price for the item being auctioned.

An **integer-valued function** is a function whose outputs are always integers. This means that for every input value from its domain, the corresponding output value is an integer. Formally, if \( f: A \rightarrow \mathbb{Z} \), where \( A \) is a set (the domain of the function), and \( \mathbb{Z} \) is the set of all integers, then \( f \) is an integer-valued function.

The theory of continuous functions is a fundamental topic in mathematics, particularly in the field of real analysis and topology. It deals with the properties, definitions, and implications of continuous functions, which are functions that preserve certain topological and analytical structures.

In mathematics, a singular function typically refers to a function that exhibits some form of singularity, which can mean different things depending on the context. Here are a few common interpretations of "singular function": 1. **Singularity in Analysis**: In the context of real analysis, a singular function might refer to a function that is not absolutely continuous.

Microbubbles are tiny gas-filled bubbles with a diameter typically in the range of 1 to 100 micrometers. They are significantly smaller than conventional bubbles and often have unique physical and chemical properties due to their size. Microbubbles are used in various applications across multiple fields, including: 1. **Medical Applications**: In medical imaging, microbubbles can be used as contrast agents in ultrasound imaging to enhance the visibility of blood vessels and tissues.

Anatoly Samoilenko may refer to different individuals, but he is most commonly associated with being a prominent figure in the field of mathematics, particularly in relation to algorithm theory, combinatorics, or similar disciplines. However, specific context or additional details might be needed to provide accurate information on the individual you're referring to, as there can be multiple people with the same name in various fields.

Igor Rodnianski is a prominent mathematician known for his work in the fields of mathematical physics, general relativity, and partial differential equations. He has made significant contributions to the study of the Einstein equations and the behavior of solutions to these equations, particularly in the context of black holes and the stability of spacetimes. Rodnianski is affiliated with academic institutions and has published numerous papers in theoretical physics and mathematics.

The 157th meridian west is a line of longitude located 157 degrees west of the Prime Meridian, which is established at 0 degrees longitude. This meridian runs from the North Pole to the South Pole and crosses through various terrestrial regions. In the Northern Hemisphere, the 157th meridian west passes through parts of Alaska, particularly the Aleutian Islands. In the Southern Hemisphere, it crosses the Pacific Ocean.

The term "Jewish Ukrainian mathematicians" refers to mathematicians of Jewish heritage who were born in or worked in Ukraine, or who have connections to Ukrainian academic and cultural life. Historically, Ukraine has had a significant Jewish population, especially before the Holocaust, and many Jewish individuals have made notable contributions to mathematics, science, and related fields.

A Submarine Escape Training Facility (SETF) is a specialized facility designed to train submariners in the procedures and techniques necessary for escaping from a submarine in the event of an emergency. These facilities typically simulate a range of underwater conditions that a submarine might encounter, allowing personnel to practice escape protocols safely. Key components of a Submarine Escape Training Facility often include: 1. **Escape Training Tower**: A vertical shaft that simulates the escape hatch of a submarine.

Functional ultrasound imaging, often referred to as functional ultrasound or fUS, is a non-invasive imaging technique used to assess and visualize physiological processes within the body in real-time. Unlike traditional ultrasound, which primarily focuses on anatomical structures, functional ultrasound provides insights into the functionality of tissues and organs by monitoring their physiological activity. Key features of functional ultrasound imaging: 1. **Real-time Monitoring**: It allows for real-time assessment of blood flow, tissue movement, and other dynamic physiological processes.